# Chronology2

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# Chronology, Data, and Observations

“Measure what is measurable, and make measurable what is not so.”

―Galileo Galilei, Astronomer (1564-1642)

Observations and calculations from a mathematical, probabilistic, and statistical points-of-view are essential in understanding and modeling the progression of COVID-19 infections, for establishing proper responses, and realizing the actual reach, scope, and range of the corresponding pandemic. These include, but are not limited to, modeling daily and cumulative time series of infections, deaths, and testing rates, computing times to doubling and order-of-magnitude increases for forecasting, detailing the particular sequence of most impacted locales by case fatality rates or other changing variables, studying the efficacy of proposed experimental treatments and potential vaccines, and comparing governmental responses by locales to determine safest and most effective actions. It remains difficult, however, to separate the effect of testing rates on actual infection rates (likely much greater than the reported cases), as both are increasing simultaneously.

## Chronology

The varying timelines of the course of COVID-19, mutations of SARS-CoV-2, and other practical considerations of healthcare robustness and infrastructure for reporting confound accurate estimation of infection rates, case fatality rates, and mortality rates[1], too, especially if the virus is virulent. Despite these inherent difficulties, we summarize the generally accepted chronology of events:

1. On December 29, 2019, four cases of viral pneumonia of unknown etiology were linked to the Huanan Seafood Market.
2. On December 30-31, 2019, the Chinese Center for Disease Control (CDC) and the WHO were informed of an outbreak of a viral pneumonia in Wuhan, Hubei Province, China.
3. On January 6, 2020, Chinese CDC activated a Level 2 Emergency Response.
4. On January 7-10, 2020, Chinese scientists identified the second novel coronavirus responsible for the aforementioned outbreak, called nCoV-2019, and released the genome sequence.
5. On January, 11, 2020, China reported its first death, a 61-year old male who had visited the Huanan Seafood Market.
6. On January 21, 2020, China reported the first confirmed human-to-human transmitted infection due nCoV-2019 (now SARS-CoV-2).
7. On January 23, 2020, the Chinese government imposed a strict Stay-in-Place order for the residents of Wuhan, China.
8. On January 30, 2020, the WHO declared a Global Health Emergency for the growing number of nCoV-2019-related clusters and outbreaks in several locations in and outside of China.
9. On February 11, 2020, the WHO defined the new name of the disease, COVID-19.
10. On February 26, 2020, the first case of human-to-human transmission in the U.S. was documented involving an individual from California who had not traveled recently. Similar cases were reported in the states of Oregon, Washington, and New York.
11. On February 29, 2020, the first U.S. COVID-19 death was reported, which differs from the first confirmed COVID-19-related death believed to have been on February 6, 2020.
12. By March 17, 2020, all 50 U.S. states had reported COVID-19 cases. On the same day, the state of California declared a Shelter-in-Place order. The daily U.S. reported cases of COVID-19 infections continued to follow those of Italy and France closely but were delayed by 7 to 14 days. By April 1, 2020, the U.S. exceeded the continent of Europe in terms of cases.
13. On March 18, 2020, China reported no new COVID-19 infections.
14. On March 19, 2020, Italy surpassed China in COVID-19-related deaths.
15. On March 20, 2020, New York City became the epicenter of the COVID-19 pandemic with 50% of the U.S. reported cases.
16. On March 22, 2020, the number of reported deaths in the U.S. exceeded 100.
17. On March 26, the U.S. became the global epicenter of the COVID-19 Pandemic surpassing China with reported COVID-19 cases.
18. By March 27, 2020, the number of reported cases in the U.S. exceeded 100,000, which quadrupled to 400,000 by April 8, 2020.
19. By April 2, the number of reported COVID-19 cases worldwide exceeded 1 million.
20. By April 8, 2020, there were 1,518,518 reported cases worldwide with 88,495 fatalities (5.8% PCFR). The U.S. led all other countries with 434,927 reported cases (29% of global total) and third to only Italy and Spain with 14,788 reported deaths (17% of global total).
21. By April 15, 2020, nearly 9,300 U.S. healthcare workers had contracted COVID-19, with 55% believed to have been exposed in the workplace, and with 27 deaths.
22. By April 23, 2020, there were 50,234 reported deaths from COVID-19 in the U.S.
23. By April 27, 2020, the number of reported cases in the U.S. exceeded 1 million and accounted for approximately ⅓ of the corresponding global count.
24. By May 8, 2020, the number of COVID-19 reported cases exceeded 4 million worldwide with 265,852 fatalities (~7% PCFR). The U.S. led all other countries with over 1.2 million reported cases (33% of global total) and 74,810 related deaths (28% of global total).
25. By May 14, 2020 and June 7, 2020, the number of global COVID-19 reported deaths exceeded 300,000 and 400,000, respectively.
26. By May 21, 2020, the number of global COVID-19 reported cases exceeded 5 million. Milestones for global and U.S. total cases and deaths are tabulated below. By May 27, 2020, the number of reported COVID-19 deaths in the U.S. exceeded 100,000. Milestones of global and U.S. death counts are tabulated below. On July 24, 2020, California surpassed New York in terms of total cases.

## Current Data, Trends, and Models

Several variables account for the worldwide growth characteristics of COVID-19 infections and deaths including the basic reproduction number, number and frequency of seeding events, and virulence of SARS-CoV-2 among other fundamental features. Moreover, the sequence of locations (e.g., continent, country, state/province, county/parish/zone, ZIP code/neighborhood) and demographics (e.g., ethnicity, race, sex, age group, BMI group, etc.) that are most impacted by COVID-19 may depend on population size, population density, in-bound and out-bound travel and tourism frequency, timing of governmental responses including public advisories and orders, the frequency of individuals to gather into large groups, the demographic of employment in certain sectors, the latter two of which may be roughly measured by entertainment revenue, and finally the propensity for citizens to heed public advisories and orders, among other known and unknown variables.

### General Definitions

A cluster is a statistically significant set of illnesses coupled spatially and temporally (i.e., several cases in close proximity in a short period of time) with a suspected common origin. If the number of such cases is sufficiently large, which is often at the discretion of a local government or the WHO, then a cluster is classified as an outbreak. An epidemic is a specific outbreak caused by an infectious disease that may cover a city, state, or country, or continent, but is otherwise confined. Not all outbreaks are caused by infectious disease (e.g., influenza, COVID-19, etc.). A pandemic is a wide-scale epidemic or cluster of epidemics that may cover several countries or continents and is sustained by seeding events, which are opportunities for several new infections to occur.

The WHO categorizes pandemics into six phases depending on zoonotic origin, acceleration and type of infection spread, locales involved, and virulence of the underlying illness:

1. Phase 1 involves the identification of a zoonotic pathogen with a high likelihood to transfer to humans but otherwise remains in the (animal) reservoir(s);
2. Phase 2 involves the identification of a case or sporadic cases of confirmed animal-to-human transmission of a previously identified zoonotic pathogen and corresponding reservoir(s);
3. Phase 3 involves sporadic cases or limited clusters of animal-to-human transmission and limited human-to-human transmission (e.g., patient infecting family, caregivers, and/or first responders) not sufficient to sustain community-level spread;
4. Phase 4 involves several clusters or outbreaks of confirmed human-to-human transmission able to sustain community-level spread; Phase 4 indicates a significant increase in spread risk and consultation with the WHO is merited;
5. Phase 5 involves human-to-human transmission through community-level outbreaks in at least two countries of increasing size and severity. Designation of WHO Phase 5 indicates a global pandemic is imminent and preparation is necessary; and,
6. Phase 6 is the highest level of the WHO pandemic phases in terms of scale, reach, and severity.

The CDC categories pandemics into five categories depending on a severity index (PSI) as measured by the case fatality rate (CFR):

1. Category 1 involves an epidemic with a CFR less than 0.1%;
2. Category 2 involves an epidemic with a CFR of 0.1%-0.5%;
3. Category 3 involves an epidemic with a CFR of 0.5%-1.0%;
4. Category 4 involves an epidemic with a CFR of 1.0%-2.0%; and,
5. Category 5 involves an epidemic with a CFR greater than 2.0%.

Epidemics and pandemics may be further subdivided into waves and episodes. A wave is defined by the rapid growth and decline of daily infection activity to near nominal levels (or when WHO issues an “At-Ease” Order). A wave may have several peaks and plateaus. In similar fashion, an episode is defined by the rapid (usually exponential) growth followed by slower (usually sub-exponential) growth or even stabilization of cumulative infection activity. Epidemics and pandemics often involve several waves each with several episodes in the cycles of acceleration of infection activity followed by saturation of infection activity, until a terminal plateau or asymptote of cumulative cases (or nominal daily cases) is achieved. A slowly-growing plateau may be intermittent, however, and an asymptote does not have to follow. If the infection activity is sustained, even if nominal, then the epidemic or pandemic is said to be endemic. The common cold and the seasonal flu are examples of endemic illnesses in the human species.

### Global Trend

Since early March 2020, the COVID-19 Pandemic is designated WHO Phase 6, CDC PSI Category 5, the maximum of combined indications, and has not yet reached its first global peak, but has sustained at least two episodes within the first global wave. Figures 2.1a and 2.1b illustrate the global daily counts of COVID-19 reported cases and related deaths from December 31, 2019 to date. The early spike in cases on February 12, 2020 in Figure 2.1a resulted from the change in diagnosis and reporting of COVID-19 cases in Wuhan, China. The origin of the apparent undulations in the daily time series data (Figures 2.1a/b) is unclear but may be consistent with periodicity of testing and/or reporting or a dynamical feature of the underlying coupled system of differential equations similar to the Kermack-McKendrick Model. In particular, in Figure 2.1a/b, one may clearly see a small local wave corresponding to a closed epidemiological system of infections in Wuhan, China, followed by a second larger wave, the first global wave, consisting of at least two episode

Figure 2.1a: Daily Global COVID-19 Reported Cases with a 7-day Moving Average (December 31, 2020 - October 19, 2020)

Figure 2.1b: Relative Change in Global Daily Reported COVID-19 Cases (August 15, 2020 - October 18, 2020)

 Milestone Case Difference Time Frame Day Count [d] Growth Rate [/d] ~0 to 1 million 1,015,843 12/1/2019 - 4/1/2020 122 8,327 1 to 2 million 1,000,503 4/1/2020 - 4/14/2020 13 76,962 2 to 3 million 1,017,825 4/14/2020 - 4/27/2020 13 78,294 3 to 4 million 1,015,118 4/27/2020 - 5/9/2020 12 84,593 4 to 5 million 984,156 5/9/2020 - 5/20/2020 11 89,469 5 to 6 million 1,073,713 5/20/2020 - 5/30/2020 10 107,371 6 to 7 million 956,997 5/30/2020 - 6/7/2020 8 119,625 7 to 8 million 1,035,385 6/7/2020 - 6/15/2020 8 129,423 8 to 9 million 903,299 6/15/2020 - 6/21/2020 6 150,550 9 to 10 million 1,034,110 6/21/2020 - 6/27/2020 6 172,352 10 to 11 million 1,127,154 6/27/2020 - 7/3/2020 6 187,859 11 to 12 million 972,157 7/3/2020 - 7/8/2020 5 194,431 12 to 13 million 880,105 7/8/2020 - 7/12/2020 4 220,026 13 to 14 million 1,146,254 7/12/2020 - 7/17/2020 5 229,251 14 to 15 million 897,172 7/17/2020 - 7/21/2020 4 224,293 15 to 16 million 1,109,840 7/21/2020 - 7/25/2020 4 277,460 16 to 17 million 984,657 7/25/2020 - 7/29/2020 4 246,164 17 to 18 million 1,063,369 7/29/2020 - 8/2/2020 4 265,842 18 to 19 million 1,013,547 8/2/2020 - 8/6/2020 4 253,387 19 to 20 million 780,143 8/6/2020 - 8/9/2020 3 260,048 20 to 21 million 1,064,949 8/9/2020 - 8/13/2020 4 266,237 21 to 22 million 976,573 8/13/2020 - 8/17/2020 4 244,143 22 to 23 million 1,073,001 8/17/2020 - 8/21/2020 4 268,250 23 to 24 million 955,160 8/21/2020 - 8/25/2020 4 238,790 24 to 25 million 1,112,749 8/25/2020 - 8/29/2020 4 278,187 25 to 26 million 1,022,066 8/29/2020 - 9/2/2020 4 255,517 26 to 27 million 867,531 9/2/2020 - 9/5/2020 3 289,177 27 to 28 million 958,407 9/5/2020 - 9/9/2020 4 239,602 28 to 29 million 1,205,144 9/9/2020 - 9/13/2020 4 301,286 29 to 30 million 823,132 9/13/2020 - 9/16/2020 3 274,377 30 to 31 million 1,175,253 9/16/2020 - 9/19/2020 3 329,510 31 to 32 million 988,530 9/19/2020 - 9/23/2020 4 266,913 32 to 33 million 1,067,652 9/23/2020 - 9/26/2020 3 342,383 33 to 34 million 1,027,150 9/26/2020 - 9/30/2020 4 276,869 34 to 35 million 1,107,475 9/30/20202 - 10/3/2020 3 319,601 35 to 36 million 958,803 10/3/2020 - 10/6/2020 3 280,005 36 to 37 million 840,014 10/6/2020 - 10/9/2020 3 355,851 37 to 38 million 1,067,552 10/9/2020 - 10/12/2020 3 310,767 38 to 39 million 932,300 10/12/2020 - 10/15/2020 3 364,642 39 to 40 million 1,093,925 10/15/2020 - 10/18/2020 3 370,252 40,264,218 12/1/2019 - Present 322 124,888

Figure 2.1c: Global Average Daily Rate of Reported COVID-19 Cases (October 19, 2020)

Figure 2.1d: Daily Global COVID-19 Reported Deaths with a 7-Day Moving Average (January 22, 2020 - October 19, 2020)

Significant global case and death milestones are given in Tables 2.0a/b.

Figure 2.1e: Cumulative Global COVID-19 Reported Cases, Recoveries, and Deaths (January 22, 2020 - October 19, 2020)

 Milestone Case Difference Time Frame Day Count [d] Growth Rate [/d] ~0 to 50,000 50,128 1/11/2019 - 4/1/2020 81 619 50,000 to 100,000 52,196 4/1/2020 - 4/9/2020 8 6,525 100,000 to 150,000 47,837 4/9/2020 - 4/16/2020 7 6,834 150,000 to 200,000 53,182 4/16/2020 - 4/24/2020 8 6,648 200,000 to 250,000 49,519 4/24/2020 - 5/3/2020 9 5,502 250,000 to 300,000 51,739 5/3/2020 - 5/13/2020 10 5,174 300,000 to 350,000 45,922 5/13/2020 - 5/23/2020 10 4,592 350,000 to 400,000 51,785 5/23/2020 - 6/4/2020 12 4,315 400,000 to 450,000 54,108 6/4/2020 - 6/16/2020 12 4,509 450,000 to 500,000 43,589 6/16/2020 - 6/25/2020 9 4,843 500,000 to 550,000 54,645 6/25/2020 - 7/7/2020 12 4,554 550,000 to 600,000 46,794 7/7/2020 - 7/16/2020 9 5,199 600,000 to 650,000 50,188 7/16/2020 - 7/26/2020 10 5,019 650,000 to 700,000 48,626 7/26/2020 - 8/3/2020 8 6,078 700,000 to 750,000 54,402 8/3/2020 - 8/12/2020 9 6,045 750,000 to 800,000 46,455 8/12/2020 - 8/20/2020 8 5,807 800,000 to 850,000 49,957 8/20/2020 - 8/30/2020 9 5,551 850,000 to 900,000 50,131 8/30/2020 - 9/8/2020 10 5,013 900,000 to 950,000 49,070 9/8/2020 - 9/17/2020 9 5,452 950,000 to 1,000,000 1,000,000 to 1,050,000 975,457 1/11/2019 - Present 255 3,807

Figure 2.1f: Global Average Daily Rate of Reported COVID-19 Deaths (October 19, 2020)

Figure 2.1g: Time Series of Global Provisional Case Fatality Rates (January 22, 2020 - October 19, 2020)

Figure 2.1g illustrates the provisional case fatality rate (PCFR) computed by the fraction of cumulative deaths to cumulative cases, while the adjusted PCFR attempts to correct for the fact that the pandemic is currently on-going. The true case fatality rate falls within the interval defined by the two curves. However, by extrapolating linear regression lines from 14-day fits of both PCFR curves, we compute a convergence to a projected CFR of approximately 3.67%. Incorporating the CDC factor of 6-24 (15 avg.) for COVID-19 infections and a 50% increase for COVID-19-related deaths, the average conclusion of several studies, we provisionally conjecture a final CFR of approximately 0.367%.

Figure 2.1h: Weekday Distribution of COVID-19 Reported Deaths (January 22, 2020 - October 19, 2020)

Figure 2.1h illustrates the non-uniformity of reported deaths across the days of the week, which results from a stable 7-day periodicity observed in the corresponding time-series data.

Figure 2.1i: Daily Global Reported COVID-19 Recoveries with a 7-Day Moving Average (January 22, 2020 - October 19, 2020)

Figure 2.1j: Daily Global Reported Severe COVID-19 Cases with a 7-Day Moving Average (January 22, 2020 - October 19, 2020)

Figure 2.1k: Current Global COVID-19 Reported Closed and Active Cases including Mild / Moderate and Severe / Critical Cases (January 22, 2020 - October 19, 2020)

#### Universal Features

Figures 2.2a-d illustrate the daily and cumulative counts of reported cases and related deaths for Earth, U.S., New York State, and New York City. Assuming a single wave of the pandemic, the cumulative data of reported cases and related deaths by world, continent, country, state/province, and county/parish/zone, collectively locale, initially grow exponentially and level-off to an approximately horizontal asymptote during each phase according to a Generalized Logistic Distribution. Daily reported cases and deaths initially grow exponentially, reach a maximum, then wane slowly (e.g., with heavy tail) according to a Fréchet Distribution.

As of May 18, 2020, a simple Generalized Logistic Distribution modeling of the time series of the global cumulative case count (above 50k cases) yields an estimate of an asymptotic total of 256 million infections (adjusted R2 > 0.9997), that is, 3.30% of the current global population (i.e., infection rate) as a result of the COVID-19 Pandemic. With a provisional case fatality rate of 6.92%, this projection leads to an estimate of 17.4 million deaths worldwide (0.21% mortality rate). This model assumes no vaccine or effective treatment and only one single wave, the current one, with a single episode, but can model and incorporate multiple episodes and waves independently. However, a second episode emerged globally in June 2020 and a third in October 2020, so these estimates must be interpreted as lower bounds.

Figure 2.2a: Fréchet Distribution Modeling of Daily COVID-19 Reported Cases for Earth, U.S., New York State, and New York City (May 22, 2020)

Figure 2.2b: Generalized Logistic Distribution Modeling of Cumulative COVID-19 Reported Cases for Earth, U.S., New York State, and New York City (May 21, 2020)

Figure 2.2c: Fréchet Distribution Modeling of Daily COVID-19 Reported Deaths for Earth, U.S., New York State, and New York City (May 22, 2020)

Figure 2.2d: Generalized Logistic Distribution Modeling of Cumulative COVID-19 Reported Deaths for Earth, U.S., New York State, and New York City (May 21, 2020)

As of 2020, the population of the Earth is approximately 7.78 billion, growing at a yearly rate of 1.05-1.10% or at least 81 million per year, with an urban population of 56.2%, a median age of 30.9 years, and a land population density of about 59.9 km-2 excluding Antarctica and all bodies of water. The U.S. population is approximately 331 million, while that of New York (NY) and New York City (NYC) are 19.4 million and 8.4 million, respectively. Similar estimates have been computed using a General Logistic Model for the U.S., NY, and NYC (adjusted R2 > 0.9995), and are given in Tables 2.1a and 2.1b. In particular, this model determines that 22.8% of the current U.S. population have become infected or will become infected with COVID-19 (i.e., infection rate) and 1.27-2.14% have succumbed or will succumb to the disease (i.e., mortality rate) corresponding to a case fatality rate of 5.57%.

 Location Cases [M] RC 10/1/20 [M] RC 11/1/20 [M] RC 12/1/20 [M] RC 1/1/21 [M] NYC TBA New York U.S. Earth

 Location Current RD [M] RD 10/1/20 [M] RD 11/1/20 [M] RD 12/1/20 [M] RD 1/1/21 [M] NYC TBA New York U.S. Earth

### International Trends

To illustrate the rapid spread of COVID-19, global density maps of reported COVID-19 cases on January 14, January 29, February 28, March 29, April 28, and May 29, 2020 are given in Figures 2.3a-f. Leading countries in terms of COVID-19 reported cases (over 50k) and related deaths are given in Table 2.3b. Included in the same table are the corresponding populations and fraction of total global population, population densities by square mile, provisional case infection rates (PIR), provisional mortality rate (expressed as deaths per million population), and provisional case fatality rates. Of particular note, though no longer on the list, is the country of Ecuador, which added 11,536 reported cases in one day on April 24, 2020, constituting 10.9% of the new cases worldwide (105,825) that day.

 Cases Active Serious Deaths Tests Top 10 28,334,552 6,399,681 49,237 762,470 337,136,526 Affected \ Top 10 12,300,023 3,251,426 23,537 360,273 407,811,564 Affected 40,634,575 9,651,107 72,774 1,122,743 744,948,090 Max 8,456,653 2,728,163 15,501 225,222 160,000,000 Mean 190,773 45,310 539 5,878 3,497,979 Median 10,691 1,442 32 240 221,782 Confidence (95%) 116,376 27,564 240 3,077 2,142,694

Figure 2.3a: Global Density Map of COVID-19 Reported Cases (January 14, 2020)

Figure 2.3b: Global Density Map of COVID-19 Reported Cases (January 29, 2020)

Figure 2.3c: Global Density Map of COVID-19 Reported Cases (February 28, 2020)

Figure 2.3d: Global Density Map of COVID-19 Reported Cases (March 29, 2020)

Figure 2.3e: Global Density Map of COVID-19 Reported Cases (April 28, 2020)

Figure 2.3f: Global Density Map of COVID-19 Reported Cases (May 29, 2020)

Figure 2.4a: Population Density of all Countries with Populations over 45M (2020)

<br Countries with at least 45M citizens and ordered by population density (per square mile) are given in Figure 2.4a, with Bangladesh, South Korea, India, Philippines, and Japan possessing the highest population densities in 2020.

Figure 2.4b: Median Age of all Countries with Populations over 45M (2020)

Countries with at least 45M citizens and ordered by median age are given in Figure 2.4b, with Japan (48), Italy (47), Germany (46), Spain (45), and South Korea (44) possessing the highest median ages in 2020.

 Location Population Global Frac. Density [km-2] Median Age Urban Frac. USA 331,589,837 4.26% 36 38 83% India 1,384,085,979 17.79% 466 28 35% Brazil 213,015,720 2.74% 25 33 88% Russia 145,953,533 1.88% 9 40 74% Spain 46,760,297 0.60% 94 45 80% Argentina 45,320,654 0.58% 17 32 93% Colombia 51,045,852 0.66% 46 31 80% France 65,317,424 0.84% 119 42 82% Peru 33,109,207 0.43% 26 31 79% Mexico 129,339,873 1.66% 67 29 84% UK 67,993,982 0.87% 281 40 83% South Africa 59,532,742 0.77% 49 28 67% Iran 84,314,980 1.08% 52 32 76% Chile 19,165,653 0.25% 26 35 85% Iraq 40,488,958 0.52% 93 21 73% Italy 60,434,663 0.78% 205 47 69% Bangladesh 165,182,885 2.12% 1,269 28 39% Germany 83,865,285 1.08% 241 46 76% Indonesia 274,392,799 3.53% 151 30 56% Philippines 110,017,637 1.41% 369 26 47% Top 10 2,445,538,376 31.43% 54.38 31.4 55.8% Earth \ Top 10 5,335,414,811 68.57% 63.16 31.1 55.3% Earth 7,780,953,187 - 60.11 31.2 55.5%

 Location Cases Deaths PIR [/k] PID [/km2] PMR [/M] PCFR USA 8,456,653 225,222 25.503 0.924 679.22 2.66% India 7,594,736 115,236 5.487 2.554 83.26 1.52% Brazil 5,251,127 154,226 24.651 0.628 724.01 2.94% Russia 1,415,316 24,366 9.697 0.086 166.94 1.72% Spain 1,015,795 33,992 21.723 2.036 726.94 3.35% Argentina 1,002,662 26,716 22.124 0.366 589.49 2.66% Colombia 965,883 29,102 18.922 0.871 570.11 3.01% France 910,277 33,623 13.936 1.662 514.76 3.69% Peru 870,876 33,820 26.303 0.680 1,021.47 3.88% Mexico 851,227 86,167 6.581 0.438 666.21 10.12% UK 741,212 43,726 10.901 3.064 643.09 5.90% South Africa 705,254 18,492 11.846 0.581 310.62 2.62% Iran 534,631 30,712 6.341 0.328 364.25 5.74% Chile 493,305 13,676 25.739 0.663 713.57 2.77% Iraq 430,678 10,317 10.637 0.992 254.81 2.40% Italy 423,578 36,616 7.009 1.440 605.88 8.64% Bangladesh 390,206 5,681 2.362 2.998 34.39 1.46% Germany 373,731 9,899 4.456 1.072 118.03 2.65% Indonesia 365,240 12,617 1.331 0.202 45.98 3.45% Philippines 359,169 6,675 3.265 1.205 60.67 1.86% Top 10 28,334,552 762,470 11.586 0.630 311.78 2.69% Earth \ Top 10 12,300,023 360,273 2.305 0.146 67.52 2.93% Earth 40,634,575 1,122,743 5.222 0.314 144.29 2.76%

Figure 2.4c: All Affected Countries with at least 80,000 COVID-19 Reported Cases ordered by Provisional Infection Rate [per 1,000 people] (September 16, 2020)

All countries with at least 80,000 COVID-19 reported cases ordered by provisional infection rate, the fraction of infections per thousand population are given in Figure 2.4c.

Figure 2.4d: All Countries with at least 80,000 COVID-19 Reported Cases ordered by Provisional Infection Density [km</nowiki>-2] (September 16, 2020)

All countries with at least 80,000 COVID-19 reported cases ordered by provisional infection density, the fraction of infections per square kilometer are given in Figure 2.4d.

Figure 2.4e: All Countries with at least 80,000 COVID-19 Reported Cases ordered by Provisional Mortality Rate (per million population) (September 16, 2020)

All countries with at least 80,000 COVID-19 reported cases ordered by provisional mortality rate, the fraction of deaths per million population are given in Figure 2.4e.

Figure 2.4f: All Countries with at least 80,000 COVID-19 Reported Cases ordered by Case Fatality Rate (September 16, 2020)

All countries with at least 80,000 COVID-19 reported cases ordered by provisional case fatality rate, the fraction of deaths per infected are given in Figure 2.4f.

 Location RC / Total Active / Total Serious / Total Rec / Total RD / Total USA 20.81% 35.69% 21.30% 18.43% 20.06% India 18.69% 9.80% 12.29% 22.54% 10.26% Brazil 12.92% 5.43% 11.43% 15.68% 13.74% Russia 3.48% 4.12% 3.16% 3.60% 2.17% Spain 2.50% 0.00% 2.55% 0.00% 3.03% Argentina 2.47% 2.25% 6.04% 2.69% 2.38% Colombia 2.38% 0.90% 2.91% 2.91% 2.59% France 2.24% 10.08% 2.88% 0.35% 2.99% Peru 2.14% 0.69% 1.50% 2.63% 3.01% Mexico 2.09% 1.91% 3.60% 2.07% 7.67% UK 1.82% 0.00% 0.81% 0.00% 3.89% South Africa 1.74% 0.67% 0.75% 2.13% 1.65% Iran 1.32% 0.95% 6.56% 1.44% 2.74% Chile 1.21% 0.19% 1.06% 1.56% 1.22% Iraq 1.06% 0.74% 0.62% 1.22% 0.92% Italy 1.04% 1.75% 1.10% 0.85% 3.26% Bangladesh 0.96% 1.03% N/A 1.02% 0.51% Germany 0.92% 0.90% 1.17% 0.99% 0.88% Indonesia 0.90% 0.83% N/A 0.97% 1.12% Philippines 0.88% 0.55% 2.15% 1.04% 0.59% Top 10 69.73% 70.87% 67.66% 70.90% 67.91% Earth \ Top 10 30.27% 29.13% 32.34% 29.10% 32.09%

Figure 2.4g: Countries ordered by Global Fraction of Reported COVID-19 Cases (September 16, 2020)

Figure 2.4h: Countries ordered by Global Fraction of Reported COVID-19 Deaths (September 16, 2020)

 Location Active / RC Serious / Active Serious / RC Rec / RC Rec Decile USA 32.26% 0.57% 0.18% 65.08% 7 India 9.86% 1.19% 0.12% 88.62% 9 Brazil 7.91% 2.00% 0.16% 89.16% 9 Russia 22.26% 0.73% 0.16% 76.02% 8 Spain N/A N/A N/A N/A N/A Argentina 17.15% 2.55% 0.44% 80.18% 9 Colombia 7.13% 3.07% 0.22% 89.86% 9 France 84.67% 0.27% 0.23% 11.64% 2 Peru 6.09% 2.06% 0.13% 90.03% 10 Mexico 17.15% 1.79% 0.31% 72.72% 8 UK N/A N/A N/A N/A N/A South Africa 7.30% 1.06% 0.08% 90.07% 10 Iran 13.57% 6.58% 0.89% 80.68% 9 Chile 2.96% 5.26% 0.16% 94.27% 10 Iraq 13.20% 0.80% 0.11% 84.41% 9 Italy 31.64% 0.59% 0.19% 59.72% 6 Bangladesh 20.23% N/A N/A 78.32% 8 Germany 18.47% 1.23% 0.23% 78.88% 8 Indonesia 17.35% N/A 0.00% 79.19% 8 Philippines 11.75% 3.70% 0.43% 86.39% 9 Top 10 19.12% 0.91% 0.17% 74.72% 8 Earth \ Top 10 18.11% 1.06% 0.19% 70.64% 8 Earth 18.81% 0.95% 0.18% 73.49% 8

Figure 2.4i: Leading Countries ordered by Testing Rate (September 16, 2020)

Testing rate is the fraction of tests relative to the population of a country. All countries with at least 80,000 COVID-19 reported cases ordered by testing rate are given in Figure 2.4i.

Figure 2.4j: Leading Countries ordered by Positivity Rate (September 16, 2020)

Testing rate is the fraction of tests relative to the population of a country. All countries with at least 80,000 COVID-19 reported cases ordered by testing rate are given in Figure 2.4j.

 Location Tests Tests / Pop Test Den [/km2] Tests / Total Positivity Rate USA 127,057,107 38.32% 13.890 17.06% 6.66% India 95,083,976 6.87% 31.980 12.76% 7.99% Brazil 17,900,000 8.40% 2.142 2.40% 29.34% Russia 54,300,208 37.20% 3.316 7.29% 2.61% Spain 15,503,165 33.15% 31.081 2.08% 6.55% Argentina 2,626,406 5.80% 0.960 0.35% 38.18% Colombia 4,467,051 8.75% 4.026 0.60% 21.62% France 13,765,883 21.08% 25.141 1.85% 6.61% Peru 4,249,458 12.83% 3.320 0.57% 20.49% Mexico 2,183,272 1.69% 1.123 0.29% 38.99% UK 29,922,135 44.01% 123.681 4.02% 2.48% South Africa 4,565,980 7.67% 3.764 0.61% 15.45% Iran 4,540,455 5.39% 2.788 0.61% 11.77% Chile 3,929,612 20.50% 5.285 0.53% 12.55% Iraq 2,644,770 6.53% 6.089 0.36% 16.28% Italy 13,639,444 22.57% 46.371 1.83% 3.11% Bangladesh 2,178,714 1.32% 16.737 0.29% 17.91% Germany 19,276,507 22.99% 55.303 2.59% 1.94% Indonesia 4,092,595 1.49% 2.259 0.55% 8.92% Philippines 4,398,498 4.00% 14.752 0.59% 8.17% Top 10 337,136,526 13.79% 7.497 45.26% 8.40% Earth \ Top 10 407,811,564 7.64% 4.828 54.74% 3.02% Earth 744,948,090 9.57% 5.755 - 5.45%

 Location Start Date (2020) RC on 10/1/20 [M] RC on 11/1/20 [M] RC on 12/1/20 [M] RC on 1/1/21 [M] USA TBA India Brazil Russia Peru Colombia Mexico Spain South Africa Argentina France Chile Iran UK Bangladesh Saudi Arabia Iraq Pakistan Turkey Italy

 Location Start Date (2020) RD on 10/1/20 [M] RD on 11/1/20 [M] RD on 12/1/20 [M] RD on 1/1/21 [M] USA TBA India Brazil Russia Peru Colombia Mexico Spain South Africa Argentina France Chile Iran UK Bangladesh Saudi Arabia Iraq Pakistan Turkey Italy

The time series of the cumulative COVID-19 reported cases and related deaths for the previously leading four countries, namely, U.S., Spain, Italy and France, from February 1, 2020 to April 14, 2020, are given in Figures 2.5a and 2.5b, respectively. This illustrates the meteoric rise of reported cases and related deaths of the U.S. compared to these countries. The growth of cases in the U.S. is consistent with that of the continent of Europe as a whole rather than any individual country therein, as discussed in the Introduction.

Figure 2.5a: Time Series of Cumulative COVID-19 Reported Cases for U.S., Spain, Italy and France (February 1, 2020 - April 14, 2020)

Figure 2.5b: Time Series of Cumulative COVID-19-Related Deaths for U.S., Spain, Italy and France (February 1, 2020 - April 14, 2020)

#### Sustained Exponential Growth

In contrast to the cumulative growth features seen in larger countries with a high number of cases that appear to follow a general logistic distribution model, however, several relatively small countries with a relatively smaller number of cases (under 100,000) exhibited multi-phase and sustained exponential growth. For example, the time series of the cumulative number of reported COVID-19 cases for the Central American country of Guatemala from March 21, 2020 to April 26, 2020 and April 10, 2020 to June 15, 2020 are given in Figures 2.6a/b. For the former time frame, the exponential fit has an amplitude of 14.708 reported cases and a growth rate of 0.0948 day-1 (R2 > 0.9951), the latter of which leads to doubling and order-of-magnitude times of approximately 7.3 days and 24.3 days, respectively. For the latter time frame, the exponential fit has an amplitude of 131.54 reported cases and a growth rate of 0.0674 day-1 (R2 > 0.9953), the latter of which leads to doubling and order-of-magnitude times of approximately 10.3 days and 34.2 days, respectively. On June 30, 2020, however, the sustained exponential trend in COVID-19 cases broke, and daily cases began to subside as expected, which is consistent with a general logistic distribution model.

Figure 2.6a/b: Cumulative COVID-19 Reported Cases in Guatemala (April 3 - April 25, April 10 - June 15, 2020)

### Domestic Trends

#### Nationwide Data

 Cases Active Serious Deaths Tests Top 10 States 4,664,476 1,375,558 - 130,305 67,486,614 Affected \ Top 10 3,555,869 1,229,185 - 89,535 58,021,513 Affected States + DC 8,220,345 8,220,345 - 219,840 125,508,127 Max 880,871 406,557 - 33,497 17,042,408 Mean 161,183 52,095 - 4,311 2,460,944 Median 107,748 23,984 - 2,180 1,480,763 Confidence (95%) 54,111 20,233 - 1,686 845,325

Beginning when the total of reported cases in the U.S. reached 100, from March 3-24, 2020, the cumulative reported cases could be well-modeled using a simple exponential fit with amplitude of 84.387 cases and growth rate constant of 0.295 day-1 yielding a doubling rate of ~2.4 days and an order of magnitude increase every ~7.8 days. Similarly, from March 14, 2020 through April 1, 2020, the number of deaths could be well-modeled using an exponential fit with an amplitude of 2.327 and rate constant equal to 0.258 day-1 yielding a doubling rate of ~2.7 days and an order of magnitude increase every ~8.9 days. These doubling times have since significantly increased.

After these periods of exponential growth, both the cumulative reported cases and cumulative reported deaths in the U.S. began increasing only approximately linearly, much less rapidly than during the exponential phase. This rate decline is likely due to a convolution of Stay-at-Home orders/advisories, social distancing measures, and mask adoptions, resulting in fewer seeding events with a certain degree of under-testing and test backlog in several laboratories combined.

Figure 2.7a: Time Series of COVID-19 Reported Cases in the U.S with a 7-Day Moving Average (January 1, 2020 - October 1, 2020)

Figure 2.7a: Time Series of COVID-19 RepoTable 2.4b: Significant U.S. Case Milestones in the COVID-19 Pandemic (September 23, 2020)

 Milestone Case Difference Time Frame Day Count [d] Growth Rate [/d] ~0 to 0.5 million 512,010 1/20/2020 - 4/10/2020 81 6,321 0.5 to 1 million 502,927 4/10/2020 - 4/27/2020 17 29,584 1 to 1.5 million 504,041 4/27/2020 - 5/16/2020 19 26,528 1.5 to 2 million 491,591 5/16/2020 - 6/7/2020 22 22,345 2 to 2.5 million 495,921 6/7/2020 - 6/25/2020 18 27,551 2.5 to 3 million 538,674 6/25/2020 - 7/6/2020 11 48,970 3 to 3.5 million 504,468 7/6/2020 - 7/14/2020 8 63,059 3.5 to 4 million 479,296 7/14/2020 - 7/21/2020 7 68,471 4 to 4.5 million 472,188 7/21/2020 - 7/28/2020 7 67,455 4.5 to 5 million 538.470 7/28/2020 - 8/6/2020 9 59,830 5 to 5.5 million 496,871 8/6/2020 - 8/15/2020 9 55,208 5.5 to 6 million 468,528 8/15/2020 - 8/26/2020 11 42.593 6 to 6.5 million 494,070 8/26/2020 - 9/7/2020 12 41,173 6.5 to 7 million 512,873 9/7/2020 - 9/20/2020 13 39,452 7,097,937 1/20/2020 - Present 246 28,850

Figure 2.7b: Time Series of COVID-19 Reported Deaths in the U.S. with 7-Day Moving Average (February 20, 2020 - October 1, 2020)

Figure 2.7c: Weekday Distribution of U.S. Reported COVID-19 Deaths

 Milestone Case Difference Time Frame Day Count [d] Growth Rate [/d] ~0 to 25,000 26,201 2/29/2020 - 4/12/2020 43 609 25,000 to 50,000 24,962 4/12/2020 - 4/23/2020 11 2,269 50,000 to 75,000 25,088 4/23/2020 - 5/6/2020 13 1,930 75,000 to 100,000 24,776 5/6/2020 - 5/23/2020 17 1,457 100,000 to 125,000 24,128 5/23/2020 - 6/22/2020 30 804 125,000 to 150,000 25,301 6/22/2020 - 7/26/2020 34 744 150,000 to 175,000 25,212 7/26/2020 - 8/18/2020 23 1,096 175,000 to 200,000 24,654 8/18/2020 - 9/15/2020 28 881 205,471 2/29/2020 - Present 206 997

Figure 2.7d: U.S. COVID-19 Case to Death Ratio (February 20, 2020 - August 24, 2020)

Figure 2.7e: U.S. Provisional Case Fatality Rates (February 29, 2020 - October 1, 2020)

Figure 2.7f: Daily U.S. COVID-19 Laboratory Tests (February 1, 2020 - August 24, 2020)

Figure 2.7g: U.S. COVID-19 Laboratory Test Positivity Rate (February 15, 2020 - August 24, 2020)

Figure 2.7h: Current U.S. COVID-19 Hospitalizations (March 18, 2020 - August 24, 2020)

Figure 2.7i: U.S. COVID-19 Hospitalization Rate (March 22, 2020 - August 24, 2020)

Figure 2.7j: U.S. COVID-19 ICU / Hospitalizations / Ventilation Rates (March 26, 2020 - August 24, 2020)

#### Statewide Data

During the rapid growth of COVID-19 reported cases and related deaths in the U.S., both state and federal guidelines and mandates had yet to appreciably abate the looming crisis. In fact, state governments were entirely responsible for their own management of their outbreaks, which were occuring with different start times, growth rates, and severities measured by the number of clusters. Several states instituted Stay-at-Home (or Shelter-in-Place) advisories and orders, but on different dates (Figure 2.8). South Carolina was the last state to adopt a Stay-at-Home advisory or order on April 7, 2020, while Arkansas, Iowa, Nebraska, and North Dakota have yet to take similar actions.

Figure 2.8: Timeline of U.S. State Stay-at-Home Advisories / Orders (April 7, 2020, Adapted from KFF)

As of July 14, 2020, New York, California, Florida, and Texas led the other contiguous U.S. states in terms of reported cases and related deaths. On July 12, 2020, the state of Florida posted a record breaking 15,300 new COVID-19 cases for the highest single-day increase in the U.S. since the beginning of the COVID-19 pandemic. The fact that population density alone does not account for the observed sequence of the most severely impacted U.S. states is evidenced in Table 2.5a, where current populations, population densities, reported cases, reported deaths, and current provisional case fatality rates for the leading U.S. states are given. A similar table for leading U.S. counties and boroughs of New York City in terms of reported cases are given in Tables 2.6 and 2.7, respectively.

 State Population U.S. Frac. Density [km-2] Median Age Urban Frac. California 39,512,223 12.04% 97.93 36.8 95.0% Texas 28,995,881 8.83% 42.86 34.8 84.7% Florida 21,477,737 6.54% 154.64 42.2 91.2% New York 19,453,561 5.93% 159.38 39.0 87.9% Illinois 12,671,821 3.86% 88.13 38.3 88.5% Georgia 10,617,423 3.23% 71.28 36.9 75.1% North Carolina 10,488,084 3.20% 83.29 38.9 66.1% Tennessee 6,829,174 2.08% 63.94 38.8 66.4% Arizona 7,278,717 2.22% 24.74 37.9 89.8% New Jersey 8,882,190 2.71% 466.33 40.0 94.7% Pennsylvania 12,801,989 3.90% 110.47 40.8 78.7% Ohio 11,689,100 3.56% 110.45 39.4 77.9% Louisiana 4,648,794 1.42% 41.54 37.2 73.2% Wisconsin 5,822,434 1.77% 41.51 39.6 70.2% Alabama 4,903,185 1.49% 37.38 39.2 59.0% Virginia 8,535,519 2.60% 83.45 38.4 75.5% South Carolina 5,148,714 1.57% 66.13 39.6 66.3% Michigan 9,986,857 3.04% 68.20 39.8 74.6% Missouri 6,137,428 1.87% 34.47 38.7 70.4% Indiana 6,732,219 2.05% 72.55 37.9 72.4% Top 10 166,206,811 50.64% 76.25 38.0 86.9% U.S. \ Top 10 162,032,712 49.36% 23.25 38.7 74.7% U.S. 328,239,523 35.88 38.3 80.9%

 State Cases Deaths PIR [/K] PID [/km2] PMR [/M] PCFR California 880,871 17,001 22.29 2.18 430.27 1.93% Texas 877,077 17,599 30.25 1.30 606.95 2.01% Florida 756,727 16,025 35.23 5.45 746.12 2.12% New York 521,215 33,497 26.79 4.27 1,721.90 6.43% Illinois 350,748 9,496 27.68 2.44 749.38 2.71% Georgia 341,310 7,657 32.15 2.29 721.17 2.24% North Carolina 247,172 3,939 23.57 1.96 375.57 1.59% Tennessee 232,061 2,922 33.98 2.17 427.87 1.26% Arizona 231,897 5,830 31.86 0.79 800.97 2.51% New Jersey 225,398 16,339 25.38 11.83 1,839.52 7.25% Pennsylvania 188,409 8,571 14.72 1.63 669.51 4.55% Ohio 183,685 5,082 15.71 1.74 434.76 2.77% Louisiana 175,982 5,766 37.86 1.57 1,240.32 3.28% Wisconsin 173,891 1,600 29.87 1.24 274.80 0.92% Alabama 173,485 2,789 35.38 1.32 568.81 1.61% Virginia 166,828 3,457 19.55 1.63 405.01 2.07% South Carolina 164,609 3,661 31.97 2.11 711.05 2.22% Michigan 164,123 7,363 16.43 1.12 737.27 4.49% Missouri 163,221 2,681 26.59 0.92 436.83 1.64% Indiana 149,166 3,960 22.16 1.61 588.22 2.65% Top 10 4,664,476 130,305 28.06 2.14 783.99 2.79% U.S. \ Top 10 3,555,869 89,535 21.95 0.51 552.57 2.52% U.S. 8,220,345 219,840 25.04 0.90 669.75 2.67%

 State Cases / Total Active / Total Serious / Total Rec / Total Deaths / Total California 10.72% 15.61% - 7.73% Texas 10.67% 4.36% - 8.01% Florida 9.21% 9.43% - 7.29% New York 6.34% 2.94% - 15.24% Illinois 4.27% 3.22% - 4.32% Georgia 4.15% 6.54% - 3.48% North Carolina 3.01% 1.41% - 1.79% Tennessee 2.82% 0.89% - 1.33% Arizona 2.82% 7.20% - 2.65% New Jersey 2.74% 1.20% - 7.43% Pennsylvania 2.29% 1.27% - 3.90% Ohio 2.23% 1.06% - 2.31% Louisiana 2.14% 0.32% - 2.62% Wisconsin 2.12% 1.36% - 0.73% Alabama 2.11% 3.70% - 1.27% Virginia 2.03% 5.54% - 1.57% South Carolina 2.00% 3.01% - 1.67% Michigan 2.00% 1.81% - 3.35% Missouri 1.99% 4.79% - 1.22% Indiana 1.81% 1.41% - 1.80% Top 10 56.74% 52.81% - 59.27% U.S. \ Top 10 43.26% 47.19% - 40.73%

 State Active / RC Serious / Active Serious / RC Rec / RC Rec Decile California 46.15% - - 51.92% 6 Texas 12.94% - - 85.05% 9 Florida 32.46% - - 65.42% 7 New York 14.71% - - 78.86% 8 Illinois 23.90% - - 73.39% 8 Georgia 49.93% - - 47.83% 5 North Carolina 14.87% - - 83.53% 9 Tennessee 10.04% - - 88.70% 9 Arizona 80.86% - - 16.63% 2 New Jersey 13.89% - - 78.86% 8 Pennsylvania 17.61% - - 77.84% 8 Ohio 15.01% - - 82.23% 9 Louisiana 4.79% - - 91.94% 10 Wisconsin 20.35% - - 78.73% 8 Alabama 55.60% - - 42.79% 5 Virginia 86.48% - - 11.45% 2 South Carolina 47.57% - - 50.20% 6 Michigan 28.77% - - 66.74% 7 Missouri 76.46% - - 21.90% 3 Indiana 24.63% - - 72.71% 8 Top 10 29.49% - - 67.72% 7 U.S. \ Top 10 34.57% - - 62.91% 7 U.S. 31.69% - - 65.64% 7

 Location Tests Testing Rate Test Den [/km2] Tests / Total Positivity Rate California 17,042,408 43.13% 42.24 13.58% 5.17% Texas 8,078,858 27.86% 11.94 6.44% 10.86% Florida 5,746,529 26.76% 41.38 4.58% 13.17% New York 12,982,175 66.73% 106.36 10.34% 4.01% Illinois 6,824,237 53.85% 47.46 5.44% 5.14% Georgia 3,633,927 34.23% 24.40 2.90% 9.39% North Carolina 3,640,086 34.71% 28.91 2.90% 6.79% Tennessee 3,371,897 49.37% 31.57 2.69% 6.88% Arizona 1,948,792 26.77% 6.62 1.55% 11.90% New Jersey 4,217,705 47.48% 221.44 3.36% 5.34% Pennsylvania 2,458,579 19.20% 21.22 1.96% 7.66% Ohio 3,930,940 33.63% 37.14 3.13% 4.67% Louisiana 2,594,376 55.81% 23.19 2.07% 6.78% Wisconsin 1,877,704 32.25% 13.39 1.50% 9.26% Alabama 1,321,900 26.96% 10.08 1.05% 13.12% Virginia 2,583,644 30.27% 25.26 2.06% 6.46% South Carolina 1,768,755 34.35% 22.72 1.41% 9.31% Michigan 4,688,396 46.95% 32.02 3.74% 3.50% Missouri 2,406,589 39.21% 13.52 1.92% 6.78% Indiana 2,533,863 37.64% 27.31 2.02% 5.89% Top 10 67,486,614 40.60% 30.96 53.77% 6.91% U.S. \ Top 10 58,021,513 35.81% 8.33 46.23% 6.13% U.S. 125,508,127 38.24% 13.72 - 6.55%

Purported Sources of Misinformation from Florida

It has been claimed by several scientists and the several U.S. news media outlets that politicians from the State of Florida are covertly misrepresenting COVID-19 laboratory testing data to skew results for political purposes. This involves two major concerns. Firstly, the positivity rate, which is the ratio of positive tests to total tests, may be misleading in the manner in which it is used and discussed by officials in Florida. Suppose an individual receives three negative tests before receiving one positive test. The positive test is counted only once in the numerator of the positivity rate, while all four tests are counted in the denominator, which could give the impression that there are fewer confirmed COVID-19 cases if a significant portion of the population takes more than a single COVID-19 test. Thus, the positivity rate may not give an accurate representation of the percentage of COVID-19 positive individuals among those who test for the disease. Secondly, in the State of Florida both molecular (RT-PCR) and antigen laboratory test counts are combined, but these methods have very different error rates due to differing specificity in their action. In fact, antigen laboratory tests, while accurate, have a higher false negative rate. RT-PCR laboratory tests, on the other hand, are more adapted to detecting an active infection of SARS-CoV-2. In the best case scenario, both tests would be given to confirm or rule out COVID-19.

#### Countywide Data

Figure 2.9: Time Series of Cumulative COVID-19 Reported Cases in

Several U.S. Counties (April 14, 2020)

 City/County State Population (% State) Pop. Density [mi-2] Reported Cases Reported Deaths PCFR New York NY 1,628,701 (8.38%) 72,056 219,670 21,941 9.99% Los Angeles CA 10,105,518 (25.55%) 2,488 100,772 3,326 3.30% Cook IL 5,180,493 (40.66%) 5,480 90,122 4,554 5.05% Maricopa AZ 4,329,580 1,219 45,178 746 1.65% Nassau NY 1,358,343 (6.99%) 4,763 41,780 2,692 6.44% Suffolk NY 1,481,093 (7.62%) 1,632 41,339 2,026 4.90% Miami-Dade FL 2,744,878 13,512 35,221 1,296 2.77% Westchester NY 967,612 (4.98%) 2,250 34,797 1,557 4.47% Harris TX 4,664,159 3,657 30,729 376 1.22% Philadelphia PA 1,584,138 (12.37%) 30,578 25,991 1,595 6.14% Middlesex MA 1,614,714 (23.39%) 5,113 23,946 1,862 7.78% Wayne MI 1,753,893 (17.55%) 2,866 22,686 2,713 11.96% Dallas TX 1,382,270 4,069 20,737 353 1.70% Suffolk MA 803,907 13,882 19,795 1,007 5.09% Bergen NJ 936,692 (10.51%) 4,070 19,638 1,985 10.11% Hudson NJ 676,061 (7.59%) 14,483 19,009 1,449 7.62%

 Borough County Population (% NYC) Pop. Density [mi-2] Reported Cases Reported Deaths PCFR Queens Queens 2,278,906 (27.13%) 21,460 68,145 7,128 10.46% Brooklyn Kings 2,582,830 (30.75%) 37,137 62,972 7,199 11.43% The Bronx Bronx 1,432,132 (17.05%) 34,653 49,646 4,816 9.70% Manhattan New York 1,628,701 (19.39%) 72,033 30,317 3,137 10.35% Staten Island Richmond 476,179 (5.67%) 8,112 14,639 1,075 7.34% Unknown - - - 19 33 - 8,398,748 28,188 225,738 23,388 10.36%

As of May 5, 2020, there were 5,359 deaths in New York City attributed to a probable COVID-19 infection. A probable COVID-19 death is defined if the decedent was a resident of NYC, had no known positive laboratory test for the presence of SARS-CoV-2, but resulted in a death certificate that lists COVID-19 or equivalent as a cause of death. From March 11 to April 16, 2020, there were an additional 9,447 deaths in New York City not known to be confirmed or probable COVID-19-related deaths.

 ZIP Code Neighborhood Population (% NYC) Pop. Density [mi-2] Reported Cases Reported Deaths PCFR 11368 Corona 109,931 (1.30%) 41,798.9 4,737 409 9.03% 10467 Van Cortlandt Park 96,279 (1.14%) 41,215.3 3,496 300 8.68% 11373 Elmhurst 92,876 (1.10%) 61,022.3 3,323 292 8.70% 11219 Borough Park 92,858 (1.10%) 62,657.2 3,124 219 7.25% 10469 Pelham Gardens 71,508 (0.85%) 28,915.5 3,082 333 11.23%

 Age Group Cases % Total Cases Deaths % Total Deaths PCFR <18 5,801 2.79% 14 0.06% 0.24% 18-44 76,261 36.65% 825 3.72% 1.08% 45-64 75,494 36.28% 4,909 22.11% 6.50% 65-74 25,672 12.34% 5,346 24.16% 20.89% >75 24,415 11.73% 11,028 49.68% 45.17% Unknown 454 0.22% 59 0.27% 13.00% Subtotal 208,097 97.59% 22,199 81.21% 10.67% Probable 5,136 2.41% 5,136 18.79% - 213,233 20,237 12.82%

As of May 11, 2020, the median age for a COVID-19 positive individual in NYC is 51 with 87,910 (47.69%) cases are younger than 50 years of age, 95,997 (52.08%) cases are aged 50 or older, and 412 (0.22%) of unknown age. Reported cases and related deaths by sex in NYC are given in Table 2.7d. Recorded and probable deaths in NYC by ethnicity are given in Table 2.7e.

 Sex Reported Cases (% Total) Reported Deaths (% Total) Probable Deaths (% Total) PCFR Female 9,658 (41.9%) Male 13,416 (58.1%) Unknown 9 (<0.01%) 23,083

 Race / Ethnicity Reported Deaths (% Total) Probable Deaths (% Total) Related Deaths (% Total) Black / African American 3,870 (30%) 1,251 (32.6%) 5,121 (30.2%) Hispanic / Latinx 4,112 (30.4%) 1,108 (28.9%) 5,220 (30.7%) White / Caucasian 3,572 (27.9%) 1,091 (28.5%) 4,663 (27.5%) Asian / Pacific Islander 1,019 (7.6%) 359 (9.4%) 1,378 (8.1%) Unknown 576 (4.1%) 24 (0.6%) 600 (3.5%) 14,162 5,378 19,540

Figure 2.10a: NYC County Infection Density as a Function of Median Income (Adapted from N.Y. Times)

Figure 2.10b: NYC County Infection Density as a Function of Household Size (Adapted from N.Y. Times)

.

### A Modified-SEIR Model

We model universal curves of reported COVID-19 daily reported infections and related deaths using a modified epidemiological Susceptible-Exposed-Infectious-Recovered (SEIR) Model.[2] Using currently available data, we determine optimized constants and apply this framework to reproducing the infection and death curves for California (the state with the largest population) and New York (the state with highest population density).

Figure 2.11: Parameter Relationships in the Proposed CSPDR Model

It is helpful to define various sets that appear in the model as time-dependent variables. In the early stages of an epidemic or pandemic, the vast majority of individuals are susceptible to infection, while few individuals have recovered from an infection. However, there are intermediate steps between infecting others with asymptomatic or pre-symptomatic, becoming symptomatic, getting tested and confirmed to be positive, all or most of which allow for further spread of the pathogen by the contagious. This is further adjusted by the removal of contagious individuals from the contagious population through self-isolation or hospitalization and complicated by imperfect testing protocols with lab saturation and false negatives. To account for these variables, we first group those intermediates into a symptomatic set S. We make the assumption that recovery rates are identical across all populations, and note that we may ignore the population of individuals who have been exposed to the pathogen but are not yet contagious. Our proposed CSPDR Model (pronounced “C-Spider”) then describes the flow of individuals from the contagious set C to the symptomatic set S to the positively confirmed set P to the deceased set D, with the possibility that at any point an individual may move to the recovered set R. This results in an initial system of coupled ODEs:

${\displaystyle {\frac {dC}{dt}}=\alpha C-(\beta +\eta )C}$
${\displaystyle {\frac {dS}{dt}}=\beta C-(\eta +\delta )S}$
${\displaystyle {\frac {dP}{dt}}=\delta S-(\gamma +\eta )P}$
${\displaystyle {\frac {dD}{dt}}=\gamma C}$

where we assume that contagious individuals are able to expose others at a variable infectivity rate ${\displaystyle \alpha }$(related to the basic reproduction number R0 of the pathogen), both of whom may become symptomatic, then self-isolate and/or are admitted to the hospital (thus discounting their ability to further infect), at fixed rate ${\displaystyle \beta }$. From there, symptomatic individuals may be tested and, if tested, a portion are confirmed to be positive with rate ${\displaystyle \delta }$, at which point they either recover from the disease to the point where they are no longer contagious at rate ${\displaystyle \eta }$or succumb to disease at rate ${\displaystyle \gamma }$. We ignore infections to healthcare workers, which is small compared to community spread. Similarly, although handling the deceased has been demonstrated to infect the healthy in certain isolated instances, it is at such a small rate that we may safely ignore any linear terms in D in the last ODE of the system. Finally, we add an elaboration for the rate ${\displaystyle \alpha }$,

${\displaystyle \alpha (t)={\frac {{\alpha }_{2}-{\alpha }_{1}}{1+{e}^{-\left(t-{t}_{0}-\Delta t\right)}}}+{\alpha }_{1}}$
${\displaystyle {\text{approximately }}{\alpha }_{1}{\text{ for t}}<{t}_{0}+\Delta {t}{\text{ , }}{\alpha }_{2}{\text{ for t}}\geq {t}_{0}+\Delta {t}}$

to account for the time dependence of the infection rate, rendering the ODE system inhomogenous and not amenable to analytical or matrix-exponentiation techniques. We use a logistic function[3] in time with fixed width parameter set to 1 day to interpolate between two extremal constant values ${\displaystyle {\alpha }_{1}{\text{ and }}{\alpha }_{2}}$for the infectivity rate before and after a Stay-at-Home advisory or order ${\displaystyle {t}_{0}}$ plus a learned time delay ${\displaystyle \Delta t}$ to reflect the response between the order and its consequence on the mitigation of pathogen spread. The difference in the two infection rates indicates the effectiveness of the order on reducing the growth of new infections. Note that if there were no symptomatic set, the set of infected and positively-confirmed individuals would be directly proportional to the set of contagious individuals at any point in time. Even with an incubation period, this would imply a sudden change in growth rates for newly confirmed cases across ${\displaystyle t={t}_{0}+\Delta t}$ (in a log-scaled graph, a sharp point), which is not observed in the data, but only rather a smooth transition.

Figure 2.12: CSPDR Model Curves and Experimental data of U.S. COVID-19 Daily Reported Cases and Related Deaths including the Predicted Contagious and Symptomatic Populations

We expect newly reported cases and deaths to vary up to ${\displaystyle {\sqrt {N}}}$ from their underlying values based on simple count statistics, although the resulting number ignores other systematic influences on our data such as time-varying testing rates or imperfect tests. To obtain a more realistic spread from our predicted parameters, we perform bootstrap sampling (i.e., sampling training data with replacement and adding samples from a Normal Distribution with a Standard Deviation of ${\displaystyle {\sqrt {N}}}$ to the recorded values), fit the rate parameters ${\displaystyle {\alpha }_{1}{\text{ , }}{\alpha }_{2}{\text{ , }}\beta {\text{ , }}\delta {\text{ , }}\gamma {\text{ , }}\eta {\text{ , }}{\Delta t}}$ and C0 using a discrete ODE solver, and minimize the Least-Squares Error over newly confirmed cases and deaths after the 100th case and death has been identified, respectively.

The symptomatic set is able to aggregate ejections from the contagious set and can exceed the contagious set if sufficiently many infected individuals self-isolate. Newly positive confirmations are proportional to the current size of the symptomatic pool ${\displaystyle {\delta S}}$. The deceased set shows additional flattening and a delayed response from the positive pool, which is supported by the observed data. Over time, the growth rate of newly confirmed cases appear to align with the growth rate of the contagious. This is apparent in the observed U.S. reported cases and deaths, as in Figure 2.12.

For the California data, we find that the daily infection rates have diminished from approximately 41% to 16% from March 1, 2020 to April 15, 2020 with the infection-to-confirmed rate averaging 0.71% (12% of 5.9%) and the new fatality to new case rate averaging 0.43%. These numbers align with a doubling time of 1.7-4.4 days, and a case fatality rate (integrated over 2 weeks) of ~6%.

Figure 2.13a: CSPDR Model Curves and Experimental Data of U.S. COVID-19 Daily Reported Cases and Related Deaths in California

For the New York data, we find that the daily infection growth rates have diminished from approximately 74% to 29% from March 1, 2020 to April 15, 2020, with the daily case fatality rate averaging 0.42%. These numbers align with the California data cutting the exposure rate by about half before and after the Shelter-in-Place order which, due to exponential growth, has an enormous impact on total cases as well as the case fatality rate.

As can be seen in Figures 2.14a and 2.14b, the infection growth rates are substantially higher for New York, the former reflecting the higher population density and greater ease with which disease can spread in the busy and dense metropolitan of New York City. Moreover, our expectations for these rates are bimodal, reflecting the two periods of intense spreading before March 1, 2020 and after March 15, 2020. Note also that the death rate, as indicated by the slope of the curve in Figure 2.14a, is currently higher than one might expect, compared to the infection rate two weeks prior. This suggests that testing rates are higher for deaths than otherwise in the state of New York.

Figure 2.13b: CSPDR Model Parameter Estimates for California

The fact that the contagious-to-positive rate (${\displaystyle \beta \delta }$is higher in the state of New York than in California remains unexplained. However, although the contagious and symptomatic numbers are hidden variables in our model, we only have observations for reported cases and deaths, and this rate is less informative and is strongly defined by two elements: the infection rates, and the sharpness of the change in infection rates before and after a Stay-at-Home advisory or order, which is noticeably stronger in New York than California. There could be many reasons for this, including changes to the testing process (corroborated by the current disparity between the case fatality rate from expectations). For instance, the two sharp slopes in infection rates suggests that testing may have been lagged between March 1-15, 2020. Note that in this study of the available COVID-19 data for California and New York, we see that the CSPDR Model cannot account for the repeatedly suggested “[continuing] flattening of the curve” well after the Stay-at-Home advisory or order date for either state, indicating that the corresponding daily infection rates have either stabilized or begun to decrease slightly or that testing is increasingly delayed. Lastly, examining the U.S. data in comparison to individual state data, we see that the former behavior better mimics California rather than New York, likely reflecting its lower overall population density. However, while the initial contagious daily growth rate reflects that of California, the current daily infection growth rate is far lower.

Figure 2.14a: CSPDR Model Curves and Experimental Data of U.S. COVID-19 Daily Reported Cases and Related Deaths in New York

Figure 2.14b: CSPDR Model Parameter Estimates for New York

Figure 2.15a: CSPDR Model Curves and Experimental Data of COVID-19 Daily Reported Cases and Related Deaths in the U.S.

Figure 2.15b: CSPDR Model Parameter Estimates for the U.S. The time shift ${\displaystyle \Delta t}$is in reference to the New York Shelter-in-Place Order of March 20, 2020.

## Symptoms of Infection

A COVID-19 infection appears to be influenza-like in its symptoms, if present at all, usually lasting about 2-3 weeks, and may include, but are not limited to, a fever (83-99%), dry and unproductive cough (59-82%), loss of appetite (40-84%), fatigue (44-70%), shortness of breath (31-40%), sputum/mucus-productive cough (28-33%), muscular ache and pain (11-35%), in addition to scratchy or sore throat, runny nose, swollen lymph nodes, skin rashes, headache, sneezing, diarrhea, nausea, vomiting, dizziness, sensory loss, conjunctivitis, and inflammation in fingers and toes.

 Disease Fever Dry Cough Dyspnea Diarrhea Sore Throat Ventilation MERS-12 98% 47% 72% 26% 21% 24.5% SARS-04 >99% 29-75% 40-42% 20-25% 13-25% 14-20% COVID-19 87.9% 67.7% 18.6% 3.7% 13.9% 4.1%

A report from ENT U.K. indicates that a loss of sense of smell and taste (anosmia or hyposmia) may be a characteristic symptom of COVID-19, and supporting evidence continues to grow. The report highlights that over ⅔ of current COVID-19 patients in Germany, for example, report this particular symptom. The report goes on to state that a growing number of doctors have been reporting a surge in isolated cases of loss of smell or taste in regions more heavily impacted with COVID-19, suggesting the symptom may be an indicator of asymptomatic and otherwise undiagnosed individuals carrying the virus. Complications that may require clinical intervention include unilateral or bilateral pneumonia, blood clots, sepsis, and, in severe cases, heart damage, cardiac arrest, stroke, septic shock, Acute Respiratory Distress Syndrome (ARDS) requiring assistive ventilation. In the most severe cases, similar to influenza and typically involving individuals with underlying pulmonary conditions, COVID-19 may result in death.

The WHO defines four degrees of a COVID-19 infection:

1. Mild (does not typically require clinical intervention)

No fever or low-grade fever of 100 °F (37.8 °C) or lower, some respiratory symptoms (dry and unproductive cough), and some aches and pains.

1. Moderate (may require clinical intervention)

Mild COVID-19 symptoms with fever above 100 °F (37.8 °C), lethargy, some shortness of breath, and possibly early pneumonia.

1. Severe (often requires clinical intervention)

Moderate COVID-19 symptoms with fever above 104 °F (40 °C), significant difficulty of breathing. Approximately 20% of moderate cases progress to severe. Approximately 14% of severe cases require supplemental oxygen.

1. Critical (requires emergency intervention)

Severe COVID-19 symptoms with further complications, including ARDS. Approximately 6% of severe cases become critical and may experience septic shock, which may lead to organ failure, and even death. Some patients have also experienced blood clots, sometimes culminating in strokes.

To see the rapid progression of the pandemic, as of March 15, 2020, there were 159,757 reported cases of COVID-19 worldwide, including 75,958 recoveries and 5,960 deaths, with 3,045 reported positive cases in the U.S. Roughly 8% of active cases worldwide (~75k, as of March 14, 2020) were severe or critical, the rest were considered mild or moderate. Today, these counts are orders of magnitude higher (See Introduction). In particular, on March 3, 2020, the WHO reported that the worldwide provisional case fatality rate of SARS-CoV-2 was 3.4%, which doubled to 6.92% by May 17, 2020, then settled back to approximately 4% by August 24, 2020, and accounts for mostly older individuals (65+), the immunocompromised, and/or those with pre-existing conditions such as diabetes, heart disease, high blood pressure, and Chronic Obstructive Pulmonary Disease (COPD). How generalizable this figure will be depends on the rate at which asymptomatic but infected individuals are tested and the adequacy of treatment of infected and symptomatic patients.

## Transmission Factors

SARS-CoV-2 is a highly contagious virus whose modes of transmission remain under scrutiny. It is particularly concerning that individuals infected with SARS-CoV-2 may become contagious before developing symptoms, a time when some first become aware of a possible infection. The time window in which the infected remain most contagious is a public health concern, which has consequences that extend to recommendations concerning quarantine practices for the sick and their contacts as well as to safety guidelines for healthcare workers that face exposure risk. For this reason, defining the latency period, the time frame from initial exposure to the virus to the time when the infected become contagious, the communicability period, the time frame the infected can spread the virus to others, and the incubation period, the time frame from initial exposure to the development of symptoms, is of the utmost importance. Figure 2.16 illustrates these three time frames in a typical disease progression.

We define these periods for COVID-19 and explore different possible routes of transmission including contact, fomite, aerosol droplet, and airborne transmission. The nature of asymptomatic cases and how they may contribute to disease transmission are considered as well.

Figure 2.16: Disease Incubation, Contagion, and Symptomatic Periods

### Incubation and Communicability Periods

A study of 181 well-described symptomatic cases of COVID-19 estimated the median incubation period of SARS-CoV-2 to be 5.1 days, with 95% of symptomatic patients developing symptoms between 2 and 14 days (Lauer et al., 2020). More specifically, the authors estimate that 2.5% cases became symptomatic within 2.2 days and 97.5% became symptomatic within 11.5 days. Figure 2.17 illustrates the estimated cumulative distribution of the proportion of symptomatic cases with respect to days since infection.

A March 2020 study of 9 SARS-CoV-2 infected individuals found that study subjects were most contagious one week before and during the first week of being symptomatic, when the virus is shedding at its maximum rate (Woelfel et al., 2020). The authors also note that in some instances of infected individuals, viral RNA was detected in sputum samples after subjects had no detectable symptoms of the disease. For this reason, Woelfel et al. note that “[b]ased on the present findings, early discharge with ensuing home isolation could be chosen for patients who are beyond Day 10 of symptoms with less than 100,000 viral RNA copies per ml of sputum. Both criteria predict that there is little residual risk of infectivity, based on cell culture.” In a study of 73 patients, SARS-CoV-2 has also been detected in fecal matter up to 12 days after respiratory tests are negative for COVID-19 infection (Xiao, F., et al., 2020).

Figure 2.17: Cumulative Distribution of Proportion of Symptomatic Cases with Respect to Days Since Infection (Adapted from Laurer et al., 2020)

### Basic Reproduction Number

The effective reproduction number, R, for an infection is the average number of people directly infected by a single case of the infection within a population. The basic reproduction number R0 of a pathogen is the value of R when the entire population is susceptible to a disease and no control measures have yet been implemented. The basic reproduction number of several pathogens and their corresponding diseases, including current estimates for SARS-CoV-2 and COVID-19, is given in Table 2.9.

 Pathogen Disease Transmission Incubation [d] R0 Measles virus (MeV) Measles Aerosol 9-12 12-18 Varicella-zoster virus Chickenpox Aerosol 9-21 10-12 Mumps orthorubulavirus Mumps Respiratory Droplets 14-18 10-12 Polio virus Polio Fecal-Oral Route 7-14 5-7 Rubella virus (RuV) Rubella Respiratory Droplets 14-21 5-7 Variola major Smallpox Respiratory Droplets 7-17 3.5-6 SARS-CoV-2 COVID-19 Respiratory Droplets, Biofluids, Aerosol 2-14 (avg. 5.1) 0.5-6 HIV AIDS Biofluids >14 2-5 Various Common Cold Respiratory Droplets 1-3 2-3 Influenza A (H1N1) Spanish Flu (1918) Respiratory Droplets 1-3 1.4-2.8 Ebola virus (EBOV) EVD Biofluids 1-42 1.5-1.9 Influenza A (H1N1) Swine Flu (2009) Respiratory Droplets 1-3 1.4-1.6 Influenza A-C (various) Seasonal Flu Respiratory Droplets 1-3 0.9-2.1 SARS-CoV-1 SARS-02 Respiratory Droplets 1-10 0.19-1.08 MERS-CoV MERS-12 Respiratory Droplets 2-14 0.3-0.8

### Contact and Droplet Transmission

When the aerosolized respiratory droplets of an infected individual come in contact with the mucus membrane (e.g., mouth, nose, or eyes, etc.) of another individual, transmission may occur. Due to gravity, however, larger respiratory droplets have a shorter range in the distance they can travel. Therefore, the largest (and most infectious) respiratory droplets that may be produced from talking, coughing, or sneezing are distance-limited. The CDC recommendation of maintaining a minimum distance of 6 feet (~2 meters) from other individuals was based on this semi-ballistic understanding of the dynamics of respiratory droplets, which limits the range of their flow in air. However, certain effects can enhance the range in which these droplets can distribute, especially favorable air flow and increased force in the emission of the droplets. For this reason, shouting, singing, and increased indoor ventilation (e.g., fans, HVAC, etc.), which enhance the force of emission or permit a wider range of fluid flow have all been associated with enhanced transmission, particularly in indoor settings, where dispersion is limited.

In a March, 2020 article in JAMA that uses a new model for respiratory emissions, Bourouiba describes sneezes, coughs, and related exhalations as turbulent gas clouds carrying clusters of respiratory droplets of various sizes. The air encapsulating the droplets limits dispersion or evaporation much longer than would be anticipated with rarefied droplets. Moreover, the forward momentum of the cloud can propel droplets farther. Bourouiba estimates that all droplet sizes within such a gas cloud could travel as far as 23-27 feet (7-8 meters). For this reason, the current CDC recommendation for maintaining 6 foot separation from others may need to be revised, as it possibly underestimates the distance that respiratory droplets can travel.

It should also be noted that stool samples taken from infected patients have also tested positive for SARS-CoV-2 (Holshue et al., 2020), which may suggest that the virus can be transmitted via the fecal-oral route. Thus, contact with infected stool could pose as another viable transmission mode.

Finally, it is important to discern pre-symptomatic individuals, those that will become symptomatic but are still in the incubation period of disease progression, from asymptomatic individuals, those who never develop symptoms of the disease (See Asymptomatic Cases and Transmission). While asymptomatic transmission has not yet been confirmed, some studies have established that infected individuals can transmit SARS-CoV-2 to others 2-3 days before onset of symptoms, and they may be most contagious up to 24 hours before notable symptoms appear (Pan et al., 2020). To complicate matters, the sputum of infected individuals may continue to act as contagion vectors for several days after the clearance of most symptoms (Woelfel et al., 2020). Some data suggest that SARS-CoV-2 may continue to shed for as long as 37 days after the onset of symptoms (Zhou, F. et al., 2020).

#### Face Masks and Other Methods for Limiting Droplet Transmission

The use of face masks has shown to be an effective way of limiting respiratory droplet dispersion into the surrounding environment, thereby lowering the risk of SARS-CoV-2 transmission. Previous studies have provided evidence that widespread use of face masks has reduced the spread of COVID-19. As a result, various government agencies have recommended and in some cases mandated the use of them in an effort to limit the spread of the disease. However, the use of face masks has been a complicated issue, particularly in the earliest stages of the epidemic, when their supply was severely limited. N95 respirators and surgical masks in particular were often recommended solely for use by medical personnel who needed them most urgently during a time of severe shortage. As a result, many medical agencies, including the CDC, recommended the use of low-cost fabrics and textiles, such as bandanas and other common cotton and polyester clothing items, for the fabrication of such masks. Despite these recommendations, natural questions concerning the efficacy of such fabrics for limiting droplet transmission, as well as how proper fitting may affect such efficacy, have arisen.

Figure 2.18: Relative Droplet Count Recorded During Use of 14 Masks and One Swath of Mask Material When Compared to No Mask Use (Adapted from Fischer et al., 2020)

### Evidence for Airborne and/or Fomite Transmission

Though it is not clear if SARS-CoV-2 can be transmitted through airborne means, respiratory droplets can remain in the air for extended periods of time and can land on surfaces rendering them fomites, or inanimate vectors. In fact, SARS-CoV-2 can remain airborne from 30 minutes to 3 hours, and can remain active for 4 hours on copper, 24 hours on cardboard, and 2-3 days on plastic and stainless steel (van Doremalen et al., 2020), though it is unclear if contact with such fomites can cause transmission.

Chin et al. (2020) tested 5 µL samples of viral culture incubated at 22℃ and at 65% humidity on various surfaces. They reported that no infectious virus could be recovered from printing and tissue papers after 3 hours, but on wood or cloth, the period until no detection was longer, at 2 days of incubation. The authors also note that SARS-CoV-2 is more stable on smooth surfaces. When samples were incubated on glass, paper money, and the inner layer of surgical masks, the infectious virus could be recovered by Day 2 but not by Day 4, and when incubated on stainless steel and plastic, the infectious virus was detectable by Day 4 but not by Day 7. Finally, when left on the outer layer of a surgical mask, infectious virus could still be recovered at 7 days of incubation.

Based on the results of five studies that found evidence for SARS-CoV-2 transmission through bioaerosols in hospitals, Harvey Fineberg, the Chair of the Standing Committee on Emerging Infectious Diseases and 21st Century Health Threats, published a letter on April 1, 2020 to the National Academy of Sciences, Engineering, and Medicine detailing the possibility that the virus could also be spread through an infected individuals’ exhalation. Since the virus can remain in air up to 3 hours, this raises the possibility of increased transmission in indoor spaces through a shared air supply. In contrast, outdoor transmission through bioaerosols is less likely, as bioaerosols will disperse more readily in open air.

In an effort to quantify viral concentration on possible hospital room fomites and in the air, Santarpia et al. (2020) conducted a study of the University of Nebraska hospital rooms of 13 COVID-19 patients in isolation. Room surfaces and the patient’s personal items were first tested by RT-PCR for detectable presence of SARS-CoV-2. Of the 163 samples tested, 126 tested positive for the virus. Of the personal items collected (which included cell phones, iPads, laptops, reading glasses, exercise and medical equipment), 81.3% tested positive, with a mean concentration of 0.217 copies/µL of recovered liquid sample. 83.3% of cell phone samples were positive for the virus with a mean concentration of 0.172 copies/µL. 64.7% of remote controls were positive with a mean concentration of 0.230 copies/µL. 81% of toilet samples were positive with a mean concentration of 0.252 copies/µL. All floor samples beneath patient beds tested positive for the virus, with a mean concentration of 0.447 copies/µL. The sample with the highest concentration of virus at 1.75 copies/µL was taken from the air handling grate in the hospital biocontainment unit, where only patients with severe COVID-19 were kept (mild cases were kept in the quarantine unit). Of the five biocontainment unit air grate samples, 80% tested positive with a mean concentration of 0.819 copies/µL. Air samples were also tested for SARS-CoV-2. 63.2% of in-room air samples tested positive with a mean concentration 2.86 copies/L of air. 66.7% of air samples taken from hallways outside the hospital rooms tested positive with a mean concentration of 2.59 copies/L of air. The air sample with the highest concentration of virus (at 19.17 and 48.21 copies/L of air) came from the biocontainment unit when a patient was receiving oxygen through a nasal cannula. It should be noted that while air samples were being collected from rooms, patients were never observed to cough. These data suggest the widespread presence of viral RNA on surfaces and in air samples of patient rooms, demonstrating the possibility for transmission through bioaerosols and fomites.

### Asymptomatic Cases and Transmission

One study conducted with the entire Italian city of Vò (~3,300 individuals) indicates that approximately 42.5% of COVID-19 infected individuals were entirely asymptomatic (Lavezzo et al., 2020). As of July, 2020, it still remains unclear what percentage of asymptomatic carriers of SARS-CoV-2 are contagious.

Long et al. (2020) conducted an assessment of 37 asymptomatic individuals who were confirmed to have SARS-CoV-2 infections and compared them to a larger cohort of symptomatic COVID-19 patients. The asymptomatic group had a significantly longer period of viral shedding with a median duration of 19 days (IQR of 15-26 days), compared to a median duration of 14 days in patients experiencing mild symptoms. While the period of viral shedding was longer in asymptomatic individuals, the authors note the finding should not be interpreted to suggest these patients were any more contagious, as many other factors may contribute to communicability.

Some limited evidence for fomite/airborne transmission from an asymptomatic carrier does exist, however. Liu, J., et al. (2020) describe a cluster of 71 COVID-19 cases that developed in Heilongjiang Province, China, attributed to one asymptomatic carrier (confirmed by IgG antibody test on April 10, 2020). The carrier had returned from international travel in the U.S. on March 19, 2020, a full 8 days after the last known COVID-19 diagnosis in the province, and quarantined at home for two weeks, then tested negative by RT-PCR and antibody tests on March 31 and April 4, 2020, respectively. On April 9, 2020, four new cases since March 11, 2020 were identified, which were contact-traced to a neighbor of the asymptomatic carrier. It is believed that the carrier transmitted the virus to the neighbor through fomite and/or airborne transmission in a common elevator, as the two parties had no other form of contact. All other individuals in the cluster were also traced to the same neighbor.

## Pathophysiology

In late 2019, during its early emergence in Wuhan, China, COVID-19 was observed as an unexplained outbreak of acute respiratory disease tied to increased rates of pneumonia in the region. The subsequent classification of the disease as a coronavirus closely related to SARS-CoV-1, which also uses the ACE2 receptor for cellular entry, drove further research into the systems most likely to be targeted by the virus. While ACE2 receptors are abundant in many organ systems, the predominance of respiratory symptoms in severely affected patients drove many early studies to focus on the SARS-CoV-2’s disruption of the respiratory system, in particular a chain of events affecting this system that could lead to Acute Respiratory Distress Syndrome (ARDS) and in some cases, septic shock and death. However, autopsy reports revealed that other systems were often implicated in the progression of the disease. The widespread prevalence of blood clotting, strokes, neurological symptoms as well as damage to other organs such as the heart and kidneys came to be known as hallmarks of the disease’s progression in some of the most severe and long-lasting cases.

An understanding of the mechanisms underlying how COVID-19 contributes to respiratory distress, coagulopathy, and the disruption of other organ systems is essential for the effective treatment of affected patients both acutely, chronically, and in recovery. Moreover, the severity and presence of COVID-19 symptoms varies widely between individuals. To effectively treat a newly diagnosed patient, it is thus crucial to identify what pre-existing risk factors, whether genetic or otherwise, may drive these differences. In this way, patients can be treated both preemptively and safely, maximizing their chance of survival and minimizing their chance of long-term deleterious effects. Furthermore, genetic variations in the virus itself may cause different pathophysiology, and such variants are only growing in number as the virus continues to mutate and evolve. The growing complexity in the multivariate system that determines the exact disease course in an affected patient underscores the need for precise, personalized treatments that address a patient’s unique risk factors directly.

### Pulmonary Pathophysiology

Severe cases of COVID-19 infection are characterized by various mechanisms, the first of which is pulmonary damage from the virus itself. As the viral RNA replicates and assembles its structural protein, which occurs predominantly in the alveolar cells of the lower respiratory tract, the newly emerging viral particles lyse the host cells. Cumulative damage can lead to structural damage in the alveolar cells of the lungs. The primary alveolar cells affected are pneumocytes I and II. These cells line the pulmonary alveoli, small sacs where gas exchange takes place in the lungs, specifically where blood becomes oxygenated.

However, the primary mechanism driving severe COVID-19 disease originates from an overactive inflammatory response to the infection itself. Mononuclear leukocytes are the early initiators of the inflammatory response in the lungs. The infiltration of these white blood cells to the site of infection results in the earliest stage of the inflammatory response: a release of cytokines, such as interleukin-1 and interleukin-6. The cytokines stimulate nearby blood capillaries to vasodilate and become more permeable to fluids passing through them, including blood plasma, which can move into the interstitial space between the blood vessels and alveoli. This fluid will increase pressure on the alveolar cells, potentially leading to their collapse. Cytokines released by the immune cells also trigger more immune cells, including neutrophils and T-cells, to infiltrate the alveolus, initiating a cascading inflammatory effect, known as a “cytokine storm”. Recruited neutrophils then release reactive oxygen species and proteases that are intended to eliminate the virus but also damage nearby alveolar cells. As these cells undergo apoptosis (cell death), they generate debris in the alveolus, preventing gas exchange from occurring. Blood oxygenation then decreases, resulting in hypoxemia (low oxygen in blood). This chain of events is the mechanism behind acute respiratory distress syndrome (ARDS), which is the leading driver of mortality in COVID-19 infection. ARDS is also often characterized by partial collapse of the lung. In some severe cases, the inflammation from the lungs may carry over into the bloodstream, leading to systemic inflammatory response syndrome (SIRS). SIRS can potentially progress into acute organ injury, septic shock, and multi-system organ failure.

Figure 2.19: Colorized SEM of apoptotic human cell infected with SARS-CoV-2 (Adapted from NIAID)

### Vascular Pathophysiology and Coagulopathy

Blood clots and large-vessel strokes are complications that may also be tied to COVID-19. From March 23, 2020 to April 7, 2020, Oxley et al. report that five patients under the age of 50 were treated at Mt. Sinai Hospital for large-vessel ischemic stroke. All tested positive for SARS-CoV-2. The five patients represented a considerable jump from the average 0.73 patients under 50 treated for large-vessel stroke for any two week period in the previous twelve months at the same hospital. Li et al. (2020) report in a retrospective study of 221 COVID-19 patients treated in Wuhan, China that 5% of the patients developed acute ischemic stroke. For those patients exhibiting signs of cerebrovascular disease, levels of D-dimer were also significantly elevated, at 6.9 mg/L versus 0.5 mg/L for patients without these symptoms (ibid.). C-reactive protein was also significantly elevated for this group. D-dimers are a fibrin degradation product and are indicative of the presence of blood clots.

Wichmann et al. (2020) report an increased risk of deep vein thrombosis in severe COVID-19 infections, as revealed from the first 12 consecutive autopsies of patients performed at a university hospital in Germany, where autopsies were mandated for patients testing positive for SARS-CoV-2 by RT-PCR. Deep vein thrombosis was confirmed in the autopsies of 58% (7/12) patients, all of whom were not suspected to have this condition before death. For these patients, DVT was found in both legs. In six of nine of the men studied, thrombosis was also found in the prostatic venous plexus. Furthermore, the authors report that pulmonary embolism was the direct cause of death in 4 of the 12 cases.

While discussing a case study of a 72-year-old patient with COVID-19, Escher et al. (2020) suggest a potential mechanism for the increased risk of coagulopathy that has been observed in these critically ill patients. Six days after the patient initially had been admitted into the hospital, he had developed ARDS, acute renal insufficiency, and mental confusion and was transferred to the ICU where he was observed for 29 days. Levels of D-dimers steadily increased over this time, beginning at 0.69 mg/L (relatively normal) and peaking at 20.63 mg/L on Day 21. On the same day, the patient was found to have elevated von Willebrand Factor (VWF), at 520% the level of what would be considered normal. VWF is released from the sub-endothelial layer below the lumen of blood vessels when the endothelial layer is damaged, and it is also indicative of thrombosis. At these high levels, the VWF measurement was suggestive of massive endothelial damage.

Escher et al. (2020) note that the endothelial cells that line the blood vessels express the ACE2 receptor, which is the cellular entrypoint of SARS-CoV-2. Aside from the potential damage to the endothelial cells that could be caused from the virus reproducing and lysing these cells, if SARS-CoV-2 is bound to ACE2, ACE2 can no longer catalyze the conversion of angiotensin-II into angiotensin-1,7 (see ACE2 Receptor), which leads to vasodilation, increased blood pressure, and increased vascular permeability. Moreover, the increased levels of angiotensin-II can stimulate catalytic activity of NADPH oxidase, an enzyme that catalyzes the conversion of oxygen into superoxide radical, a reactive oxygen species (ROS) that can build up in endothelial cells. Build-up of ROS can lead to intracellular oxidative stress, which can cause cell death. In mice, ACE2 has been shown to attenuate the oxidative stress caused by increased NADPH oxidase activity induced by elevated angiotensin-II levels, as well as atherosclerosis (Lovren et al., 2008). Thus, the decreased availability of ACE2 catalytic sites due to SARS-CoV-2 infection may be mediating the damage to the endothelial cells, leading to a cascade of events that result in increased blood clot formation and potentially stroke. Furthermore, for patients with dysfunctional super oxidase dismutase (SOD) or other enzymes that catalyze the conversion of ROS into non-reactive oxygen species, such as oxygen or water, risk of oxidative stress may be especially heightened during SARS-CoV-2 infection. This may explain why COVID-19 patients with diabetes and cardiovascular disease have heightened risk for worse clinical outcomes. In a 2014 retrospective report, Umapathi T. et al. note a similar incidence of ischemic stroke (roughly 5%) in patients diagnosed with SARS-CoV-1 infection. Risk of deep vein thrombosis and pulmonary embolism was similarly elevated for patients critically ill with SARS-02. Given that SARS-CoV-1 also gains cellular entry through the ACE2 receptor, a similar mechanism leading to elevated risk of cerebrovascular disease may be at work with SARS-CoV-2.

### Central Nervous System Involvement

There are studies in the emerging COVID-19 literature that suggest some advanced cases in the infected Chinese population exhibited potential spread to the nervous system (Li et al., 2020). There is also evidence that with some at-risk individuals viruses, toxins, and other pathogens can be transported from peripheral infection sites (e.g. lungs) to the brainstem causing neurological symptoms. Infection with SARS-CoV-1 has been reported to be associated with similar neurological pathologies. Additionally, ACE2 expression has been observed within some autonomic regions of the brain, consistent with the possibility of SARS-CoV-2 infection in this locale, possibly explaining the breathing pathology of some patients.

Since aerosol transmission via nasal and oral droplets is a primary contributor to infection, and the nasal cavity cells that are targets for the virus are under investigation, a recent study looking at the involvement of immune cells in the nasal transmission of SARS-CoV-2 has shown that T cells interacting with the brain’s innate immune cells, microglia, protect the brain from viral transmission via the nasal route to the brain (Moseman et al., Science Immunol, 2020). However, the investigators point out that one’s genomics may generate risk for mutations that do not always lead to this kind of protection. In addition, the virus’s ability to infect a variety of cells adds to the risk for systemic disease in some involving any target of the olfactory, respiratory, and GI system. Transmission to the brain through the olfactory nerve may be possible. While the pathway has not been definitively shown for SARS-CoV-2, it was demonstrated in an animal model using transgenic mice infected with SARS-CoV-1 (McCray et al. 2007). The transgenic mice expressed human ACE2 receptors, and after infection with the SARS-CoV-1 virus, researchers observed that the infection had spread to the olfactory bulb, which later progressed into the subcortical and cortical regions of the brain. McCray et al. suggest that spread to the brainstem, which is not connected to the olfactory bulb, may occur via specific neurotransmitter pathways or by other means. Neurons express the ACE2 receptor, suggesting that such a pathway may be possible. Moreover, one of the most common neurological symptoms of COVID-19 is anosmia, the loss of smell, suggesting that the involvement of the olfactory bulb as a route of infection of the central nervous system may also be at play as it is in SARS-CoV-1.

Song et al. (2020) successfully demonstrated that SARS-CoV-2 can replicate in two-week old human neural progenitor cells (hNPCs) propagated in cell culture, and this replication is accompanied by an increase in hNPC cell death. To test the potential of SARS-CoV-2 to infect the central nervous system (CNS), the research team created human-induced pluripotent stem-cell-derived brain organoids, as a means of studying a 3-dimensional model of SARS-CoV-2 infection in neurons. They observed infection in nine-week old organoids within 24 hours of infection, and organoid infection was associated with elevated rates of neuronal death. The researchers also studied the effect the virus had on the enrichment of various cellular mechanisms in the cell post-infection. The authors observed that SARS-CoV-2 upregulated pathways related to cell division, organelle division, and various metabolic processes, which included electron transport coupled proton transport, such as electron transfer from cytochrome c to oxygen, and electron transfer from NADH to ubiquinone. This hypermetabolic state may contribute to the ability of the virus to efficiently replicate. The authors also noted the presence of a locally hypoxic environment in regions with close proximity to SARS-CoV-2 infected cells.

Song et al. (2020) were able to inhibit SARS-CoV-2 infection by incubating the organoids with anti-ACE2 blocking monoclonal antibodies before cells received exposure to the virus, demonstrating that ACE2 is a requirement for infection in brain organoids. The team also tested if cerebrospinal fluid isolated from a COVID-19 patient with acute encephalopathy could successfully neutralize the virus in the organoids, as the fluid had detectable levels of IgG antibodies specific to the spike protein. The fluid successfully blocked infection in the organoids; the result pointed to the ability of the CNS to be infected and develop a robust antibody response following infection. Perhaps the most striking result of the study was an in vivo demonstration of SARS-CoV-2 infection in murine neurons overexpressing human ACE2. Using this mouse model, the authors successfully demonstrated that the neuroinvasion by the virus was associated with elevated mortality in the animals.

Concerning CNS involvement in COVID-19, Korainik and Tyler, 2020 (in press) point out that there are post-infection necrotic encephalopathies, vascular changes that can contribute to stroke, and a variety of other neurological disorders that constitute a global health crisis, according to the authors. Furthermore, it is possible that viral infection of the GI tract could contribute to spread to the brainstem, as has been proposed for flu and coronaviruses. Not only could the virus be directly transmitted to the brain, but it may also spread through the CNS by hijacking the connectome, a pathway exploited by a variety of pathogens. These issues have been discussed (Candelario and Steindler, 2014; Candelario et al., 2020) with regard to the role of microvesicle and exosome transmission of viruses and other pathogens. Both mechanisms can preempt the need for direct viral transmission/transport to the CNS; instead the pathogen reaches the brain by concentrating inside exosomes and other microvesicles, from which it is released. Once released, the virus can spread its infectious contents via extracellular and cell-to-cell spread. Knowing these cell and molecular bases for route of entry and system-to-system transmission will help future researchers better design precision therapies that can target particular virus-cell, cell-cell and multisystem interactions. A recent prospective study of patients hospitalized for COVID-19 in New York (Frontera et, Neurology, 2020) found that 13.5% exhibited neurological disorders that appeared to be associated with severity of illness, e.g. hypoxia and vascular and blood abnormalities, rather than direct viral effects on the CNS. This was a prospective, multicenter observational study that demands larger studies in the future in order to confirm this observation. With a history and literature on influenza (e.g. the H5N1 1918 flu) and other viruses (e.g. Zika) showing neurotropism in still to be determined ways, the heterogeneous phenotype of COVID-19, across all age groups as the number of worldwide infections rise, warrant additional studies to determine the precise omically-driven risks for acute and latent CNS risks from SARS-CoV-2 infection.

### Cardiovascular Pathophysiology

As many as 1 in 5 COVID-19 patients may experience cardiac injury during their hospital stay (Shi, S. et al., 2020). Many COVID-19 patients have experienced heart failure and cardiac arrest without any sign of severe respiratory symptoms. Factors that may be contributing to increased heart failure may be tied to the inflammation characteristic of moderate to critical COVID-19. The increased systemic inflammation can contribute to the movement of already existing arterial plaques, which can lead to cardiac arrest. Furthermore, systemic inflammation can cause inflammation of the myocardium itself, which can deleteriously impact heart function. It is also possible that the virus can directly infect the heart muscle, since ACE2 receptors are also abundant in the cell membranes present in this tissue. If so, the virus may be contributing to enhanced apoptosis in the heart muscle directly, much as it does to alveolar pneumocytes.

Puntmann et al. (2020) conducted a study on 100 recently recovered COVID-19 adult patients from the University Hospital Frankfurt between April and June 2020 to determine the frequency of cardiac involvement in patients who had recovered from the disease. Subjects underwent cardiac magnetic resonance to assess and determine these effects. The authors report that independent of previous conditions and severity of COVID-19 infection, 78% of subjects showed signs of cardiac involvement and 60% showed ongoing myocardial inflammation.

## Immunity and Reinfection

Antibody response to viruses is highly variable over time and is also affected by a variety of factors, such as the severity of the initial infection. Understanding how concentrations of blood-circulating SARS-CoV-2 reactive antibodies vary over time is particularly important for describing the potential for COVID-19 immunity that may be conferred onto recovered patients. If antibody response is not sufficient, reinfection may be possible, whereas a strong antibody response that lasts for an extended period of time may provide longer-term protection against the virus. Moreover, understanding the SARS-CoV-2 epitope can provide greater insight into vaccine development and design; in particular, more highly conserved regions of the epitope may be useful to target in such efforts as a means of conferring some immunity to future emergent coronaviruses. Understanding the adaptive immune response is also highly relevant, as prior infections with endemic coronaviruses may offer some protection against severe SARS-CoV-2 infection. Le Bert and collaborators (Nature, 2020) have shown that some uninfected individuals possess memory T cells with the potential to recognize SARS-CoV-2. This is suggested to arise from recognition of protein fragments from previous exposures to common cold viruses. One area of intensive investigation is understanding the cell and molecular contributions to initial and long term immunity; should not be in introduction to this section.... needs to be moved and elaborated ontoward that cause, we are beginning to better understand distinctive myeloid signatures as described by Mann et al.. (2020) who showed, “...shifts in neutrophil to T cell ratio, elevated serum IL-6, MCP-1 and IP-10, and most strikingly, modulation of CD14+ monocyte phenotype and function..”

### SARS-CoV-2 Epitope

Characterizing the protein structure of the SARS-CoV-2 epitope, the region of the virus that binds to an antibody, may provide further insight into the development of an effective vaccine. Of particular interest are vulnerable regions that neutralizing antibodies, antibodies that can deactivate the pathogenicity of the virus, can target. Because the receptor binding domain (RBD), located on the S1 domain of the spike glycoprotein, binds strongly to the ACE2 receptor, the host cellular entrypoint of the virion, the RBD and neighboring regions serve as promising targets for neutralizing antibodies. Meanwhile, the fusion peptide, located on the S2 domain of the spike glycoprotein, near the N-terminus, is another promising target, since its exposure is necessary for fusion to the host cell membrane to occur. For this reason, epitopes of the spike glycoprotein, where the RBD and fusion peptide are both located, have been studied intensively. Nevertheless, the spike protein may not be the most ideal target for vaccine design since the protein is not as well conserved as other protein components of the virion, such as the nucleocapsid protein (N protein). Moreover, the N protein is also highly immunogenic, and so the identification of its epitopes warrants further study.

CR3022 is a human monoclonal antibody that is specific to the receptor binding domain of SARS-CoV-1. In February 2020, Tian et al. published results showing CR3022 was able to bind with high affinity to a portion of the SARS-CoV2 RBD outside of the ACE2 binding region of the RBD. Yuan et al. (2020) determined the crystal structure of the SARS-CoV-2 RBD in complex with the CR3022 antibody and found that the SARS-CoV-2 epitope (the region of the RBD that was buried by CR3022) consisted of 28 amino acids, and most intermolecular attraction resulted from hydrophobic interactions between the epitope and antibody. Furthermore, 24 residues of this 28 amino acid sequence were shared between SARS-CoV-1 and SARS-CoV-2. This structural similarity likely accounts for the ability of the antibody to bind to the SARS-CoV-2 RBD, although it does so with significantly less affinity than it does to SARS-CoV-1 RBD (Contrast the dissociation constant with SARS-CoV-2, which was 115 nM, to the lower constant with SARS-CoV-1, which was 1 nM).

In March 2020, Zheng, M. and Song, L. published results concerning the Spike protein epitopes of MERS-CoV, SARS-CoV-1, and SARS-CoV-2. The authors note that the three proteins had differing degrees of antigenicity, with MERS-CoV spike protein showing the greatest ability to elicit antibody response, followed by the SARS-CoV-2 spike protein, which was then followed by the SARS-CoV-1 spike protein. While 75.5% of the amino acid sequence of SARS-CoV-2 spike protein is conserved with SARS-CoV-1, the vast majority of the sites on the SARS-CoV-2 spike protein that produced the greatest antigenic response were in the non-conserved regions. More specifically, the non-conserved epitopes made up 85.3% of all SARS-CoV-2 spike epitopes and 85.7% of RBD epitopes.

Poh et al. (2020) identified two distinct peptides sequences of the spike glycoprotein that were recognized by IgG antibodies in convalescent COVID-19 blood sera. Using blood sera collected from six convalescent COVID-19 patients and five recovered SARS-02 patients, the group tested the immunogenicity of various peptide sequences from the SARS-CoV-2 and SARS-CoV-1 spike proteins in both groups. Two peptide sequences, one in close proximity to the SARS-CoV-2 RBD and another that overlapped with the fusion peptide sequence, were associated with a strong IgG response in the blood sera of COVID-19 patients but not of SARS-02 patients. Furthermore, the group confirmed that sera depleted of antibodies targeting these two regions had a significantly reduced ability to neutralize SARS-CoV-2 pseudovirus infection, suggesting that antibodies targeting these two epitopes are responsible for the majority of the anti-spike-neutralizing response. In particular, two of the COVID-19 patients’ blood sera contained antibodies that responded to a SARS-CoV-1 peptide that contains the SARS-CoV-1 fusion peptide, a region more conserved among coronaviruses. The finding suggests that this epitope containing the fusion peptide may function as a broader antibody target for various coronaviruses.

A July, 2020 publication in Nature reported on the isolation of 19 potently SARS-CoV-2 neutralizing monoclonal antibodies from 5 patients affected with severe COVID-19 (Liu, L., et al.). Of these 19, nine were able to effectively inhibit 50% of the virus in vitro at very low concentrations, between 0.7 and 9 ng/mL. The epitopes of the 19 neutralizing antibodies were then studied. About half of the antibodies targeted the RBD of the spike protein, and the other half targeted the N-terminal domain. Using cryo-electron microscopy, the researchers also found that two of the antibodies had quaternary epitopes found at the site of the three RBDs of the spike trimer, specifically when all the RBDs were in the “down” conformation. These antibodies likely neutralized the virus by locking the RBDs of the spike trimer in the inactive down confirmation, rendering the virion unable to effectively bind to the ACE2 receptor.

### The Kinetics of SARS-CoV-2 Specific Antibodies and Memory Immune Cells

SARS-CoV-2 neutralizing antibodies show some binding affinity to the S1 Protein of SARS-CoV-1, which is enhanced when binding to the S1, RBD, and S2 regions of the SARS-CoV-2 protein (Wu, F. et al., 2020). While there is limited binding to SARS-CoV-1 proteins, the SARS-CoV-2 antibodies cannot inhibit SARS-CoV-1 infection and have only been confirmed to inhibit SARS-CoV-2 infection. A group of 175 COVID-19 patients with mild disease were tested for the presence of SARS-CoV-2 antibodies throughout their stay at the Shanghai Public Health Clinical Center. Wu, F. et al. report that all patients showed low levels of SARS-CoV-2 neutralizing antibodies before Day 10 of infection. Between Days 10 and 15, antibody levels steadily rose until they leveled off around Day 15. After discharge from the clinic, patients received follow-up antibody tests and antibody levels did not significantly differ from levels at the time of discharge. Titers of neutralizing antibodies were most strongly correlated with S2 and RBD levels. Researchers also observed that SARS-CoV-2 neutralizing antibodies concentrations varied significantly between patients. In 30% of the patients studied, levels of antibody titer were below the detection limit, demonstrating that a significant proportion of recovered patients may not develop high levels of antibodies. Furthermore, middle-aged and older patients (aged 40-59 and 60-85 years, respectively) showed significantly higher levels of SARS-CoV-2 specific antibodies than younger patients (aged 15-39 years). SARS-CoV-2 neutralizing antibodies titers were also negatively correlated with blood lymphocyte count and positively correlated with C-reactive protein levels.

Figure 2.20: Antibody Titer Kinetics as a function of COVID-19 Severity (Adapted from Okba et al., 2020)

Okba et al. (2020) developed serological assays for detecting antibodies specific to a variety of SARS-CoV-2 proteins and protein domains. Figure 2.20 illustrates the antibody titers detected in serum collected from two patients with mild COVID-19 (green and black) and from one patient with severe COVID-19 (red) on different days after the onset of symptoms. Detectable antibody titer levels are indicated by the horizontal dotted line. Antibody response was tracked for spike protein (A), the S1 subunit of the spike protein (B), the N-terminal domain of S1 (C), the receptor binding domain (D), the SARS-CoV-1 N protein (E), and the presence of SARS-CoV-2 neutralizing antibodies was tracked over time (F) as well. Detectable levels of antibodies specific to the spike protein, the S1 domain of the spike protein, the receptor binding domain, and the SARS-CoV-1 N protein, which is 90% similar to the SARS-CoV-2 N protein, were found in all patients by day 21 after symptom onset. All three patients also developed SARS-CoV-2 neutralizing antibodies.

A review of over 1,281 scientific articles concerning antibody mediated immune response to coronaviruses revealed numerous key findings concerning the kinetics of antibody protection and the correlation between severity of disease and antibody production for coronaviruses that affect humans. The median time to detection of antibodies was 12 days for SARS-CoV-1, 11 days for SARS-CoV-2, and 16 days for MERS-CoV (Huang, A. et al., 2020). IgG antibodies were found to decline over time and were typically detectable for at least one year but up to three years after initial infection. Furthermore, increased symptom severity was associated with a longer duration of detectable antibodies. Humans could be re-infected with a human coronavirus one year after onset of symptoms, but generally the severity of the symptoms were significantly reduced (ibid.). Also, SARS-CoV-1 and MERS-CoV have demonstrated the ability to induce an antibody response from antibodies produced after prior endemic human coronavirus infections, such as HCoV-229E. Human coronavirus seroprevalence rises sharply during childhood and remains steady throughout adulthood.

Long et al. (2020) tracked 285 hospitalized COVID-19 patients and tested them for the presence of IgG and IgM antibodies on different days after the onset of symptoms. The researchers report that 100% of tested patients had detectable IgG antibodies specific to SARS-CoV-2 at around 17-19 days after symptom onset, and this number remained steady the following week of testing (Figure 2.21). The percentage of patients testing positive for IgM antibodies reached a maximum of 94.4% at 20-22 days after symptom onset. This percentage began to slowly decline after Week 3, while the percentage of patients testing positive for IgG antibodies after Week 3 remained steady. The median time after initiation of symptoms to detection of IgG and IgM antibodies in all patients was 13 days. As found in previous studies, IgM and IgG titers were higher in patients with more severe disease, but the differences were not statistically significant except for the IgG titers in patients after two weeks of symptom onset. For 26 patients tested every three days, Long et al. report that IgG titers leveled off for an average of 6 days after the first positive measurement. For these 26 patients, nine first tested positive for both antibodies on the same day, seven patients tested positive for IgM antibodies first and ten patients tested positive for IgG antibodies first.

Long et al. (2020), a team composed of many of the same researchers that conducted the previous study, conducted a clinical and immunological assessment of 37 asymptomatic individuals who were confirmed to have SARS-CoV-2 infections by RT-PCR. The asymptomatic group, which comprised roughly 20% of the patients assessed in the study, was compared to a larger group of 141 symptomatic COVID-19 patients. The asymptomatic group had a significantly longer period of viral shedding with a median duration of 19 days (IQR of 15-26 days), compared to a median duration of 14 days in patients experiencing mild symptoms. While the period of viral shedding was longer in asymptomatic individuals, the authors note the finding should not be interpreted to suggest these patients were any more contagious, as contagiousness is associated with various other contributing factors. Despite asymptomatic participants experiencing no characteristic symptoms, abnormal radiological findings specific to one lung were still found in two-thirds of all asymptomatic individuals, while one-third of the group showed abnormalities in both lungs. Symptomatic individuals showed higher overall levels of 18 pro- and anti-inflammatory cytokines, demonstrating that a reduced inflammatory response was associated with asymptomatic disease progression.

Immunological testing revealed further distinguishing characteristics between the two groups but also a common trend of a steady decline in antibody titers in the early months of recovery. In the early acute phases of disease progression, IgG levels in the symptomatic group were significantly higher, although rates of their detection were roughly similar between the two groups. However, rates of IgM detection were approximately 10% lower in asymptomatic patients tested 3-4 weeks after exposure. Patients in both groups were tested for antibody levels in the early convalescent phase, defined as 8 weeks after hospital discharge. While the symptomatic group continued to show significantly higher levels of IgG levels at this stage, both symptomatic and asymptomatic patients experienced a substantial decline in detectable IgG levels. The median percentage of IgG decline was 71.1% for the asymptomatic group and 76.2% in the symptomatic group. For neutralizing serum antibody levels, a decline in levels was detected in 81.1% of all asymptomatic patients tested and in 62.2% of the symptomatic individuals tested. For the asymptomatic patients showing a decline in levels, the median percentage decrease was 8.3%, compared to 11.3% for the corresponding group of symptomatic patients. Moreover, in this early convalescent stage, 40% of asymptomatic individuals became completely seronegative for IgG, as did 12.9% of symptomatic individuals tested. The result is striking, as previous studies have revealed that sustained IgG levels are maintained for at least one year after SARS-CoV-1 infection and may last well over two years for many individuals. The study of SARS-CoV-2 antibody prevalence during convalescence should continue to be prioritized, as these results have urgent consequences that affect potential reinfection rates.

Figure 2.21: IgM and IgG Prevalence in COVID-19 Patients as a function of Days from Symptom Onset (Adapted from Long et al., 2020)

Seow et al. (2020) corroborated these results, demonstrating both a positive correlation between neutralizing antibody response and disease severity and a steady decline in antibody titers that begins after a peak in serum antibody titers is reached, estimated at around 5 weeks after the onset of symptoms. A total of 65 individuals with COVID-19, including 59 hospitalized patients and 6 healthcare workers, were tested for antibody response at specific times over the course of 94 days following the onset of symptoms. Figure 2.22 illustrates how disease severity (higher severity score is associated with a more severe clinical course) is a determinant of serum-neutralizing antibody concentrations in the initial days following the onset of symptoms, where higher disease severity is associated with elevated antibody response. However, regardless of disease severity, declines in antibody response were detected in patients tested after 40 days from the onset of symptoms. Moreover, some patients with low severity scores reached undetectable levels of neutralizing antibodies during the latter portion of the study. Similar results were observed in the participants’ blood sera for IgM, IgA, and IgG antibodies specific to the SARS-CoV-2 spike protein, nucleocapsid protein, and receptor binding domain.

Figure 2.22: Neutralizing Antibody Levels vs. Time after Onset of Symptoms (Adapted from Seow et al., 2020)

With in silico studies, machine learning, and a focus on the potential rapid repurposing of existing drugs to treat as well as prevent COVID-19, some new insights have been gained on a most important systems biological understanding of distinct immunity (e.g. Low plasma levels of IFN-alpha during infection) and other elements of disease severity (Arunachalam et al., 2020). Initial studies of antibody kinetics of the mildly symptomatic and whether modest antibody response can affect protection against future infections have commenced (Rijkers et al., 2020). One study comparing antibody response in serum (439) and saliva (128 patients) from convalescent patients 3-115 days post-symptom onset (Isho B et al. Science Immunol, 2020). Even though this is a relatively small patient study, the investigators found the presence of IgG responses up to three months. Thus, IgG responses may serve as a good surrogate measure of systemic immunity to SARS-CoV-2, supporting a notion from other studies of antibody persistence and decay (Iyer, A. S. et al., Science Immun, 2020) where circulating RBD antibodies showed to be good biomarkers of previous and recent infection for, again, at least up to three months.

Crotty et al. (2020) analyzed longer-term kinetics of SARS-CoV-2 immunity in 185 COVID-19 patients between the ages of 19 and 81 from the United States. They represented a wide range of disease severity and were recruited from multiple sites in the U.S. Only 7% of the patients had been hospitalized, and 97% of the patients experienced a symptomatic version of the disease. Of these 185 subjects, 147 provided a single blood sample between 6 and 240 days post-symptom onset, of which 41 provided blood samples after 6 months post-symptoms onset. The remaining 38 subjects provided samples over a duration of several months. The researchers found that spike IgG antibodies were stable over 6+ months, with an estimated half life of 140 days post-symptom onset and a 95% confidence interval of 89-329 days. Spike IgG titers were heterogeneous among subjects, with a wide range and a median of 575, a finding that corroborated results of previous studies. The best fit curve for decay of antibody tiers was a linear decay model, which the authors attributed possibly to the titer heterogeneity among subjects. The nucleocapsid IgG antibody titers had a half life of approximately 67 days, with a 95% confidence interval of 49-105 days. Furthermore, 98% of subjects were seropositive for IgG spike at 1 month post-symptom onset and 90% remained seropositive between 6-8 months post-symptom onset. The estimated half life for RBD specific IgG antibodies was 83 days, with a 95% confidence interval of 68-123 days. 90% of subjects were seropositive for SARS-CoV-2 neutralizing antibodies 6-8 months post-symptom onset.

In addition to measuring the kinetics of IgG antibody decay in COVID-19 patients, Crotty et al. analyzed the levels of spike-specific memory B cells, as well as SARS-CoV-2 CD4+ T helper cells and CD8+ T killer cells over time. SARS-CoV-2 specific memory B cells increased over the first 150 days post-symptoms onset and then flattened. RBD-specific B memory cells were present as early as 16 days post-symptom onset and steadily increased over 4-5 months. Nucleocapsid-specific B cells exhibited a similar behavior. The researchers also identified SARS-CoV-2 CD8+ memory T cells in 155 subjects and found that these cells recognized spike protein, membrane protein, nucleocapsid protein, and ORF3a. 61% of participants had circulating levels of these cells within one month post-symptom onset. This level had dropped to 50% by 6 months post-symptom onset. The half-life of SARS-CoV-2 CD8+ cells was 166 days for the subjects in the study. The most common proteins recognized by SARS-CoV-2 CD4+ cells in the subjects were the spike protein, the membrane protein, the nucleocapsid protein, ORF3a, and nsp3. Approximately 35% of the subjects at one month post-symptom onset had greater than 1% SARS-CoV-2 specific CD4+ cells, showing a robust response early on. The levels of these cells steadily declined over 6 months, with a half life of 166 days post-symptoms onset. The percentage of subjects with SARS-CoV-2 specific CD4+ cells at 1 month post-symptom onset was 94%, which declined to 89% at 6 months post-symptom onset. Overall, these results show robust immune memory responses even at prolonged periods following infection.

### Reinfection

On February 14, 2020, Taiwan News reported that a doctor from Hubei Province, who wished to retain anonymity, claimed that it is possible for patients to become reinfected with SARS-CoV-2. The source claimed that various patients would recover and would then have a more precipitous decline upon reinfection because the medication they had been treated with had damaged heart tissue. The doctor also suggested that antibodies may have enhanced the severity of the second reinfection (implying that antibody-dependent enhancement may have been at work). As of March 20, 2020, there were no credible sources or peer-reviewed research showing that these reports were, in fact, true. It is important to note that the sensitivity of RT-PCR for detecting viral shedding of SARS-CoV-2 is fairly low, reportedly as low as 59% (Ai et al., 2020). Sensitivity is a measurement of the proportion of all people who have the disease that will test positive on a diagnostic test. Thus, with a test with 59% sensitivity, 41% of people who do have the virus will test negative (while only 59% will test accurately as positive). With a diagnostic test with such low sensitivity, it is not uncommon for infected individuals being tested to get strings of positives, negatives, followed by positives again. This may at least partially explain the so-called “reinfections” that were reported by this news source.

However, reinfection with a virus is actually possible during a very brief window after initial infection occurs, though it is rare. Antibody protection begins after exposure to an antigen, often shortly after recovery from illness spurred on by some pathogen. The initial antibody produced by the spleen is IgM (Immunoglobulin M), which is the largest antibody produced, limiting its abundance in blood serum. IgM is the first line of immunity for patients and is present in the lymph and blood. Guo et al. (2020) report that for 81 COVID-19 patients studied, the median duration of IgM detection was 5.1 days. IgM production begins to steadily decrease after the first weeks of its production, dropping to undetectable levels as soon as two months after initial infection. For this reason, immunoassays which detect IgM in serological tests indicate that the patient was recently exposed to an antigen, perhaps within the last few days or months. IgG is a much smaller antibody that is produced in plasma B-lymphocyte cells. It is the most abundant antibody in the lymph and bloodstream and is responsible for longer-term immunity. Guo et al. (2020) report in their study of 81 COVID-19 patients that the median time until detection of IgG antibodies was 14 days after initiation of symptoms, although there are no long-term immunity data yet available. For SARS-CoV-1 infection, IgG titers reach their maximum levels at 4 months after infection and taper off for as long as three years after infection. Because its production is delayed, it is possible that reinfection can occur when a patient is re-exposed to the virus during the brief window between the drop in IgM production and the initiation of IgG production.

On March 19, 2020, a research team led by Qin and Bao published results of a study, which has not yet been peer-reviewed, supporting that rhesus macaques were not able to become reinfected with SARS-CoV-2 after initial infection with the coronavirus. Researchers infected four rhesus macaques, an old world monkey that is close both genetically and physiologically to humans, with SARS-CoV-2. The animals showed symptoms that included weight loss and moderate interstitial pneumonia. The monkeys were tested for viral shedding by Reverse Transcription Polymerase Chain Reaction (RT-PCR). Samples were taken using nasal/pharyngeal swabs and anal swabs, and researchers found that the total viral load reached their highest levels in all four animals at three days post-infection. Also of note, viral replication was detected in the nose, pharynx, lung, gut, spinal cord, heart, skeletal muscle, and bladder. After 14, 21, and 28 days post-infection, the monkeys were tested for antibodies, and researchers found increasing production of antibodies during this period. At 28 days after infection, the animals were tested for viral load, and no detectable virus was found in any of the remaining animals (their chest X-rays were also normal by this point). On this day, the monkeys were reinfected with the same strain of the virus, and besides a very brief spike in temperature, none of the monkeys demonstrated the symptoms observed during primary infection. Five days after reinfection, the animals were tested for viral shedding using RT-PCR 96 times, and all results came back negative for the virus. One animal was sacrificed and further studied; no viral replication was observed in any tissue layer, and no pathological damage was found in the lung tissue. The data suggests that the animals developed immunity to this specific strain of the virus, which protected them from reinfection.

Chandrashekar et al. (2020) corroborated these results in a study performed on nine rhesus macaques that were inoculated with a range of titers of SARS-CoV-2. Viral RNA was detected in both bronchoalveolar lavage (BAL) and nasal swabs. In these animals, viral load peaked on Day 2 and was undetectable in BAL by Day 10-14 and in nasal swabs by Day 21-28. All animals developed an antibody response specific to the SARS-CoV-2 spike protein and all developed SARS-CoV-2 neutralizing antibodies. Thirty-five days after initial infection, the animals were inoculated again with the same dose of the virus that they had initially received. These animals showed a significantly reduced level (a 5-log10 reduction) in median viral titer in BAL and in nasal swab samples, suggesting that the animals had developed a robust antibody response that strongly inhibited secondary infection. Deng et al. (2020) have shown a similar primary exposure protection against reinfection in rhesus macaques.

On April 16, 2020, the Korean Centers for Disease Control and Prevention (KCDC) announced that 141 people who had previously tested positive, then been cleared of the virus, had tested positive again. By May 6, this number had grown to 350 suspected reinfections. At a press conference the following day, Oh (Myoung-Don), a South Korean infectious disease expert who leads the central committee for emerging disease control, said the RT-PCR tests were detecting ribonucleic acid of the inactivated virus. The nucleic acid, which is amplified by RT-PCR, can remain in the body for months after the active infection has subsided, and because RNA from the active or inactive forms of the virus are indistinguishable in an RT-PCR test, the reports of reinfection likely resulted from false positives. The KCDC published a press release on May 19, 2020 summarizing results stemming from the epidemiological contact investigation of a subset of 285 individuals from the 447 suspected cases of reinfection that had amassed by May 15, 2020. A total of 790 contacts of the 285 investigated individuals were contacted and monitored for a 14-day period, and none had reported a newly confirmed case from exposure during the potential re-infection period alone. Furthermore, neutralizing antibody protection was detected in all 285 suspected reinfections. Also of note was that 108 of the 285 individuals were tested for virus isolation in cell culture, and none of these laboratory results came back positive. This suggests that the original RT-PCR tests that detected a possible reinfection were instead detecting RNA from the inactivated virus, as Oh (Myoung-Don) had indicated over a week before.

It is still unknown whether the virus can be reactivated or if reinfection is possible by a secondary source. If the virus is indeed capable of reactivation, it is not known under what conditions (external and internal stimuli, humidity, temperature) this can occur. Furthermore, it remains to be understood whether the dormant or active form of SARS-CoV-2 can damage the human body over a given period of time.

### Pre-Existing Immunity

Grifoni et al. (2020) found evidence of T-cell reactivity with epitopes of SARS-CoV-2 in individuals with no previous exposure to SARS-CoV-2. The researchers collected 20 blood samples from donors between 2015 and 2018, over a year preceding the emergence of SARS-CoV-2. The group tested the reactivity of the samples’ CD4+ T cells with spike and non-spike specific epitopes and found that CD4+ T cell response was detectable in both cases for some of the samples. Moreover, in over 50% of the samples tested, a non-spike specific CD4+ T cells response was above the limit of detection. While the mechanism driving this response is largely unknown, the authors hypothesized that exposure to endemic respiratory “common cold” coronaviruses, such as HCoV-OC43, for example, may confer some adaptive T-cell immunity. However, it is important to note that concentrations of spike RBD specific IgM, IgG, and IgA antibodies in these samples were significantly lower than in recovered COVID-19 patients (p < 0.0001).

Mateus et al. (2020) identified a total of 142 T-cell SARS-CoV-2 epitopes, 66 of which were from the spike protein. The research team used blood samples collected from 18 donors between the years 2015 and 2018, well before SARS-CoV-2 was established as a zoonotic virus and worldwide pandemic; donors were still tested and confirmed to all be seronegative for SARS-CoV-2. The donors’ peripheral blood mononuclear cells (PBMCs) were tested for activity in the presence of a wide array of peptide sequences isolated from SARS-CoV-2. The researchers found that CD4+ T cells made up the vast majority of cells responding to SARS-CoV-2 peptide stimulation, representing 93.2% of such activity identified in the sampled PBMCs. In 4.5% of such cases, CD8+ T cells were identified as the active cell type, and in 2.3% of cases, both cell types were identified. Thus, the SARS-CoV-2 T-cell epitopes primarily stimulate CD4+ T cell response, a result established by previous studies. Moreover, each donor’s PBMCs recognized an average of 11.4 epitopes, and 40 of the 142 epitopes were recognized by more than two donors. After confirming that almost all 18 donors were seropositive for three widely circulating human coronaviruses (HCoV-NL63, HCoV-OC42, and HCoV-HKU1), the team further investigated the possibility for reactivity to SARS-CoV-2 in these unexposed individuals to be attributable to cross-reactivity for widely circulating endemic coronaviruses to which donors may have been exposed. Such epitope cross-reactivity was confirmed in 24% of the T-cell lines, with a stronger antigenic response to the other human coronavirus peptide sequences. The finding confirms that some adaptive T-cell immunity may be acquired from previous exposure to other endemic human coronaviruses.

There is a great deal of interest in the relationship of disease phenotype to age. Even though we do not have enough information to understand why children are reportedly less vulnerable to COVID-19 than adults, and especially older adults, it is possible that children’s immune systems may harbor cell and molecular agents that might help prevent infection as well as contribute to a milder form of disease (except for the case of Kawasaki-like disease described in to date a relatively small number of children). Because their innate and adaptive immune responses are more immature, they may contribute less to cytokine storms and other immune responses that may contribute to ARDS. Toward that end, Pierce et al. (2020) compared hospitalized adult and young patients with COVID-19 to determine any differences in immune system responses that may contribute to the differential in disease severity between the two groups. They found that circulating IL-17A and IFN-γ levels during the first week of hospitalization were more elevated in younger patients but that three weeks later, circulating CD4+ were substantially higher in older patients. Neutralizing antibody titers were positively correlated with age. These data support that adults have a robust adaptive immune response, and so poor clinical outcomes of adult patients are not likely tied to adaptive immunity.

## Herd Immunity

Herd immunity for a given population occurs when a large enough proportion of individuals in that population are no longer susceptible to an infectious disease, perhaps through vaccination or conferred immunity from a previous infection, thereby protecting the susceptible individuals within the population from infection. More precisely, herd immunity is reached when the proportion of non-susceptible individuals in a given population rises above the herd immunity threshold (HIT). At the HIT level, the effective reproduction number for an infectious disease, R, is equal to 1, meaning that one case of infection should generate on average only one secondary case within that population, a scenario known as the endemic steady state. As soon as the proportion of non-susceptible individuals rises above this level, R falls below 1, and the number of cases begins to decline.

In the simplest model, where it is assumed that everyone in a population mixes homogeneously and each individual is equally susceptible (when susceptible) and equally contagious (when contagious), and no control measure to contain the virus has been implemented, the value of R is dependent on only two values: the proportion of individuals in a population that are susceptible to the infection, S, and the basic reproduction number for a disease, R0 (see Basic Reproduction Number). In this scenario, R = R0S, and if we let p be the proportion of individuals in the population that are immune (i.e. not susceptible), then R = R0(1 - p). Then letting pc = the critical proportion of immune individuals in a population where the herd immunity threshold is reached, 1 = R0(1 - pc), and pc = 1 - 1/R0. When p > pc , the condition for herd immunity is met. Thus, for more infectious diseases with higher R0 values, the critical proportion of immune individuals required to reach herd immunity threshold will increase.

However, the above model is overly simplified, as it does not take into account a variety of factors which vary widely across the world, even on regional or local levels. Such factors include the implementation of non-pharmaceutical control measures to contain the spread of infection, such as the use of masks and mandatory lockdowns or quarantining. If control measures are included in the model, then letting q be the relative reduction in transmission rates due to such non-pharmaceutical control measures, and again, assuming homogeneous population mixing and equal rates of susceptibility and contagiousness, R = R0(1 - p)(1 - q), and in this instance, pc = 1- 1/(R0(1 - q)). As better control measures for containing the virus are implemented, q will increase, and pc will thereby decrease. However, as better control measures are implemented, it becomes more difficult to attain herd immunity, as more individuals in the population remain susceptible, and in the absence of a vaccine, herd immunity may not be achievable.

### Effect of Population Heterogeneity

A variety of other factors can further affect the effective reproduction number, such as the variability of individual contact stemming from the age groups of the individual, or the variability of susceptibility and contagiousness within a population. Using an estimate of R0 = 2.5, Britton et al. (2020) used an age-stratified population model, where a population was divided into six age cohorts with heterogenous mixing assumed between any two cohorts, to predict the necessary pc required to reach COVID-19 herd immunity for a given population. The authors fit contact rates between groups to empirical data collected from a contact study. The average number of infectious contacts that an infected individual had in any one age cohort with another cohort was dependent both on contact rates for the two cohorts but also on the infectivity of the infected individual’s cohort and the susceptibility of the other age cohort. The model also used network models to account for variation in individual social activity levels within a particular age cohort. Assuming a small fraction of infected individuals on February 15 and the implementation of preventative measures one month later while the infected fraction was still small, Britton et al. used a scale factor, α, to scale down the subsequent generations of cases until June 30, when the scale factor was set back to 1, modeling the effect of a complete relaxation of preventative measures. Using these assumptions, the authors illustrated the possibility of reducing a herd immunity level down to ~43%, considerably lower than the 60% predicted by the simplest model that assumes homogeneous population mixing and uniform susceptibility/infectivity rates, as well as the implementation of no preventative measures.

The authors note that this low value can be attained because the majority of immune individuals will be in younger age groups, which are assumed to contain people that are more socially active and less vulnerable to the disease. Super-spreaders with more contacts will thus get infected early on, transmitting the infection amongst each other and becoming immune, and as this happens, the susceptible population will diminish rapidly, considerably slowing the spread of the disease after this stage. The model is only meant to be illustrative that pc can be further reduced from the simplest model assuming homogeneous mixing and should not be taken as an estimate. The model of course has several short-comings, as it assumes that superspreaders are concentrated within the same set of individuals, and it does not consider the impact of super-spreading events, nor does it consider spatial heterogeneities, which may also have substantial impact on herd immunity thresholds. Figure 2.23 illustrates the predicted cumulative fractions of the population infected as a function of days after February 15 for four different levels of α, each corresponding to different levels of preventive measures taken during the March 15-June 30, 2020 period. Note that only when preventative measures are too strict (when α is lowest, as seen in the purple curve), a strong second surge is predicted once restrictions are lifted. However, some degree of preventative measures show a considerable reduction in herd immunity threshold (as seen in the yellow curve where α = 0.6) with no observable strong second surge.

Figure 2.23: Cumulative Fraction of Infected Individuals Predicted in a Model as a Function of Days after February 15 for Different Levels of Preventive Measures Taken when R0 = 2.5 (Adapted from Britton et al., 2020)

## Factors Concerning Severity

A striking feature of COVID-19 is that its symptomatic manifestation and progression is incredibly variable between patients. Soon after the initial emergence of the disease, a variety of factors were identified as potential risk factors for greater severity, including increased age and pre-existing conditions such as cardiovascular disease or diabetes. Meta-analyses of large groups of patients have been incredibly helpful in identifying and quantifying such risk factors. Machine learning models (Shrock et al., 2020) will become more important for predicting disease severity in different patient populations as we better understand how differences in viral spike proteins, through viral epitope profiling, along with characterizing distinct patient antibody responses, together contribute to distinct disease phenotypes. We outline below some of the most significant of these results. Further research has also unveiled a wide range of molecular factors that may be associated with heightened disease severity, such as elevated levels of circulating C-reactive protein and Interleukin-6. Moreover, certain molecular markers have been linked to specific clinical progressions of the disease, including elevated D-dimer in patients experiencing coagulopathy. Identifying these molecular markers will assist medical professions in delivering the most relevant and personalized treatment course that optimizes patient survival. Finally, the identification of genomic variants that may contribute to heightened disease severity has also uncovered certain populations with heightened risk. An understanding of the associations these variations have with clinical disease progression will also aid in more personalized and effective treatments.

### Age, Sex, Pre-Existing Conditions, and Clinical Course

The severity of COVID-19 infection appears to depend on a number of factors. Substantial data appears to indicate a direct proportionality of severity with age, with the most severe and critical cases occurring in the 65+ population. As of writing, there have been very few reported deaths in patients aged 0-24, and the infection rates of this population are the lowest for all other age groups. Preliminary data from Wuhan, China showed that out of 45,000 diagnosed cases, less than 1% were under 9 years of age. Furthermore, just over 1% of cases were patients aged 10-19. Tables 2.10a-c compare U.S. reported and coded deaths resulting from seasonal flu (J09-J11), COVID-19 (U07.1), pneumonia (J12.0-J18.9), and a comorbity of the latter two from February 1, 2020 to May 9, 2020 by sex, age, and state, respectively. These data do not represent the total number of reported deaths from these diseases in this period.

 Sex Seasonal Flu Pneumonia + COVID-19 COVID-19 Pneumonia All Causes Male 3,135 13,636 30,387 42,098 431,692 Female 2,975 10,510 24,473 36,167 403,884 Unknown 0 1 1 1 31 6,110 24,147 54,861 78,266 835,607

Pre-existing conditions, such as hypertension, diabetes, cardiovascular disease, chronic respiratory disease, and cancer also elevate mortality risk. Roughly 10.5% percent of affected patients with cardiovascular disease, 7.3% of patients with diabetes, 6.3% percent of patients with chronic respiratory illness, 6.0% with hypertension, and 5.6% with cancer succumb from a critical COVID-19 infection (American College of Cardiology Bulletin, 2020). For individuals with Type 1 or Type 2 diabetes, elevated blood sugar level is associated with diabetic complications, as well as weakened immunity and increased viral-induced inflammation. Consequently, diabetics with A1C levels between 6 and 7 are only considered to be at slightly elevated risk of developing COVID-19 severe complications over the general population, while increased A1C levels are associated with increased risk of COVID-19 severity. Blood sugar management should be prioritized during this time to lower the risk of severe COVID-19 complications. Smoking is also associated with elevated risk. There is no current data to suggest that pregnant women are at an increased risk of contracting SARS-CoV-2; however, since pregnant women are more susceptible to other respiratory infections, they are considered at-risk for COVID-19.

 Age Group Seasonal Flu Pneumonia + COVID-19 COVID-19 Pneumonia All Causes <1 11 1 4 37 4,258 1-4 35 2 2 33 832 5-14 43 0 6 41 1,223 15-24 42 21 59 157 7,452 25-34 135 170 388 556 15,975 35-44 214 387 973 1,240 22,887 45-54 529 1,154 2,772 3,310 44,291 55-64 1,136 2,996 6,725 9,537 106,004 65-74 1,334 5,155 11,524 16,378 164,217 75-84 1,357 6,788 14,930 21,649 206,121 >84 1,274 7,473 17,478 25,328 262,347 6,110 24,147 54,861 78,266 835,607

Zhu, L. et al. (2020) conducted a retrospective analysis of 7,337 hospitalized COVID-19 patients from Hubei, China, of whom 952 had pre-existing type 2 diabetes. Their analysis found that patients with type 2 diabetes experienced a significantly higher case fatality rate (7.8%) when compared to patients without the disease (2.7%). Furthermore, having type 2 diabetes was associated with higher risk of multiple organ injury and with an elevated need for medical intervention. However, type 2 diabetic patients with well controlled blood glucose, where glycemic variability ranged between 3.9 and 10.0 mmol/L, was associated with a lower case fatality rate (1.1%) when compared to patients with poorly controlled blood glucose (11%). Patients with well-controlled blood glucose also needed less medical intervention and experienced less lymphopenia and had lower levels of D-dimer and C-reactive protein when compared to their poorly controlled blood glucose counterparts.

Though multiple death rates for different age groups have received intense media coverage, it is not apparent how weakened immune systems due to other illnesses among victims may have been factored into the cause of deaths. Similarly, if more than one serious health condition was at work among victims, it is not known how those causes of deaths were recorded thereby impacting analysis.

 Age \ Race & Ethnicity Non-Hispanic American Indian or Alaska Native Non-Hispanic Black Hispanic or Latino Non-Hispanic Asian or Pacific Islander Non-Hispanic White <18 3.5 5.6 7.5 1.9 1 18-49 7.8 5.8 8.4 1.7 1 50-64 6.2 5.2 5.7 1.6 1 65+ 2.5 3.7 2.7 1.1 1 All (Age-Adjusted) 4.5 4.6 4.6 1.3 1

 Location Seasonal Flu Pneumonia + COVID-19 - Seasonal Flu COVID-19 Pneumonia - Seasonal Flu All Causes All Causes (Avg. 2017, 2018, 2019) New York 1,170 13,302 31,592 19,790 110,224 71,301 NYC 961 7,867 20,423 10,449 51,295 24,900 New Jersey 121 6,685 13,749 9,202 50,742 34,285 New York \ NYC[4] 209 5,435 11,169 9,341 58,929 46,401 Massachusetts 162 2,781 7,701 4,827 34,964 27,749 Pennsylvania 209 2,578 7,130 5,600 64,260 63,000 California 577 3,690 6,671 12,386 131,701 125,430 Illinois 176 3,290 6,592 6,501 57,376 49,039 Michigan 240 2,728 5,552 5,394 51,004 44,740 Connecticut 73 890 3,938 1,595 15,291 14,703 Florida 310 1,944 3,840 8,002 102,808 96,989 Maryland 126 1,326 3,567 2,967 27,533 23,137 Texas 342 1,368 3,116 7,496 95,505 93,632 Louisiana 71 1,430 3,029 2,365 23,524 21,004 Indiana 131 1,102 2,641 3,169 32,433 30,597 Ohio 260 1,091 2,624 3,766 57,197 57,197 Georgia 110 1,087 2,446 3,089 40,603 39,041 Arizona 114 1,168 2,158 2,959 32,481 28,001 Top 10 3,164 39,214 90,332 76,264 645,903 550,373 U.S. \ Top 10 3,375 15,435 36,315 58,894 774,755 777,841 U.S. 6,539 54,649 126,647 135,158 1,420,658 1,328,214

Table 2.10d: U.S. Reported and Coded Death Fractions of the Seasonal Flu, COVID-19,
Pneumonia, and all Causes for Several Leading States (February 1, 2020 - July 17, 2020, CDC)

 Location Seasonal Flu / All Causes Pneumonia + COVID-19 - Seasonal Flu / All Causes COVID-19 / All Causes Pneumonia - Seasonal Flu / All Causes Pneumonia + COVID-19 + Flu / All Causes All Causes (2020) / All Causes (2017-19) New York 1.06% 12.07% 28.66% 17.95% 13.13% 155% NYC 1.87% 15.34% 39.81% 20.37% 17.21% 206% New Jersey 0.24% 13.17% 27.10% 18.13% 13.41% 148% New York \ NYC 0.35% 9.22% 18.95% 15.85% 9.58% 127% Massachusetts 0.46% 7.95% 22.03% 13.81% 8.42% 126% Pennsylvania 0.33% 4.01% 11.10% 8.71% 4.34% 102% California 0.44% 2.80% 5.07% 9.40% 3.24% 105% Illinois 0.31% 5.73% 11.49% 11.33% 6.04% 117% Michigan 0.47% 5.35% 10.89% 10.58% 5.82% 114% Connecticut 0.48% 5.82% 25.75% 10.43% 6.30% 104% Florida 0.30% 1.89% 3.74% 7.78% 2.19% 106% Maryland 0.46% 4.82% 12.96% 10.78% 5.27% 119% Texas 0.36% 1.43% 3.26% 7.85% 1.79% 102% Louisiana 0.30% 6.08% 12.88% 10.05% 6.38% 112% Indiana 0.40% 3.40% 8.14% 9.77% 3.80% 106% Ohio 0.45% 1.91% 4.59% 6.58% 2.36% 100% Georgia 0.27% 2.68% 6.02% 7.61% 2.95% 104% Arizona 0.35% 3.60% 6.64% 9.11% 3.95% 116% Top 10 0.49% 6.07% 13.99% 11.81% 6.56% 117% U.S. \ Top 10 0.44% 1.99% 4.69% 7.60% 2.43% 100% U.S. 0.46% 3.85% 8.91% 9.51% 4.31% 107%

Figure 2.24: Weekly U.S. Deaths (Expected vs. Observed, January 1, 2017 - July 11, 2020)

A study of 3,615 patients admitted to hospital care during the month of March 4 to April 4, 2020 observed that increased body mass index (BMI) was positively correlated with increased likelihood of admission for acute and critical care, with a BMI in excess of 34 indicating a doubling or trebling, respectively (Lighter et al., 2020). These data are given in Table 2.11a. Note that approximately 40% of adults in the U.S. aged 60 or younger have a BMI of 30 or greater. Hazard ratios for in-hospital deaths derived from a detailed study with a population of 17,425,445 in the U.K. is given in Table 2.11b.

Table 2.11a: BMI Likelihood Factor of U.S. Acute and Critical Care Admission for COVID-19

 BMI Range Acute Care Factor Critical Care Factor <30 Not Obese 1.0 (ref) 1.0 (ref) 30-34 Obese Class I 2.0 1.8 >34 Obese Classes II & III 2.2 3.6

A study of 416 hospitalized COVID-19 patients from Wuhan, China revealed that 19.7% of study subjects experienced cardiac injury during their hospital stay (Shi, S. et al., 2020). Cardiac injury during the clinical course of the disease was associated with increased need for support with both noninvasive mechanical ventilation (46.3% for patients with cardiac injury vs. 3.9% for subjects without cardiac damage) and invasive mechanical ventilation (22.0% for patients with cardiac injury vs. 4.2% for patients with no cardiac injury). Risk for serious complications was elevated in these patients as well: ARDS occurred in 58.5% of patients with cardiac injury vs. 14.7% of patients without cardiac injury, and risk of acute kidney injury and overall mortality was also considerably higher for patients experiencing cardiac damage. It should also be noted that patients experiencing cardiac damage were disproportionately older and had increased prevalence of comorbidities, such as hypertension.

Table 2.11b: BMI Hazard Ratio of U.K. In-Hospital Death for COVID-19
 BMI Range Hazard Ratio <30 Not Obese 1.0 (ref) 30-34.9 Obese Class I 1.27 (1.18-1.36) 35-39.9 Obese Class II 1.56 (1.41-1.73) >40 Obese Class III 2.27 (1.99-2.58)

Montopoli et al. (2020) have reported an association between androgen-deprivation therapy (ADT) for prostate cancer and SARS-CoV-2 infection. They note that TMPRSS2 is expressed in localized and metastatic prostate cancer and that its expression is under the regulation of the androgen receptor. In vitro studies have shown that androgen treatment induces TMPRSS2 expression in human lung cancer epithelial cells (A549) and androgen depletion reduces TMPRSS2 expression in mouse lung (Mikkonen et al., 2010). They posited that alteration of androgen levels might influence SARS-CoV-2 infectivity of human lung epithelial cells.

Table 2.11c: U.K. TPP Active Patients and Confirmed COVID-19 (CPNS) Deaths by Age
 Age Group TPP Active % Total CPNS Deaths % Total 18-<40 5,990,809 34.4% 40 0.70% 40-<50 2,875,561 16.5% 94 1.65% 50-<60 3,068,883 17.6% 355 6.25% 60-<70 2,405,327 13.8% 693 12.2% 70-<80 1,948,095 11.2% 1,560 27.5% >80 1,136,770 6.5% 2,941 51.8% 17,425,445 5,683

Using data obtained from the Veneto Archive of COVID-19 subjects, the Tumor Registry Archive, and the Regional Medicines Technical Commission, Montopoli et al. compiled information on the incidence and course of COVID-19 infection in individuals without cancer, those with cancer, those with cancer of the prostate who were or were not receiving ADT. The primary endpoints of the study were frequency and severity (measured by hospitalization, admission to an intensive care unit, or death) of COVID-19 for these groups. Of a total male population of 2,399,783, SARS-CoV-2 positivity was seen in 4,532 (0.2%), compared with 430 of 127,368 (0.3%) male cancer patients (OR 1.79 (1.62-1.98) p<0.0001). For men with diagnoses of prostate cancer, 4 of 5,273 of those on ADT were SARS-CoV-2 positive compared with 114 of 37,161 men not on ADT (OR 4.05 (1.55-10.59) p = 0.0059). Of the cases of COVID-19 diagnosed in men receiving ADT, 3 of 4 were mild and there were no deaths, compared with 83 of 114 mild cases and 18 deaths in men with prostate cancer not receiving ADT. This is an interesting observation, which may be limited by variable testing of these populations, other comorbidities, and possible differences in social behavior which clearly warrant review of COVID-19 frequency and behavior in other populations before implementing trials of ADT as a preventive or treatment. It should also be noted that some recent trials have failed to show an effect of androgens on TMPRSS2 expression in murine lung (Baratchian et al., 2020) and have suggested that levels of current smoking (as distinct from prior pack-years) may have a rapid effect on expression of both TMPRSS2 and ACE2. It has also been suggested that androgen effects, if robustly confirmed, may be mediated through changes in immune reactivity rather than TMPRSS2 (Sharifi et al., 2020).

### Kawasaki-like Disease (MIS-C)

Though younger age is associated with improved clinical outcome, reports of outbreaks of Kawasaki-like disease in children and young adults have substantially increased during the COVID-19 pandemic. Kawasaki disease is an illness that primarily affects children under the age of five and is characterized by three phases. The pathophysiology of the disease originates from inflammation in the blood vessels and manifests in symptoms that include rashes, fever, swollen lymph glands in the neck, strawberry tongue, and sore throat during its first phase. In the second phase of the illness (occurring about two weeks after the initiation of fever), patients may experience joint pain, worsening gastrointestinal symptoms, and peeling skin on the hands and feet. Serious complications that may arise if the disease goes untreated include aneurysm of the coronary arteries, inflammation of the myocardium or pericardium, arrhythmias, and other heart problems, which characterize the third phase of the disease.

Toubiana et al. (2020) describe an outbreak of Kawasaki-like disease in children, now called Multisystem Inflammatory Syndrome (MIS-C), admitted to the pediatrics department of a university hospital in Paris, France between April 27 and May 7, 2020. A total of 17 children were admitted for MIS-C in this period, compared to a mean of 1.0 cases per 2-week period during the 2018-2019 period, showing a pronounced spike in cases during the COVID-19 pandemic. The median patient age for the 2020 study period was 7.5 years (the age range was from 3.7 to 16.6 years), and it is notable that 59% of patients had a parent that originated from sub-Saharan Africa or the Carribean islands, and 12% had a parent born in Asia (considered a risk factor for the disease). Eleven of the 17 patients developed MIS-C shock syndrome and required support in the ICU, and twelve patients developed myocarditis. Fourteen patients showed evidence of SARS-CoV-2 infection (7/17 tested positive for viral RNA by RT-PCR and 14/17 tested positive by antibody detection). As of May 13, 2020, roughly 100 cases of the rare disease had been reported in the state of New York, including three cases where the patient died. Of these 100 cases, over 50% had tested positive for SARS-CoV-2 antibodies, further suggesting the spike in the inflammatory condition is associated with SARS-CoV-2 infection. Verdoni et al. (2020) conducted an observational cohort study on patients diagnosed with a Kawasaki-like disease at a health center in Bergamo, Italy between January 1, 2015 and April 20, 2020. Subjects were divided into two groups: 19 patients that presented with the disease before the COVID-19 pandemic had affected the region (January 1, 2015 until February 17, 2020) and 10 patients diagnosed during the height of the pandemic, from February 18 until April 20, 2020. Eight out of the ten patients were positive for SARS-CoV-2 IgG or IgM antibodies. The group diagnosed during the COVID-19 pandemic had a higher incidence of cases (10 cases per month vs. 0.3 cases per month before the pandemic), a higher mean age (7.5 years vs. 3.0 years), a higher incidence of cardiac involvement (6 of 10 vs. 2 of 19), a higher incidence of shock syndrome (5 of 10 vs. 0 of 19), and a higher incidence of macrophage activation syndrome (5 of 10 vs. 0 of 19). The authors report many other clinical and biochemical features that differentiated the two groups, and they highlight that the patients diagnosed during the pandemic tended to have a more severe disease course.

Consiglio et al. (2020) have reported results of immunologic profiling of children with MIS-C and compared this with patterns seen in normal children, children with Kawasaki disease (diagnosed prior to the emergence of SARS-CoV-2), and adults with COVID-19. They studied 41 children with COVID-19 (all mild), 13 with MIS-C, and 28 presenting with classic Kawasaki disease in the 2017-2018 period and compared these with normal children or adults with severe COVID-19. Principal component analysis of plasma proteins showed significant differences between adults and children with either Kawasaki disease or MIS-C, with higher levels of IL-8 and IL-7. The patterns of MIS-C and Kawasaki disease partially overlapped. Differences were also seen in T-cell subsets discriminating patients with MIS-C and Kawasaki disease, and in the level of IL-17 which was elevated in patients with Kawasaki disease but not MIS-C. They concluded that the “...differences in T-cell subsets and cytokine mediators place MIS-C at the intersection of Kawasaki disease and acute SARS-CoV-2 infection immune states in children as well as the hyperinflammation seen in adults with severe COVID-19”. The observation of autoantibodies targeting immune cell signalling and structural proteins in heart and blood vessels in MIS-C also suggested possible therapeutic strategies.

### Molecular and Cellular Factors

It has been reported that patients with more severe COVID-19 have higher viral loads than patients with mild symptoms. In a study performed on 76 COVID-19 patients in a hospital in Nanchang, China, patients were tested for viral load using nasopharyngeal swabs. The samples taken from patients with severe COVID-19 disease had a mean viral load that was 60 times higher than the mean viral load for patients with mild symptoms (Liu, Y. et al., 2020). Viral clearance was also significantly shorter in mild cases, with 90% of mild patients testing negative for SARS-CoV-2 by 10 days after onset of symptoms, whereas all severe COVID-19 patients continued to test positive by this point. These data suggest that severe cases have a significantly longer viral shedding period.

A March 26, 2020 correspondence from the Oxford COVID-19 Evidence Service Team provides some possible evidence linking initial viral load of SARS-CoV-2 at time of initial exposure to severity of COVID-19 disease. Not only may exposure to a higher initial viral load increase the chance of transmission, but it may also be associated with worsened COVID-19 outcomes, putting healthcare workers who are regularly exposed to COVID-19 patients with higher viral loads at greater risk.

In a study of 40 COVID-19 patients in a German hospital, where 13 ended up requiring mechanical ventilation, levels of IL-6 (interleukin-6) were found to be strongly associated with both respiratory failure and need for mechanical ventilation (Herold et al., 2020). The authors reported that 92% of subjects with IL-6 levels above 80 pg/mL experienced respiratory failure, which was 22 times the rate experienced in patients below the 80 pg/mL threshold. Only one patient with IL-6 concentration below 80 pg/mL was reported to experience respiratory failure, and only one patient above this threshold did not require intubation, demonstrating a fairly high accuracy rate for the 80 pg/mL cut-off for predicting outcome.

A retrospective study of 150 patients in Wuhan, China, revealed that serum ferritin levels were elevated in hospitalized COVID-19 patients but even more so in patients that died from the illness than for those who survived (Ruan et al., 2020). The study found that in the 68 patients who died, the mean serum ferritin level was 1297.6 ng/mL, whereas for the 82 survivors, the mean ferritin level was reported as 614.0 ng/mL. In contrast, the normal range for blood serum ferritin is 21.8-274.7 ng/mL. High levels of ferritin are indicative of a variety of conditions, including inflammatory conditions, where particularly high ferritin levels may be a molecular marker associated with increased risk of death.

Patients infected with SARS-CoV-2 also show significantly reduced levels of Natural Killer (NK) and CD8+T cells (Zheng et al., 2020). This specific cell count reduction is likely tied to the upregulation of NKG2A, an inhibitory C-type lectin receptor expressed on the surface of NK and CD8+T cells, in patients with the virus (ibid.). Upregulation of the receptor results in inhibition of the cytotoxic activity of NK cells, an important line of defense against viral infection in the innate immune system. Zheng et al. (2020) found in their study of 68 hospitalized COVID-19 patients that neutrophil count was higher in severe cases of the disorder but that cytotoxic lymphocyte (CTL), NK, and CD8+T cell counts were dramatically decreased in patients with severe disease. Furthermore, the authors noted that NKG2A was significantly upregulated on NK cells and on CTLs in early stages of COVID-19 disease when compared to NK cells and CTLs from individuals without the disease. For patients that recovered, NK and CD8+T cells increased during convalescence, but the number of NKG2A+NK and NKG2A+CTL cells was reduced, further suggesting that NKG2A regulation is a key modulator of COVID-19 progression.

Diao et al. (2020) describe similar findings of reduced overall total T-cell count and specifically reduced CD8+ T cell and CD4+ T cell counts in COVID-19 patients, an effect that is amplified in patients over age 70 or for those requiring ICU care. The authors report that for COVID-19 patients with total T cell count below 800/µL, CD8+T cell count below 300/µL, and CD4+T cell count below 400/µL, survival rate was significantly reduced, even when no obvious symptoms were apparent. Furthermore, T cell count was found to be negatively associated with blood serum concentrations of IL-6, IL-10, and TNF-α. Diao et al. (2020) also report that CD4+T and CD8+T cells from COVID-19 patients had increasingly higher expression of PD-1 (Programmed Death Cell Protein 1) and TIM-3 as symptoms and disease progression became more severe, that is, progressing from asymptomatic to symptomatic to requiring ICU care. These cell membrane proteins are markers of T-cell exhaustion, a form of T-cell dysfunction that often occurs during chronic infection.

Coagulopathy is a common finding in patients with severe COVID-19 and is associated with increased mortality. D-dimer is a fibrin degradation product, that is, resulting from blood clot degradation, and is therefore a molecular indicator of clot formation. D-dimer levels are routinely tested when a patient is suspected to have deep vein thrombosis, pulmonary embolism, disseminated intravascular coagulation (DIC), or other coagulopathies. Several studies have reported that increased D-dimer levels are associated with increased risk of COVID-19 death. Tang, N. et al. (2020) report findings from 183 patients with confirmed COVID-19 and treated at Tongji Hospital in Wuhan, China. Of this pool of patients, 11.5% died expressing significantly higher levels of D-dimer and fibrin degradation product than found in survivors, with mean D-dimer levels of 2.12 mg/L in non-survivors compared to 0.61 mg/L in survivors. Patients who succumbed to the disease also had a significantly longer prothrombin time, and 71.4% of non-survivors showed signs of intravascular coagulation (blood clots) compared to 0.6% of survivors. In a study of 191 hospitalized COVID-19 patients from China, Zhou, F. et al. (2020) report that D-dimer levels in excess of 1 mg/L upon admission was associated with an 18-fold increased risk of death. These results are corroborated by results reported by Huang et al. (2020) who found that in 13 patients receiving ICU care, median D-dimer levels were 2.4 mg/L, significantly lower than the mean level of 0.5 mg/L reported in the 28 hospitalized COVID-19 patients that did not require ICU care.

In a study published on March 11, 2020, Wuhan and Shenzhen researchers have observed in a sample of 2,000 infected patients that individuals with type-O blood, regardless of age and gender, generally experience less severe COVID-19 symptoms, while those with type-A blood experience the worst symptoms. The researchers also remark that healthy individuals with type-O blood may have a lower risk of contracting COVID-19 for reasons not yet understood, while those with type-A blood may be more susceptible to infection and should take extra precautions.

### Genetic Risk Factors

Ellinghaus et al. (2020) have sought to identify potential genetic risk factors that may determine some of the variation hitherto observed in COVID-19 severity. The group recruited hospitalized COVID-19 patients that had experienced respiratory failure. All participants were recruited from Spain or Italy, which at the time of the study were epicenters for the disease. They compared the genotypes of these severely affected patients to control participants from the same regions in an effort to identify over-represented genotypes in the severely affected group. The final subject pools were comprised of 835 patients and 1255 control subjects from Italy and 775 patients and 950 control subjects from Spain. A genome-wide comparison of the two groups was conducted, and the authors reported two genetic loci associated with COVID-19-induced respiratory failure. These were the rs11385942 insertion-deletion GA or G variant at the locus 3p21.31, where the GA allele was associated with heightened risk, and the rs657152 A or C single nucleotide polymorphism at locus 9q34.3, where the A allele was associated with elevated risk. Both loci were also identified in the Italian and Spanish subanalyses. The authors reported an additional 24 genomic loci that showed suggestive evidence for association with COVID-19-induced respiratory failure.

The authors then proceed to describe how the two allele variants associated with elevated risk may contribute to heightened disease severity. The 3p21.31 locus is made up of six genes, and the GA variant is associated with lowered expression of the CXCR6 gene and heightened expression of the SLC6A20 gene. Furthermore, the variant is associated with increased expression of the LZTFL1 gene in lung cells. The frequency of the variant associated with heightened risk was more strongly associated with patients receiving mechanical ventilation over receiving oxygen supplementation.

The second site associated with heightened COVID-19-induced respiratory failure was at the 9q34.2 locus, a site that includes the ABO blood group locus. The authors’ meta-analysis uncovered a heightened risk for disease severity for patients with Type A blood and a protective effect for those with Type O blood, an observation that had been previously corroborated in the literature. This elevated risk was only seen in the comparison of patients to control subjects, but no significant difference in the blood type distribution of patients receiving ventilation or oxygen supplementation was found.

Baillee et al. (2020) identify five gene loci associated with heightened risk of developing severe COVID-19. The group conducted a genomic analysis on 2,224 critically ill hospitalized COVID-19 patients from the U.K., across 208 intensive care units. They report five genome-wide genetic loci with significant association with severe disease. One was found on chromosome 12q24.13 in a gene cluster that encodes three antiviral restriction enzyme activators OAS1, OAS2, and OAS3. Another identified site was on chromosome 19p13.2, near the gene TYK2, the gene that encodes tyrosine kinase 2. A third locus associated with severe disease was on chromosome 19p13.3 in a locus inside the gene DPP9 that encodes dipeptidyl peptidase 9. Another locus of significance was on chromosome 21q22.1 in the IFNAR2 gene that encodes for an interferon receptor. Finally, the CCR2 gene, which encodes a chemotactic receptor for macrophages and monocytes, was found to be highly expressed in the lung tissue of severe COVID-19 patients.

## Fatality, Recovery, and Potential for Lasting Damage

The case fatality rates for the untreated and unvaccinated for several pathogens and related diseases, including SARS-CoV-2 and COVID-19, is given in Table 2.12 and classified according to their highest status: Outbreak (O), Epidemic (E), or Pandemic (P). The daily death rate for COVID-19 is given alongside those for several endemic diseases in Table 2.13.

COVID-19 patients in ICU care are more likely to succumb to the disease, particularly those requiring mechanical ventilation (as opposed to non-invasive oxygen supplementation) and early estimates of fatality in these patients painted a grave picture, in some cases estimating fatality over 80%. However, this case fatality rate may be much lower than anticipated in the case of ICU patients treated in U.S. hospitals. Auld et al. (2020) conducted an observational cohort study of 217 critically ill hospitalized COVID-19 patients at 6 COVID-19 designated ICUs at three hospitals in Atlanta, GA from March 6, 2020 to April 17, 2020. Of these 217 patients, 165 required invasive mechanical ventilation, and the fatality rate for this group was 35.7%, with 4.8% still on ventilators by the end of the study. The fatality rate for the 217 critically ill patients studied was 30.9%, whereas 60.4% of the patients recovered enough to be discharged from the hospital.

In a March 28, 2020 retrospective, multi-cohort study of 191 COVID-19 patients published in the Lancet, Zhou et al. report that the median time from onset of symptoms until death in non-survivors was 18.5 days (with an IQR from 15.0-22.0 days). Typically, older patients who succumb, do so sooner, whereas younger patients do so later. For those patients that recovered and were discharged from the hospital, the median time from onset of symptoms until discharge was 22.0 days (IQR 18.0-25.0 days). The authors also report that all patients who succumbed to a COVID-19 infection had detectable viral load and severe lymphocytopenia (low circulating lymphocytes) until time of death.

A study of 416 patients with COVID-19 disease from Wuhan, China found that 19.7% of hospitalized patients experienced cardiac injury during their hospital stay. The fatality rate for study subjects with cardiac injury was reported as 51.2% versus the mortality rate for patients showing no cardiac injury at 4.5% (Shi, S. et al., 2020), showing that cardiac injury is a significant risk factor for death in COVID-19 patients. Furthermore, the CDC reports that from February 1, 2020 to July 11, 2020, approximately 43% of U.S. patients who succumbed to COVID-19 also had pneumonia, strongly indicating pneumonia as another contributing condition associated with COVID-19 mortality.

In late February, 2020, the WHO reported that the median time from onset of symptoms until recovery is approximately 14 days for mild cases, which comprise roughly 80% of all reported COVID-19 cases. The median time from symptom onset until recovery was reported as 3-6 weeks for moderate to severe cases. Over 80% of COVID-19-infected individuals make a full recovery within 2-3 weeks from the onset of COVID-19 symptoms.

However, many recovered patients that no longer test positive for viral RNA continue to experience lingering symptoms in the months after active infection and supposed recovery. Such persistent symptoms include low-grade fever, muscle weakness, fatigue, shortness of breath, rashes, cardiac irregularities, anosmia, and other neurological symptoms. Some of these symptoms may be indicative of longer-term tissue damage, such as pulmonary fibrosis, which has been observed in some individuals. Such tissue damage can result in reductions of 20-30% lung function in some cases. As COVID-19 is still very much a nascent zoonotic disease, long-term damage that may result from SARS-CoV-2 infection should be prioritized for close monitoring and study.

Table 2.12: Case Fatality Rates of Several Diseases for the Untreated/Unvaccinated (September 29, 2020)
 Pathogen Disease Highest Status Vaccine CFR Prions (various) TSEs O N 100% Lyssavirus Rabies O Y ~99% Variola major Smallpox Disease E Y ~95% Ebola virus (EBOV) EVD E N 83-90% HIV AIDS P N 80-90% Bacillus anthracis Anthrax O Y 45-85% Influenza A (H5N1) Avian Flu P Y ~60% Rickettsia prowazekii Typhus Fever E Y 10-60% Yersinia pestis Bubonic Plague P Y 5-60% Mycobacterium tuberculosis Tuberculosis (TB) P Y 43% MERS-CoV MERS-12 O N ~35% Varicella-zoster virus Chickenpox (neonatal) O Y ~30% Salmonella enterica Typhoid Fever E Y 10-30% SARS-CoV-1 SARS-02 E N 11% SARS-CoV-2 COVID-19 P N 3.1-3.3% Vibrio cholerae Cholera P Y 1.8-5% Measles virus (MeV) Measles E Y 1-3% P. falciparum Malaria P Y ~0.3% Influenza A-C (various) Seasonal Flu O Y <0.1% Influenza A (H1N1) Swine Flu P Y 0.02% Varicella-zoster virus Chickenpox (children) O Y 0.001-0.02%

The average global daily deaths for several endemic diseases is given in Table 2.13.

Table 2.13: Daily Death Rates of Several Endemic Diseases and
COVID-19 for Comparison (September 29, 2020)
 Disease Average Daily Death Rate COVID-19 3,834 (261 days) Tuberculosis 3,014 Hepatitis B 2,430 Pneumonia 2,216 AIDS 2,110 Malaria 2,002 Shigellosis 1,644 Rotavirus 1,233 Seasonal Flu 1,027 Swine Flu (H1N1) 2009 743 Norovirus 548 Whooping Cough 440 Typhoid 396 Cholera 392 Measles 247 Rabies 162 Yellow Fever 82

The average daily death rate of COVID-19 is computed as the ratio of the cumulative reported COVID-19 deaths with respect to the known time frame of these reported deaths.

1. The Case Infection Rate (CIR) of a disease X is the percentage of the population that is confirmed X-infected, which is a lower bound on the probability of becoming X-infected in said population. The Case Fatality Rate (CFR) of a disease X is the percentage of confirmed X-related fatalities among confirmed X-infected individuals of a population or demographic, while the Mortality Rate (MR) of a disease X is the percentage of confirmed X-related fatalities within the population, regardless of the number of actual X-infected.
2. Code and data used to create these plots are freely available on GitHub with the link provided in Hyperlinks.
3. A logistic function as opposed to a step function allows for a differentiable loss function with respect to time t.
4. These data do not include the contributions from New York City. That is, the data sum NYC + (New York \ NYC) equals the total contributions for the state of New York.