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The first three months of the COVID-19 epidemic:
Epidemiological evidence for two separate strains of SARS-
CoV-2 viruses spreading and implications for prevention
strategies
Two epidemics of COVID-19
KNUT M. WITTKOWSKI1*
1 ASERA LLC, New York, NY
* Corresponding author:
E-mail: knut@asdera.com (KMW)
Abstract
About one month after the COVID-19 epidemic peaked in Mainland China and SARS-CoV-2
migrated to Europe and then the U.S., the epidemiological data begin to provide important insights
into the risks associated with the disease and the effectiveness of intervention strategies such as
travel restrictions and social distancing. Respiratory diseases, including the 2003 SARS epidemic,
remain only about two months in any given population, although peak incidence and lethality can
vary. The epidemiological data suggest that at least two strains of the 2020 SARS-CoV-2 virus
have evolved during its migration from Mainland China to Europe. South Korea, Iran, Italy, and
Italy’s neighbors were hit by the more dangerous “SKII” variant. While the epidemic in continental
Asia is about to end, and in Europe about to level off, the more recent epidemic in the younger
US population is still increasing, albeit not exponentially anymore. The peak level will likely
depend on which of the strains has entered the U.S. first. The same models that help us to
understand the epidemic also help us to choose prevention strategies. Containment of high-risk
people, like the elderly, and reducing disease severity, either by vaccination or by early treatment
of complications, is the best strategy against a respiratory virus disease. Social distancing or
“lockdowns” can be effective during the month following the peak incidence in infections, when
the exponential increase of cases ends. Earlier containment of low-risk people merely prolongs
the time the virus needs to circulate until the incidence is high enough to initiate “herd immunity”.
Later containment is not helpful, unless to prevent a rebound if containment started too early.
About the Author
Dr. Wittkowski received his PhD in computer science from the University of Stuttgart and his ScD
(Habilitation) in Medical Biometry from the Eberhard-Karls-University Tübingen, both Germany.
He worked for 15 years with Klaus Dietz, a leading epidemiologist who coined the term
“reproduction number”, on the Epidemiology of HIV before heading for 20 years the Department
of Biostatistics, Epidemiology, and Research Design at The Rockefeller University, New York. Dr.
Wittkowski is currently the CEO of ASDERA LLC, a company discovering novel treatments for
complex diseases from data of genome-wide association studies.
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author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the(which was not peer-reviewed) The copyright holder for this preprint .https://doi.org/10.1101/2020.03.28.20036715doi: medRxiv preprint
Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -2-
Table of Content
Introduction 3
Materials and Methods 4
Data 4
Methods and models 4
Statistical and Bioinformatics Methods ................................................................ 4
Epidemiological Models ....................................................................................... 4
Results 5
Incidence by Country. Norther Hemisphere 5
Time-course by country/region 7
Discussion 15
Strengths and shortcomings 15
Evidence for (at least) two different strains of SARS-CoV-2 15
Changes in infectivity and lethality between China and Europe 16
Predictions for COVID-19 in North America 17
A historical perspective 18
Implications for prevention 18
References 20
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Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -3-
Introduction
The first cases of a new coronavirus strain, termed SARS-CoV-2 (Severe Acute Respiratory Syn-
drome CoronaVirus) by the International Committee on Taxonomy of Viruses (ICTV) (Cascella 2020),
were reported on 31-12-2019 in Wuhan, the capital of the Hubei province of China.(Jernigan 2020) As
of 2020-03-28, 10:00 CET, 591,971 symptomatic cases and 27,090 deaths have been reported
from virtually every country in the northern hemisphere (see Section Data), The disease was
termed COVID-19 by the WHO on 2020-02-11, and categorized as a pandemic on 2020-03-12,
yet the details of the spread and their implications for prevention have not been discussed in
sufficient detail.
Between 02-14 and 03-16, the Dow Jones fell 31% from 29,440 to 20,188, raising fears for the
economy, in general, and retirement savings, in particular. Several administrations have imposed
severe restrictions aimed at containment of the virus. For instance,
• On 03-08, the Italian government imposed a quarantine on 16 million people in the north of
Italy, which was followed up on 03-11 with a nationwide closure of all restaurants and bars
along with most stores.(WSJ, 2020-03-11)
• on 03-11, the U.S. administration banned travel from 26 European countries (Austria, Belgium,
Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy,
Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slo-
vakia, Slovenia, Spain, Sweden, and Switzerland). https://www.cnn.com/world/live-news/coronavirus-outbreak-03-12-20-
intl-hnk/index.html.
• On 03-15, New York’s Mayor de Blasio reversed his previous position that NY schools should
remain open to avoid health care workers from “staying home and watching their children”
and announced NY public schools to be closed, following many other school systems.
• From 03-17, all New York, New Jersey, and Connecticut restaurants were had to close. From
03-22, hairdressers and barbers were also closed.
• From 03-19 California was “shut down”.(Executive order N-33-20)
• On 03-22, the lockdown in the Italian region of Lombardy was tightened to ban sports and
other physical activity, as well as the use of vending machines.
• Also on 03-22, the National Guard was activated in New York, California, and Washington
State, five senators self-quarantined. NY governor Cuomo mandated that all nonessential
businesses close or work from home.
By the end on 03-20, the Dow Jones was down at 19,173 (35%) from 02-14. On 03-26, the U.S.
Senate approved a $2T stimulus package.
For most of the first three months of the epidemic, much of the response was driven by “fear,
stigma, or discrimination”(Ren 2020), including naming SARS-CoV-2 the “China virus”(Rogers 2020), de-
spite the fact that seasonal respiratory zoonotic pathogens typically originate in China, where life-
animal markets provide chances for animal viruses to transmit to humans.(Malik 2020)
After three months, enough data are available to discuss important epidemiological characteris-
tics of COVID-19 and the potential impact of interventions. In particular, we have now seen the
number of new cases (and deaths) to decline in China and South Korea and to at least stabilize
in some European countries. Changes in number of deaths follow the changes in number cases
(albeit at a lower level) by about two weeks. Hence, we can discuss both the infectiousness and
the lethality of the virus, two important characteristics to assess public health impact of the dis-
ease.
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author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the(which was not peer-reviewed) The copyright holder for this preprint .https://doi.org/10.1101/2020.03.28.20036715doi: medRxiv preprint
Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -4-
One of the key findings published herein is evidence that at least two strains of SARS-CoV-2 with
different infectiousness and lethality have evolved, and by following the likely path for each of
these strains we can obtain novel insights into the nature of the epidemic and, thus, the effective-
ness of prevention strategies.
Materials and Methods
Data
All data were downloaded on 2020-03-27 from the European Centre for Disease Prevention and
Control (ECDC) Web site at https://www.ecdc.europa.eu/en/publications-data/download-todays-
data-geographic-distribution-covid-19-cases-worldwide, where data are collected daily between
6:00 and 10:00 CET. Updates were collected from the Johns Hopkins online tracker available at
https://systems.jhu.edu/research/public-health/ncov/.Population data were accessed from
https://www.worldometers.info/world-population/population-by-country/ on 2020-03-12. Data on
ages by country were accessed from https://data.worldbank.org/indicator/SP.POP.65UP.TO.ZS.
Methods and models
Statistical and Bioinformatics Methods
The data were processed with MS Excel. To avoid biases from inappropriate model assumptions
only basic descriptive statistics were employed. In some cases, data from only the day before or
after (or both) was averaged (up to a three day moving average) to reduce the effects of apparent
reporting artifacts (Darwin’s natura non facit saltum,(Berry 1985)) without creating undue biases. The
two “smoothers” applied were:
• averaging x0 with a previous x−1 (or, rarely, following x+1) data and
• applying a moving average of (x−1, x0, x+1)→(2 x−1 + x0, x−1 + x0 + x+1, x0 +2 x+1)/3
No other changes were applied to the data.
Like China in mid-February, the German Robert-Koch-Institute (RKI) changed the reporting sys-
tem in mid-March, which resulted in a near 6-fold increase of the data reported on 03-20 over the
data reported on 03-19. Such changes in reporting systems add to the difficulties in interpreting
the data.
Epidemiological Models
If a disease causes immunity after an infectious period of a few days only, like respiratory dis-
eases, an epidemic extinguishes itself as the proportion of immune people increases. Under the
SIR model,(Kermack 1991) for a reproduction number(Dietz 1993) (secondary infections by direct contact
in a susceptible population) of R0=1.5–2.5 over 7 days (recovery rate: γ=1/7=.14), the noticeable
part of the epidemic lasts about 90–45 days (R0/γ=β=.21–.36) in a homogeneous population of
10M. The period is shorter for smaller more homogenous and longer for larger, more hetero-
genous populations. For a given infectious period 1/γ (here, e.g., 7 days. SARS and COVID-19
incubation period plus 2 days(Lauer 2020)), R0 also determines how long it will take for early cases to
become visible after a single import (150–60 days), the peak prevalence of infections (5–22%),
and how many people will become immune (55–90%). An arbitrary low rate of disease-related
death (0.00001*I/d) has been added to allow for comparison between models.
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author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the(which was not peer-reviewed) The copyright holder for this preprint .https://doi.org/10.1101/2020.03.28.20036715doi: medRxiv preprint
Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -5-
Fig 1: SIR Model of SARS. Number of susceptible (blue), infectious (red), and resistant (green) people after a popu-
lation of 10,000,000 susceptible people is exposed to 20 subjects infected carrying a novel virus. Assumptions: R0 =
2.2, infectious period = 7 days,(available from https://app.box.com/s/pa446z1csxcvfksgi13oohjm3bjg86ql )
Results
Incidence by Country. Norther Hemisphere
Table 1 shows the raw daily incidence by population sizes for countries with epidemiological rel-
evance in the northern hemisphere. Countries within proximity are grouped by their peak inci-
dence (red background).
The Hubei province in China (with the capital Wuhan), South Korea, Iran, Italy (especially the
Lombardy region), and Spain have the highest peak incidence, followed by the countries neigh-
boring Italy.
It should be noted, however, that there is no uniform definition of “cases”. In some countries a
case needs to have symptoms, in other countries, it suffices to have antibodies (be immune).
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author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the(which was not peer-reviewed) The copyright holder for this preprint .https://doi.org/10.1101/2020.03.28.20036715doi: medRxiv preprint
Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -6-
Table 1: Incidence by Country. Dates: Feb 13 (peak intensity in Mainland China, mostly Hubei and neighboring prov-
inces), Feb 19 to Mar 22. Countries with low population size (PSz) or low number of cases (Total) are hidden. Red
background indicates countries/dates with high incidence. Countries/regions are sorted by proximity among each other
and distance from Mainland China.
Country PSz [M] Tot al Total/ M 02-05
2-21
2-22
2-23
2-24
2-25
2-26
2-27
2-28
2-29
03-01 03- 02 03-03 03-04 03- 05 03-06 03- 07 03-08 03- 09 03-10 03- 11 03-12 03- 13 03-14 03- 15 03-16 03- 17 03-18 03-19 03- 20 03-21 03- 22 03-23 03- 24 03-25 03- 26 03-27 03- 28
CN(Hubei) 58.5 82,213 1405. 35 66.2 15 14 11 4978679. 81 3.5 2.17 2. 03 22.91 1.73 0. 79 0.77 0. 34 0.5 0.41 0. 38 0.32 0.38 0. 43 1.88 0.56 1. 28 1.69 1. 35 1.42 2.56 1. 69 1.69 2.07 1. 9 2.29
Vie tnam 97 169 1.74 0.01 000000000 0 0 0 0 0 00.01 0. 04 0.09 0. 01 0.04 0.04 0. 05 0.05 0.04 0. 04 0.04 0. 05 0.08 0.11 0. 04 0.11 0.19 0. 07 0.1 0.13 0. 11 0.11
Cambodia 17 102 6.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.06 0000.06 0.06 0. 06 0.12 0. 29 0.71 0 0 0. 68 0.68 1.15 1. 15 0.12 0.2 0. 27 0.12 0. 24
South_Korea 51 9,478 185. 84 0.04 145335912 13 13.7 13.5 11. 8 10.1 9. 37 9.37 8.71 7. 18 5.64 3.66 3. 66 2.24 2. 16 2.1 1.49 1. 45 1.65 1.82 2. 56 2.52 2.49 1. 92 1.25 1. 49 1.96 2.04 2. 32 2.32
Singapore 6732 122.00 1 0010000100.67 0. 67 0.33 0. 33 0.33 1.28 1. 44 1.61 21.67 1 2 1.5 2. 17 2.33 22.83 3. 83 6.58 6.58 7. 06 6.11 5. 17 98. 17 2.56 9. 67 16.8
Malaysia 32 2, 161 67.53 0.06 000000000 00.06 0. 06 0.22 0. 44 0.52 0.52 0. 31 0.31 0.38 0. 44 0.45 0. 45 1.22 2.83 3. 71 4.58 3.75 3. 58 3.72 3. 85 4.47 5.08 5. 7 45. 34 6.69 4. 06
Japan 126 1,499 11. 90 0.04 0000000000.07 0.12 00. 11 0.39 0.33 0. 37 0.4 0.26 0. 21 0.43 0.4 0. 44 0.49 0. 34 0.27 0.08 0. 19 0.19 0.56 0. 46 0.36 0. 33 0.39 0.45 0. 6 0.76 1.07
Taiwan 24 267 11.13 0.04 0000000000.04 00. 04 0.04 00.08 0. 04 0000.13 00.04 0. 17 0.25 00.33 0. 42 0.86 0. 81 0.75 0.67 0. 83 10. 88 0.79 0. 71 0.63
Thailan d 70 1,136 16.23 0. 09 000000000 00.01 0 0 0.03 0. 03 0.02 0.02 0 0 0.13 0. 16 00. 17 0.23 0. 23 0.45 0.45 0. 25 0.25 2.58 2. 42 2.27 1. 52 1.54 1.57 1. 3 0
Indonesia 274 1,046 3. 82 0 000000000 00.01 00000000.02 0.02 0. 05 0.06 0.06 0. 09 0.09 0. 1 0.1 0.07 0. 17 0.27 0.37 0. 37 0.31 0.31 0. 38 0.44 0.5
Philippi nes 110 803 7.30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.02 0.01 0. 04 0.21 00.15 0. 03 0.11 0.35 0. 35 0.21 0.21 0. 2 0.2 0.68 0. 68 0.25 0.52 0. 79 0.76 0. 76 0.76
India 1380 873 0.63 0 000000000 0 0 0 00. 02 00000.01 00. 02 00.01 0. 01 0.01 0.01 0. 01 0.01 0. 02 0.04 0.05 0. 06 0.06 0.05 0. 06 0.08 0. 09
Pakist an 221 1,197 5.42 0 0000000000.01 00000000. 02 0.02 00.02 0 0 0.04 0. 36 0.36 0.26 0. 26 0.56 0. 52 0.48 0.57 0. 52 0.47 0.47 0. 47 0
Afghani stan 39 91 2. 33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.04 0.04 00.04 0. 04 0000.08 0. 15 0.13 0.03 0 0 0.05 0. 09 0.14 0.19 0. 45 0.45 0. 21 0.21
Sri_L anka 21 106 5.05 0000000000000000000000.05 0.05 0. 14 0.24 0.38 0. 48 0.41 0.38 0. 35 0.62 0. 57 0.43 0.48 0. 24 0.1 0.1 0
Iran 84 32,332 384.90 0 0000001122.44 4.58 6.23 8. 46 8.46 10.9 10. 9 10.8 10.8 8. 79 8.79 11. 4 12.8 15.3 15. 6 14.4 13. 2 14 14.2 13.2 12. 9 12.6 12. 2 16.8 21 26.3 28. 4 34.8
Iraq 40 458 11. 45 0 0000000000.15 0. 15 0.05 0. 13 0.13 0.18 00. 4 0.18 0 0 0. 23 0.1 0.28 0. 49 0.49 0. 38 0.38 0.29 0. 29 0.46 0.46 0. 59 0.85 1. 11 0.8 1.18 1. 57
Saudi_Arabia 35 1,104 31.54 0 000000000 00. 01 0.01 00.06 0. 06 0.03 0.03 0. 11 0.11 0. 14 0.71 0.49 0. 69 0.46 0.46 0. 43 0.36 11.64 1. 81 2.6 3.39 3. 66 3.66 3. 8 3.2 2.63
United_Arab_
10 405 40.50 0 000000010 0. 200.3 0. 3 0.1 0.1 0. 8 0.8 0.7 0. 7 1.5 0.55 0. 55 0 0 0.65 0. 65 11.4 1.8 0. 65 0.65 1.5 3.17 4.83 5. 67 5.23 4.8
Oman 5131 26.20 0 000000000 0 0 0.2 01.6 0. 2 0 0 0.2 0. 2 0 0 0. 2 0.2 00.4 0. 4 1111.3 1.3 0.6 2.2 3. 6 33.2 3.2
Kuwait 4225 56. 25 0 000112441 00. 25 1.25 1.25 0. 25 0.25 0.38 0. 38 0.75 0. 25 11. 17 2.58 4122. 75 2.17 2.08 23. 5 3.5 30.25 0. 5 1.75 2.83 3. 92
Qatar 3562 187.33 0 0000000000. 33 0.67 0. 83 0.83 00.5 0.5 0. 33 1 1 27. 8 27.1 26.4 19. 3 5.67 18.4 11. 7 4.89 3. 33 2.67 3.33 3. 67 4.33 4.33 4. 78 5.22 44.33
Bahrain 2466 233.00 0 0001111 503 1.5 1.5 1.5 11.5 0 2 3.5 87. 75 7.75 13 13 24 0.5 1.5 57978.33 9.67 14 10. 2 14.2 18.2 11. 8 11.8
Jordan 10 212 21.20 0 000000000 0 0 0.1 000000000000.7 0.7 1 1 1.05 1. 05 1.4 1.4 1. 5 1.3 1.5 2. 37 2.83 3.3
Israel 93, 035 337.22 0 000000000 00. 33 00.28 0. 28 0.22 0.22 0. 67 1.56 1.72 1. 72 1.33 1. 56 2.22 6.89 86. 93 6.78 6.63 15. 5 15.5 19 20. 9 41.2 54.2 43. 5 40.9 38.3
Lebanon 7391 55.86 0 0000000000. 14 0.86 0.43 0 0 0.43 0. 86 01. 43 1.29 02.86 0. 71 1.93 1. 93 0.86 1.5 1.5 1. 86 2.19 4. 62 7.05 2.57 2. 71 4.9 4.81 4. 71 3.29
Palestine 591 18. 20 0 000000000 0 0 0 0 0 1.4 1.8 0.6 00.2 1. 8 0.2 0.5 0. 5 0.6 00.2 0. 4 0.6 0. 6 0.5 0.5 1. 4 00.2 2.4 2. 4 1.4
Russia 146 1,036 7.10 0 000000000 0 00.01 0.01 0 0 0. 02 0.02 0 0 0. 05 0.05 0.06 0. 08 0.1 0.12 0. 12 0.17 0. 24 0.31 0.37 0. 55 0.72 00.39 1. 12 1.25 1.34
Azerbai jan 2165 82.50 0 000000001 0 1 0 00.75 0.75 1.5 0 0 0.5 0.5 1 0 1.5 1. 5 02. 25 2.25 4 4 2.25 2.25 5. 17 5.67 6.17 8. 75 8.75 21. 5
Georg ia 481 20.25 0 0000000000.25 00000.75 0. 75 0.75 0.25 0. 5 20. 25 0.25 1.25 0 0 0.75 0. 25 0.75 0.75 0. 75 1.5 1.25 1. 75 2.25 0. 75 1.5 0.5
Belaru s 994 10.44 0 000000000 0 00. 17 0.17 0. 22 00000.17 0.17 0. 33 0.5 0.5 0. 33 0.33 0.67 0. 7 0.74 1.22 1. 06 1.06 0.28 0. 28 0.28 0. 28 0.44 0.44
Italy 60 86, 498 1441.63 0 001122144 49.35 2. 43 11.1 9. 78 12.8 13 20. 8 24.9 30 23.7 33 42.3 42.5 52.7 52.7 62. 7 62.7 76. 3 86.2 96.1 104 93.9 84.1 87.3 92.3 97. 3 99.3
Switzerland 912,104 1344.89 0 0000000100.67 0.67 0.67 0. 78 2.22 3.33 13. 6 6.11 7.56 4. 67 12.9 16. 9 23.6 29.7 26. 4 46.7 46. 7 50 59.2 81.1 103 118 118 101 101 106 123 140
Austri a 97,697 855.22 0 0000000000.33 0.44 0.44 0. 67 0.56 1.33 3. 67 2.78 0.33 3. 22 5.67 7. 11 12.8 15.9 16. 8 21 25.1 29. 2 43.6 48.8 53. 9 50.3 68 85. 8 88.4 87.1 89. 4 91.7
Slovenia 2632 316.00 0 000000000 0 0 0 0 0. 5 2.5 1.5 1. 5 23. 75 3.75 13 19.5 22.5 20 19 17 11 11 11 16 16 15. 5 15.7 19 22.3 24.5 27.5
France 65 32, 964 507.14 0 0000000000. 66 0.46 0.74 0. 52 1.12 2. 12 2.92 3.16 4. 1 5.04 5.72 7. 65 9.15 12.1 12. 9 14.2 18. 6 18.5 22.4 26. 3 24.9 26.9 37. 1 47.4 40. 1 47.7 55.3 58. 6
Spain 47 64, 059 1362.96 0 0000000000. 68 0.36 0.66 0. 79 1.04 1.3 2. 4 1.19 8.23 8. 23 9.26 14. 5 14.5 26.1 32. 4 36.6 36.6 42. 3 54 73 75. 3 81 86.8 96.1 140 169 183 167
Portugal 10 4, 299 429.87 0 000000000 0 0.1 0. 1 0.2 0.1 0. 4 0.4 0. 8 0.9 0.9 1 1 1.9 3.4 5. 7 7.6 8.6 11. 7 17.7 19.1 23. 5 28 34.7 41. 3 41.2 49.5 57. 7 72.4
Germa ny 84 48,582 578.36 0 0000000000.64 0.21 0.33 0. 46 0.79 1.64 2. 9 1.99 1.08 2. 35 2.35 6.39 6. 39 8.25 8. 73 12.4 14 13. 2 32.2 51.3 48. 2 39 39.4 40. 4 40.4 59 68.8 74. 9
United_Kingd
68 14,543 213.87 0 0000000000.07 0.19 0. 06 0.16 0.5 0. 44 0.71 0. 63 0.99 0.71 0. 76 1.22 1.97 1. 72 6.37 3. 69 2.24 7.99 7. 99 9.95 9.95 12. 5 12.5 17. 6 17.6 21.4 31. 3 42.4
Poland 38 1, 389 36.55 0 000000000 0 0 00.03 00.05 0.05 0.03 0. 13 0.16 0.13 0. 24 0.47 0. 72 0.72 0.96 0. 96 1.45 1.45 1. 81 2.18 2. 56 2.58 3.03 3. 98 4.14 4.3 4. 42
Romania 19 1, 292 68.00 0 000000000 0 0 00.05 00.11 0. 05 0.32 0.11 0. 11 0.42 1. 05 11. 32 1.26 1. 37 2.16 2.12 2. 09 1.14 1.88 2. 61 4.82 6. 93 9.04 7.21 9. 3 11.4
Bulgaria 7293 41.86 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.29 0.29 00. 21 0.21 1. 71 1.71 1.43 1. 43 1.57 2.14 2. 14 2.29 3. 38 4.48 3.14 2. 43 2.71 33.14 4. 14
Netherlands 17 8,603 506. 06 0 0000000000.29 0. 35 0.29 0. 59 0.59 2.59 2. 98 3.59 4.2 3. 29 3.59 7.12 8. 08 8.94 9.8 10. 4 16.4 17. 2 20.4 24.1 33. 4 34.2 35 37. 3 43.3 49.3 59. 9 68.9
Belgium 12 7,284 607. 00 0 000000000 00. 08 0.5 0.42 0. 83 2.25 4.92 52. 58 3.25 2.33 3. 92 7.08 13.3 13. 6 13.6 14. 9 14.9 20.3 25. 8 38.5 47.3 41. 3 35.3 47. 8 69.2 90.7 87. 4
Czech_Repub
11 2,279 207.18 0 000000000 00. 27 0.18 00.27 0. 36 0.64 0. 64 0.55 0.73 2. 09 2.82 23.09 5. 82 6.48 6.67 6. 85 11.8 11. 8 13.7 13.7 11 11 17.5 25 32.6 19.7
Slovakia 2295 147.50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.5 10.5 0. 5 11. 5 5.5 4. 5 78. 5 11.5 6.5 6. 5 6.5 11.5 10. 3 9.17 4.75 4. 75 619.8 19.8
Greece 10 966 96.60 0 000000000 0. 3 0000.3 2.2 1. 3 2.1 0. 7 1.1 0.6 0. 9 3.4 5.7 5. 97 5.4 4.83 3.37 3. 73 4.1 3.3 3. 3 9.4 7.1 6. 3 6.3 7. 1 7.4
Hungary 10 343 34.30 0 000000000 0 0 0 0.1 0.1 0.1 0. 1 0.3 0.1 0. 1 0.2 0.2 0. 6 0.6 0. 7 0.7 0.55 0.55 1. 75 1.75 2.3 2.3 3. 07 3.17 3.27 3.7 3. 7 4.3
Denmark 62, 046 341.00 0 0000000000. 17 0.17 0. 17 0.5 0.33 1. 67 0.5 1.33 1. 17 12.5 25.2 42 26.7 21.3 3.83 8.5 10. 9 13.4 15.2 11. 7 11.7 11. 8 11.3 14.7 18. 2 22.2 25.5 28. 2
Finland 61,025 170. 83 0 000000000 00.25 0.25 0.17 0. 42 0.42 1.17 0. 92 0.92 1.67 1. 58 1.58 8 8 9.17 6.61 6. 06 5.5 6.75 6. 75 8.33 11. 8 15.8 15.1 14. 3 14.7 13 11. 2
Sweden 10 3,046 304.60 0 000000011 0.1 0. 1 0.1 0.9 1. 1 2.6 5 5 4.2 4.5 7.8 13. 6 15.8 15. 5 14.9 10.8 8. 9 4.6 12.8 12. 8 16.2 16.2 14. 3 17.5 20.7 23. 8 29.6 24
Norway 53, 581 716.20 0 000000010 1.8 0. 8 1.2 1.6 4. 6 65.4 6.8 4. 4 4.6 25.5 28. 6 31.7 28.6 28. 6 28.8 26. 7 24.7 23.9 28. 9 33.9 38.3 41. 9 45.6 54. 5 54.5 66.5 66. 5
Icel and 2890 445.00 0 000000001 0 1 1.5 5 5 4.5 4515558810. 5 15.3 15.3 16. 5 21.8 27. 2 35.8 35.8 28. 8 28.8 37.3 37. 3 38.3 38. 3
Irel and 52,121 424.20 0 000000000 0. 2 0 0 0. 2 0.8 1.4 10. 2 0.4 1.4 1. 4 1.6 5. 4 4.2 7.6 810. 8 13.8 14.8 33. 9 27.9 22 24. 2 42.8 43.9 44. 9 55.7 55. 7
Croatia 4586 146. 50 0 000000001 0 0. 5 0.25 0. 25 00. 25 0.25 0.25 0 0 0.25 0. 75 2.25 1.5 1.5 2. 75 23. 25 35.75 12. 8 12.8 10.8 14. 7 18.6 12.4 17 21.6
Serbi a 9457 50.78 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.11 0 0 0.22 0. 22 1.06 1.06 1. 22 1.22 0. 61 0.61 1.67 2. 44 2.28 2.28 1. 56 4.33 3. 78 4688.11
No rth _Mace d
2219 109.50 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0.5 0.5 0110.5 0. 5 110365.5 7 7 11 11 9. 33 10.5 11. 7 10.5 10.5
Lithuania 3358 119.33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.33 0.33 00. 5 0.5 1.33 1. 33 12.67 2.67 5 7 12 12.7 12 15.8 15.8 14 14
Latvia 2280 140. 00 0 000000000 00.25 0. 25 0000.25 0. 25 0.5 1.25 1. 25 2 2 1. 5 3 3 2. 5 8.75 8.75 10 10 7 7 16. 5 13.7 10.8 14. 8 14.8
Egypt 102 495 4.85 0 000000000 00.01 00000. 12 0.17 0.17 0. 06 0.04 0.1 0. 1 0.08 0.1 0. 11 0.16 0.39 0. 29 0.29 0. 29 0.22 0.23 0. 25 0.56 0.56 0. 26 0.26
Algeria 44 305 6.93 0 000000000 00.05 00.05 0.16 0.11 00. 03 0.03 0000. 09 0.05 0.25 0. 25 0.18 0.19 0. 2 0.23 0.16 0. 09 1.08 1. 08 0.89 0.88 0. 87 0
Morocco 37 345 9.32 0 000000000 00. 01 0.01 00.01 0. 01 00000.04 0.04 0. 03 0.03 0.3 0. 27 0.24 0.19 0. 27 0.43 0. 43 0.39 0.39 0. 51 0.97 1.44 1. 58 1.71
Tunisia 12 227 18. 92 0 000000000 00.04 0.04 000000.04 0.04 0. 25 0.17 0.5 0. 25 00.17 0.17 0. 33 0.42 0. 83 1111.17 2.08 3. 28 3.14 3
United_States
331 ###### 316.27 0 0000000000. 01 0.06 0. 04 0.07 0.1 0. 22 0.32 0.29 0. 37 0.6 0.82 0. 87 1.06 1.54 2. 35 2.49 2. 68 5.34 9.03 14. 6 16.2 21.5 25. 6 33.9 26. 6 42.2 50.7 56. 5
Mex ic o 129 717 5.56 0 0000000000. 02 0.01 000000. 01 0.01 00.02 0. 02 0.04 0.08 0. 12 0.09 0.22 0. 09 0.19 0. 36 0.3 0.37 0. 47 0.4 0.33 0. 54 0.85 1.02
Canada 38 4,689 123. 39 0.03 0000000000.11 0.11 0. 08 0.08 0.2 0. 2 0.16 0.16 0. 13 0.39 0. 42 0.48 0.73 0. 97 1.72 2.18 2. 63 3.61 3.7 3. 8 5.07 5.07 5. 24 5.68 8. 24 37.5 16.7 17. 7
Nigeria 206 24.21 0000000000000000000000000000.01 0. 02 0.01 0. 02 0.04 0.04 0. 04 0.03 0.05 0. 05 0.08
South_Africa 59 19.83 0 000000000 0 0 0 0 00.02 00.02 0. 02 0.07 00.1 0. 07 0.12 0.23 0. 23 0.19 0. 39 0.53 0.69 0. 7 0.71 1.11 1. 79 2.47 2.95 3. 46 3.98
Cameroon 27 3.26 0 000000000 0 0 0 0 00.02 0.02 0. 02 0.02 000000. 04 0.04 0.11 0. 11 0.07 0. 07 0.24 0.24 0. 54 0.54 0.59 0. 3 0.3 0
Senegal 17 7.00 0 000000000 00. 03 0.03 0.06 0. 06 0.06 0000000. 12 0.76 0.12 0. 29 0.06 0. 24 0.29 0.32 0. 32 0.53 0.65 0. 71 0.59 0. 59 0.59 0.59
Togo 83.13 0 000000000 0 0 0 0 00.06 0.06 0000000000000.5 0.5 0.38 0. 38 0.38 0. 31 0.31 0.13 0. 13
Australia 25 135.12 0.04 0000000000.04 0.12 0.16 0. 32 0.44 0.28 0. 16 0.44 0.24 0. 8 0.48 0.56 1. 2 1.79 1.89 23. 08 3.16 4.44 5. 76 6.6 16.7 16. 7 14.3 14. 3 14.9 14.9 8. 48
New_Ze aland
583.20 0 000000000 0 0 0.1 0.1 0.2 0. 2 0.2 0000000.2 0. 2 0.2 1.2 1. 2 1.6 2.2 2. 73 4.2 5.67 812.5 13. 1 13.6 15. 6
Brazil 212 16.12 0 000000000 0 0 0 0 00.02 0.02 00. 06 00.04 0.08 0. 12 0.1 0.2 0. 21 0.23 0.27 0. 65 0.91 1.24 1. 45 1.67 1. 63 1.46 1.49 1. 91 2.34
Colombia 51 10.57 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.02 00.02 0. 02 0.06 0.06 0. 07 0.07 0.35 0. 22 0.24 0. 44 0.44 0.54 0. 71 0.88 0.94 0. 94 1.54 1. 21 0.88 0.94
Argentina 45 15.33 0 000000000 0 00. 01 0.01 0.01 0. 01 0.13 0.02 0. 07 0.08 0. 08 0.13 0.13 0. 07 0.24 0.24 0. 2 0.31 0.4 0. 69 0.94 1.02 1. 1 1.16 1.75 2. 34 1.93 2. 24
Peru 33 19.24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.03 0.09 0.09 0.06 0. 06 0.18 0. 15 0.48 0.15 0. 85 0.45 0.91 1. 49 2.08 1. 27 1.27 1.36 0. 97 1.86 1.87 1. 88 1.67
Chile 19 23184.74 0 000000000 0 0 00.05 0.11 0. 05 0.05 0.13 0. 13 0.16 0. 21 0.32 0.53 0. 53 0.84 0.84 3. 32 3.32 3. 71 3.71 5.13 5. 13 5 6 9. 26 11.6 12.3 12. 3
Ecuador 18 90.39 0 0000000000.06 0.28 0.06 0.08 0. 08 0.17 0 0 0. 06 0.06 0. 11 00. 17 0.17 0. 28 0.5 1.17 2. 94 3.17 5.35 6. 74 8.13 13.1 10. 2 7.3 8.33 10. 1 11.9
Dominican_Re
11 52. 82 0 000000000 00.09 00000.09 0 0 0.27 0000. 55 00000.45 0. 45 4.14 4.14 8. 18 3.91 6. 09 7.27 8.73 8. 45
Costa Ri ca 552.60 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.2 00. 8 0.8 0.8 1. 8 0.2 0. 6 0.9 0.9 1. 2 1.8 3.8 4. 13 3.2 2.27 3. 4 4.47 4.47 4.47 66.4
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Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -7-
Time-course by country/region
Among the Hubei population of 58.5M, the incidence rose from the first case reported in late 2019
to about 60 new cases per million people per day by 02-05 and then steadily declined (Fig 1) from
~4000 on 02-05 to below 50 cases per day since 03-08.
Fig 2: COVID-19 cases in Mainland China. Blue: cases/M/d, red: deaths/M/d. Around Feb 13, the case definition was
expanded, resulting in additional cases from previous days being added. Hence, the 02-13 cases have been truncated.
Most cases were seen in the Hubei province of 58.5M people (see Table 1 for population sizes).
By Mid-January 2020, the first cases of COVID-19 were seen in other Asian countries, but inci-
dence remained below about 1/M/d outside of continental China, except for an increase to about
2.5/M/d in Malaysia/Brunei and 10/M/d in Singapore, but including Japan with the largest propor-
tion of people 65 years of age and older in the world (28%).
Fig 3: COVID-19 cases in Maritime Asia. See Fig 1 for legend.
In continental South Korea (population 51M, cumulative incidence 185/M), however, the incidence
soon rose to a peak of about 14/M/d between 02-29 and 03-02, before declining to less than 150
cases per day (3/M/d) since 03-12 (Fig 2a).
In Iran (cumulative incidence 385/M), incidence rose about a week after South Korea. The top
incidence before 03-23 (~15.5 cases/M/d) was about the same (the recent increase on 03-24..28
may indicate a “rebound” into a population not immunized by the previous wave(s)). Lethality in
Iran was notably higher and followed the increase in cases with a delay of several days (Fig 2b)
as also seen in South Korea (Fig 2a, 03-06 for deaths vs 02-28..03-01 for cases).
0
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China
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Maritime Asia
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Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -8-
Fig 4: COVID-19 cases in South Korea and Iran. See Fig 1 for legend.
From 03-19 to 03-20, several European countries have seen a more than two-fold increase in the
number of cases reported (Germany: 570%, San Marino: 340%, Ireland: 260%, Switzerland:
240%, Austria: 202%). As natura non facit saltum (Darwin: nature doesn’t jump),(Berry 1985) such
abrupt increases must be, at least in part, the result of reporting or other artifacts. In Germany, for
instance, the reporting system was changed between 03-16 and 03-19, so that the number is
likely includes cases previously reported only through a parallel system. France, Italy, and Spain
also reported an unusual increase by 27–35 percent. All these countries reported lower in the
following days. As more data are reported, some averaging has been applied.
0
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Iran
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Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -9-
Fig 5: COVID-19 cases in Italy and it’s neighboring countries. Italy (top), European countries neighboring Italy (IT+,
middle. Spain also shown separately. See Fig 1 for legend.
Among European countries with a population of more than 2M, Italy has the highest cumulative
incidence per capita (Table 1, Fig 3a), followed by its neighbors Spain and Switzerland (included
in Fig 3b). In all three European countries, the cumulative incidence is now similar to that in the
Hubei province (their population of 50–60 M is also similar).
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Italy
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IT Neighbors (CH/F/ES/AT/SI )
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Spain
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Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -10-
The overall epidemic in Europe (Fig 4a) is a population weighted average of the high incidence
regions (Fig 4a, weighted average of Fig 3) and the remaining low incidence countries (Fig 4c).
Fig 6: COVID-19 cases in Europe. Early onset/high lethality (IT and neighbors, top), total (middle), and late onset/low
letality (other European countries, bottom). See Fig 1 for legend.
The incidence in the countries with early onset and high lethality (Italy and its neighbors, including
Spain and France) now seems to be leveling off, after about 4 weeks from 1/M (Italy: 02-26..~03-
22, neighbors: 03-01..~04:01), compared to Hubei’s and South Korea’s 2 weeks (01-19..02-05
0
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EU/high
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Europe
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EU/low
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Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -11-
and 02-21..03-06). Other European countries, where the epidemic started more slowly, may see
the peak in early April. Germany is notable for reporting 48,582 cases, but only 325 deaths (03-
28).
Fig 7: COVID-19 cases in selected European countries. See Fig 1 for legend. Data in Germany is based on cases
reported electronically to the Robert-Koch-Institute (RKI) and transmitted to the ECDC, but the RKI also provides two
sources of data on its Web site that are difficult to reconcile with these data.
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Germany
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France
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Austria
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Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -12-
The epidemic in North America started later, especially in the US (except for a few isolated cases
likely imported directly from Asia). The incidence is still lower than in the older European popula-
tion, but keeps rising, as “more and more states are reporting” (https://www.cdc.gov/coronavirus/2019-ncov/cases-
updates/summary.html, accessed on 03-18). The increase seen is consistent with the dynamics of an emerging
epidemic. Cumulative incidence in the US (260/M) is still about half of that in Europe (507/M),
which reflects, at least in part, the later onset of the epidemic in the US.
Fig 8: COVID-19 cases in the North America. See Fig 1 for legend. The high peak in the Canadian data on 03-26
cannot be reconciled with the dynamics of a respiratory disease spreading.
A Widow of Opportunity for Containment (Social Distancing)
The effect of reducing the reproduction number by reducing the number of contacts (“contain-
ment”, “Social Distancing”) depends on when it starts in the course of the epidemic. Fig 10 shows
the effect of a one- month intervention cutting R0 in half starting at the point of the peak prevalence
of infectious subjects. Compared to Fig 1, the duration of the epidemic is shortened, albeit at the
price of reducing the R/S ratio, so that a subsequent epidemic with the same are similar virus
(cross-immunity) could start earlier.
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Canada
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United_States_of_America
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Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -13-
Fig 9: SIR Model of SARS, Window of Opportunity for Fast Eradication of the Epidemic. (see Fig 1 for legend).
The gray area indicates the period where containment can give a “coup de grace” to a respiratory disease epidemic.
The more narrow bell curve with a post-peak intervention indicates the reduction in number of infections and, thus,
deaths.(spreadsheet for model calculations available from https://app.box.com/s/pa446z1csxcvfksgi13oohjm3bjg86ql )
Fig 11 shows a one-month intervention starting about two weeks earlier, at the turning point where
the curve of the new cases changes from increasing faster to increasing more slowly. This inter-
vention reduces the number of deaths, but the epidemic is extinguished two months later and the
R/S ratio (“herd immunity”) is further decreased.
Fig 10: SIR Model of SARS, Window of Opportunity for Maximal Reduction of Total Deaths. (see Fig 1 for legend).
The gray area indicates the period where containment can have the most impact on total number of deaths. However,
the epidemic is not eradicated.(spreadsheet for model calculations available from https://app.box.com/s/pa446z1csxcvfksgi13oohjm3bjg86ql )
Fig 12 shows the effect of an intervention that starts even earlier, about two weeks before the
intervention in Fig 11. Even if the intervention is extended from one to four months no herd im-
munity is created and, thus, the epidemic rebounds.
`
``
`
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Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -14-
Fig 11 : SIR Model of SARS, Effect of Early Social Distancing / Lockdown. (see Fig 1 for legend). It is assumed
that a highly effective intervention reduces R0 by 50% for 4 months, beginning after the appearance of a novel type of
cases is noticed. The death rate of 5K/10M is arbitrary.(spreadsheet for model calculations available from
https://app.box.com/s/pa446z1csxcvfksgi13oohjm3bjg86ql )
In summary, there is a narrow window-of-opportunity for interventions (“flattening the curve”) aim-
ing to improve public health by reducing R0:
• Starting after the peak prevalence (of infections) has little effect (not shown). The curve
goes down, but is not “flattened”.
• Starting at the peak prevalence gives the epidemic a “coup de grace”, shortening its du-
ration, albeit at the price of reducing the R/S ratio. The curve is narrower, but not “flat-
tened”.
• Starting at the peak incidence “flattens” the curve without broadening it and maximizes
the number of deaths prevented during the current epidemic, but reduces herd immunity
and, thus, the chance of another epidemic coming sooner.
• Starting before the peak incidence “flattens the curve”, but also broadens it and causes
a rebound, unless the intervention is continued for many more months.
It is herd immunity that stops the spread of an infectious disease, so in general, one would want
to let the epidemic initially run its natural course (or even accelerate it, as people have traditionally
done with “measles parties”) to build immunity as fast as possible.
To reduce the duration of the epidemic and its impact on the economy (and also increase the time
until the next epidemic can spread), one would wait until the prevalence of infectious people (I)
reaches its peak (in the above model: day 83, red).
Without repeated broad testing, however, this date cannot be directly observed, but it is known
that peak prevalence of infected people is followed about a week by peak number of new cases.
This is too late to make a decision, but the SIR model shows that this peak preceded by two
weeks by the “turning point” in cases where the curve of the new cases changes from increasing
faster to increasing more slowly (day 76), which can be estimated from the observed cases in
time to making a decision. (It is also about 50% of the peak number of new cases, which one
might be able to predict.) Hence, peak prevalence (of infections) follows the turning point/half
peak (in number of cases) by about a week. The window of opportunity for starting an inter-
vention is the week following the turning point in number of cases per day.
`
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Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -15-
Discussion
Strengths and shortcomings
A major strength of this analysis of the epidemiological data is that it does not rely on epidemio-
logical models with questionable assumptions. Instead, the results reflect raw incidences over
time as reported by the ECDC, depicted by country or region of neighboring countries.
A shortcoming of such an entirely data-based approach is that it lacks the sophistication and
potential additional insights that could come from fitting, e.g., differential equation models. The
only modeling assumption made is that curves should be “smooth” (except when reporting arti-
facts are suspected), but even then, data were redistributed only to the directly neighboring day.
Still, the evidence is strong enough to draw qualitative conclusions about possible scenarios for
the spread of SARS-CoV-2 in the near future. Also, the results suggest strategies to explore the
variability of the SARS-CoV-2 virus strains and to select prevention strategies.
Evidence for (at least) two different strains of SARS-CoV-2
During the 2003 SARS epidemic the number of new cases peaked about three weeks after the
initial increase of cases was noticed and then declined by 90% within a month. Table 1 shows the
relevant timepoints for the 2020 COVID-19 epidemic. The SARS-C0V-2 data also suggest that it
takes at least a month from the first case entering the country (typically followed by others) for the
epidemic to be detected, about three weeks for the number of cases to peak and a month for the
epidemic to “resolve”. This data is consistent with the results from the SIR model (see Epidemio-
logical Models).
Table 2: Epidemiological Timepoints by Country Top : 2003 SARS, Bottom: 2020 SARS-CoV-2
First
cases
Gap
[d]
Begin
(>.1/1M)
Gap
[d]
Peak
Gap
[d]
End
(<.1/1M)
Begin to
End [d]
CA/SGH
02-23
03-02
18
03-20
28
04-18
28
(Svoboda 2004)
CA/NYG
04-20
04-27
30
05-27
6
06-03
36
(Svoboda 2004)
Guangdong
2002 (10)
>50
01-19
22
02-11
81
05-02
103
(Cao 2019)
Shanxi
03-15
34
04-19
30
05-19
64
(Cao 2019)
Beijing
03-05
49
04-24
30
05-24
69
(Zhou 2003; Cao 2019)
Mongolia
03-22
22
04-14
40
05-24
62
(Cao 2019)
Hebei
04-04
20
04-24
24
05-19
44
(Cao 2019)
Tianjin
04-14
8
04-22
12
05-04
20
(Cao 2019)
HK/PWH
02-21
03-11
6
03-17
HK/AG
03-20
4
03-24
29
04-13
(Zhou 2003; Leung 2004)
HK/
04-12
54
06-06
Taiw a n
02-24
23
03-17
38
04-25
50
06-14
88
(Small 2003; Yeh 2004)
Singapore
03-15
20
04-05
24
04-29
44
(Small 2003; Goh 2006)
Vietnam
02-23
11
03-04
28
04-06
39
(Shi 2003)
Median 2003
03-15
20
04-13
29
05-19
44
China (Hubei)
2019 (27)
>50
01-17
18
02-05
27
03-18
60
0 in Hubei
S- Korea
01-20
31
02-19
12
03-01
>25
>03-25
>37
Ongoing low level
Iran
02-20
2
02-22
14
03-07
Several waves?
Italy
01-31
22
02-22
30
03-22
2nd wave?
Germany
01-28
30
02-27
France
01-25
31
02-27
>30
?04-01
~04-15?
US
01-25
40
03-05
>30
?04-o7
~05-01?
Median 2020
31
02-22
25
03-25
~04-15?
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The 2003 SARS and the 2020 SARS-CoV-2 are not only similar with respect to genetics (79%
homology),(Lu 2020) immunology,(Ahmed 2020) involvement of endocytosis (also with influenza and syn-
cytial viruses),(Behzadi 2019) seasonal variation (same season in the northern hemisphere also with
influenza, syncytial, and metapneumo viruses)(Olofsson 2011), evolution (origin in bats, 88% homol-
ogy),(Benvenuto 2020; Malik 2020) but also with respect to the duration between emergence and peak of
cases as well as between this peak and resolution of the epidemic (Table 1). Based on these
similarities, one could predict the COVID-19 epidemic to end before 04-15 in Europe and about
two weeks later in the U.S.
The time and height of the peak incidence if cases in the different countries are consistent with
the hypothesis that SARS-CoV-2 moved step-by-step westward from China, via other Asian coun-
tries to Middle East (Iran. Qatar, and Bahrain), Southern Europe (Italy, followed by its neighbors
CH/F/ES/AT/SI), central and northern Europe, and, finally, the US.
Viruses improve their “survival” if they develop strategies to coexist with the (human) host.(Woolhouse
2007) Multiple coronaviruses have been found to coexist in bat populations.(Ge 2016) The emerging
COVID-19 data is consistent with the hypothesis that (at least) two SARS-CoV-2 strains have
developed. One strain, which traveled through South Korea, remained more infectious, while the
other strain, which traveled through other Asian countries lost more of its infectiousness. The
strain that passing through South Korea and then Iran and Italy (SKII strain) showed high lethality
in Iran and Italy, but less lethality when it traveled to Italy’s neighbors, either because of differ-
ences in health systems, because the strain mutated back, or because a strain arriving directly
from Asia had the advantage of spreading first. Only sequencing samples from these countries
can help to answer these questions.
Fig 12: Hypothetical virus transmission pathways. Connection width: number of contacts, box colors: infectious-
ness, box borders: lethality, dotted connections/borders: unknown. The end date of a box indicates the date of peak
incidence, if known (bold date).
Changes in infectivity and lethality between China and Europe
Mainland China is not reporting relevant numbers of novel cases anymore and Hubei reports no
new cases since 03-19. The number of new cases in South Korea also has declined to low levels
since its peak around 02-30. Maritime Southeast Asia continues to show low levels of new cases
only (<2.5/M/d), with the possible exception of Singapore and Malaysia/Brunei.
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The data are consistent with the same “SKII” strain traveling from China via South Korea and Iran
to Italy. Iran was hit about a week after South Korea (around 03-07), with a similar peak incidence,
but higher lethality (red bars in Fig 2). The data also suggests a second wave of infections in Iran,
which may have peaked on 03-15. Italy was hit a week after the first wave in Iran (which peaked
around 03-07/08, Fig 4a). Incidence in Italy reached a substantially higher incidence than reported
in Iran. The peak incidence in Italy may have been reached on 03-22 (at about 100/M/d).
Without sufficiently detailed genetic data, it is not clear whether the high lethality in Italy is due to
genetic variations in the virus or to Italy having the second oldest populations in the world (after
Japan). A 03-20 report by the Istituto Superiore di Sanita,(COVID-19 Surveillance Group 2020) however, impli-
cates that age and comorbidities played a role – among 3200 deaths, mostly in Lombardy and
Emilia-Romana, median age was 80 years (IQR 73-85, only were 36 below the age of 50), 98.8%
had at least one comorbidity (hypertension: 74%, diabetes: 34%, ischemic heart disease: 30%,
atrial fibrillation, 22%, chronic renal failure: 20%, …).
The epidemiological data does not support the hypothesis that SARS-CoV-2 spread from Munich
in Germany to Italy.(Kupferschmidt 2020) Instead, the virus may have spread from Italy to its neighboring
countries, Switzerland, France, Spain, Austria, and Slovenia, within just a few days of arriving
from Iran. The top incidence seems to be less than half of that in Italy and the lethality is lower,
too. While Italy has many people 65 years and older (23%, second only to Japan data.worldbank.org/indi-
cator/SP.POP.65UP.TO.ZS), the relatively small differences or age distribution within Europe (e.g., Ger-
many: 21%) are unlikely to account for much of this difference. A possible explanation (indicated
in Fig 6) is that the less virulent strain(s) arriving from other parts of Asia may have had a head
start in those countries, so that imported infections from Italy met subjects who had already de-
veloped (cross) resistance against both strains.
Infections in Scandinavia arrived yet another half week later, but peaked around 03-12. The recent
data may indicate a second wave more similar to other European countries. The parts of Europe
not hit by the SKII strain may remain at much lower levels (below 30/M/d, except for effects of the
recent changes in the reporting systems). Overall, incidence in Europe seems to be leveling off.
After the effects of the changes I the reporting system have ceased, incidence in Europe may
peak soon at about 40/M/d.
Predictions for COVID-19 in North America
From Table 1, SARS-CoV-2 has arrived in the U.S. almost a week after it arrived in Europe. The
incidence is still low (currently at about 55/M/d) and is likely to continue to increase until early
April. If incidence in the U.S. were to peak at about 75/M/d, as in Europe as a whole (Fig 4b), one
would expect new cases to peak at up to 25,000 per day and the cumulative incidence could
reach 600/M (3 times the number of cases per million people in South Korea to account for a
longer course because of the size of the countries) or a total of 200,000 cases, and, at 2% lethality,
about 4,000 deaths, about four times the currently reported cumulative number of 1,079. These
are conservative estimates, because only 1% of cases died in South Korea over the course of the
epidemic and both countries have a similar proportion of people older than 65 years (14% vs
16%) On the other hand, the numbers could double if the SKII strain should have hit the US
earlier. A number of 4000–8000 U.S. death over the course of the epidemic compares to an ex-
pected number of 16,000–78,000 influenza deaths per season from pneumonia and respira-
tory/circulatory complications alone, which also occur predominantly among people at 65 years
of age and older.(Rolfes 2018).
The precise number of people dying depends on (a) which virus strain got to the US first and (b)
how early people are being treated against severe complications (e.g., pneumonia).
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A historical perspective
This is not the first, and likely not the last time, that well-intentioned public health policies are
inconsistent with our understanding of how epidemics spread. For instance, during much of the
HIV epidemic, there was widespread fear that HIV could establish itself in the population as a
whole, even though the data (including data showing absence of transmission to the wives of
hemophiliacs)(Wittkowski 1995a) and models(Wittkowski 1992; Seydel 1994) contradicted this fear.(Wittkowski 1995b; 1996)
These results have been repeatedly confirmed.(Centers for Disease Control and Prevention 2019; H addad 2019) In the
case of heterosexual transmission of HIV one could argue that there was little risk associated with
a the public health policy promoting condom use, but in the case of COVID-19 prevention, ignoring
models and data may carry substantial risk.
During the AIDS epidemic, epidemiologists had the advantage that, in addition to the date of re-
port, the date of diagnosis was available for analysis so that variations in reporting delays, such
as mid-February in China, 03-20 in Germany, and 03-26 in Canada, could be accounted for. Un-
fortunately, the public COVID-19 data lacks that information.
Implications for prevention
A major problem with respiratory diseases is that one cannot stop all chains of infections within
families, friends, neighbors, … . Even after a couple of weeks of “lockdown” there will be a few
infectuous persons, and as long as there are enough susceptible people in the society, this is
enough to re-start the epidemic until there are enough immune people in the society to create
“herd immunity”. Hence, one would expect the cases to appear in waves (Fig 12, the period of
the “lockdown” corresponds to March to May, 2020 in the U.S.). Such waves of cases have been
seen in different countries and the longer than expected duration of the epidemic supports the
hypothesis that the social distancing / lockdown interventions had some effect, albeit at a high
cost for approx. 10% of deaths saved.
This analysis of the publicly available data suggests that at the time Italy imposed quarantine on
the Lombardy and adjacent regions on 03-08, the SKII virus strain had already reached the adja-
cent countries (Switzerland, France, Spain, Austria, Slovenia). Even though the lockdown started
early (03-08), which may have caused a rebound consistent with a decline in compliance.
In the US, the growth in reported cases per day slowed down after 03-20, yet there is no sign of
a turning point, yet. Still, New York, New Jersey, and Connecticut restaurants were ordered to
closed from 03-20; the shutdown of California was ordered on 03-19 (Executive order N-33-20). As social
distancing was ordered before the epidemic reached its turning point, a “flattened curve” is to be
expected, but the curve will also be broader.
Some containment strategies could even be counterproductive in other ways. For instance, the
simple model used in Fig 12 does not account for age-stratification. In diseases such as COVID-
19, where children develop mostly mild forms, while elderly people have a high risk of dying.(Zim-
mermann Curtis 2020) Hence, containment of high-risk groups, like elderly people in nursing homes (see
the Washington State example) is highly effective in protecting them from becoming infected and
reducing the pool that would have to reach herd immunity. A substantial increase in the duration
of the epidemic, however, might make effective containment of the elderly more difficult and, thus,
increase the number of deaths among the elderly.
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In the U.S. as a whole, the “turning point” for cases cannot be earlier than 03-25, but the New
York Times reports that New York and Detroit reached the turning point on 03-19. Hence, the
optimal time point for starting a New York public health intervention to reduce duration and impact
of the COVID-19 epidemic was around 03-27. Social segregation against COVID-19 in NY, as
one of the epicenters of the U.S. epidemic, started about 03-17 (day 73) with restaurants being
closed, and intensified on 03-22 (day 78) with all non-essential businesses being closed. Because
of the Easter holiday, restrictions are discussed to be lifted on 04-12 (day 100). The model predicts
that such an intervention would reduce the number of deaths in New York and Detroit (and pos-
sibly some other parts of the U.S., but the virus would linger on for another two months, so that it
would not be safe for (elderly) high-risk people to participate in this year’s Easter activities.
Fig 13: SIR Model of SARS, Phased in Restrictions. (see Fig 1 for legend). The gray areas indicates the periods of
low and high intensity restrictions).(spreadsheet for model calculations available from https://app.box.com/s/pa446z1csxcvfksgi13oohjm3bjg86ql )
Conclusions
Until a vaccine will become available, the only pharmacological strategy to reduce the number of
deaths is to reduce the damage the infection (and immune system) does, e.g., by reducing the
initial viral load,(Chu 2004) and making sure that people get treated at the earliest signs of pneumonia.
Aside from separating susceptible populations (elderly and high-risk subjects, e.g., in nursing
homes) from the epidemic, which is effective as long as virus is circulating, public health interven-
tion aiming to contain a respiratory disease need to start within a narrow window of opportunity
starting at or a week after the curve of the new cases changes from increasing faster to increasing
more slowly. Unless the containment efforts started earlier and prevented the epidemic from gen-
erating a sufficient number of immune people, the containment efforts can cease after about a
month or two (depending on late or early start, respectively), when the ratio of infectious vs im-
mune people is too low to for the disease to rebound. When the window of opportunity has been
missed, containment has only limited impact on the course of the epidemic.
To determine that time point, case data collected and reported needs to contain not only the date
of report, but also the date of “diagnosis” and whether the patient had clinical symptoms or was
merely tested positive and whether the patient was positive for circulating virus RNA/DNA (cur-
rently infectious) or antibodies (already immune).
``
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References
Ahmed SF, Quadeer AA, et al. (2020). Preliminary Identification of Potential Vaccine Targets for the
COVID-19 Coronavirus (SARS-CoV-2) Based on SARS-CoV Immunological Studies. Viruses 12(3).
Behzadi MA, Leyva-Grado VH (2019). Overview of Current Therapeutics and Novel Candidates Against
Influenza, Respiratory Syncytial Virus, and Middle East Respiratory Syndrome Coronavirus Infections.
Frontiers in microbiology 10: 1327.
Benvenuto D, Giovanetti M, et al. (2020). The global spread of 2019-nCoV: a molecular evolutionary
analysis. Pathog Glob Health: 1-4.
Berry RJ (1985). Natura non facit saltum. Biological Journal of the Linnean Society 26(4): 301-5.
Cao W, Fang L, et al. (2019). What we have learnt from the SARS epdemics in mainland China? Global
Health Journal 3(3): 55-9.
Cascella M, Rajnik M, et al. (2020). Features, Evaluation and Treatment Coronavirus (COVID-19).
StatPearls. Treasure Island (FL), StatPearls Publishing.
Centers for Disease Control and Prevention (2019). Estimated HIV incidence and prevalence in the
United States, 2010-2016. HIV Surveillance Supplemental Report 24(1).
Chu CM, Poon LL, et al. (2004). Initial viral load and the outcomes of SARS. Cmaj 171(11): 1349-52.
COVID-19 Surveillance Group (2020). Characteristics of COVID-19 patients dying in Italy Report based
on available data on March 20th, 2020. Rome, Italy, Istituto Superiore di Sanita.
Dietz K (1993). The estimation of the basic reproduction number for infectious diseases. Stat Methods
Med Res 2(1): 23-41.
Ge XY, Wang N, et al. (2016). Coexistence of multiple coronaviruses in several bat colonies in an
abandoned mineshaft. Virol Sin 31(1): 31-40.
Goh KT, Cutter J, et al. (2006). Epidemiology and control of SARS in Singapore. Ann Acad Med
Singapore 35(5): 301-16.
Haddad N, Robert A, et al. (2019). HIV in Canada-Surveillance Report, 2018. Can Commun Dis Rep
45(12): 304-12.
Jernigan DB (2020). Update: Public Health Response to the Coronavirus Disease 2019 Outbreak - United
States, February 24, 2020. MMWR Morb Mortal Wkly Rep 69(8): 216-9.
Kermack WO, McKendrick AG (1991). Contributions to the mathematical theory of epidemics--I. 1927.
Bull Math Biol 53(1-2): 33-55.
Kupferschmidt K (2020). Genome analyses help track coronavirus' moves. Science 367(6483): 1176-7.
Lauer SA, Grantz KH, et al. (2020). The Incubation Period of Coronavirus Disease 2019 (COVID-19)
From Publicly Reported Confirmed Cases: Estimation and Application. Ann Intern Med.
Leung GM, Hedley AJ, et al. (2004). The epidemiology of severe acute respiratory syndrome in the 2003
Hong Kong epidemic: an analysis of all 1755 patients. Ann Intern Med 141(9): 662-73.
Lu R, Zhao X, et al. (2020). Genomic characterisation and epidemiology of 2019 novel coronavirus:
implications for virus origins and receptor binding. Lancet 395(10224): 565-74.
Malik YS, Sircar S, et al. (2020). Emerging novel coronavirus (2019-nCoV)-current scenario, evolutionary
perspective based on genome analysis and recent developments. Vet Q 40(1): 68-76.
Olofsson S, Brittain-Long R, et al. (2011). PCR for detection of respiratory viruses: seasonal variations of
virus infections. Expert Rev Anti Infect Ther 9(8): 615-26.
Ren SY, Gao RD, et al. (2020). Fear can be more harmful than the severe acute respiratory syndrome
coronavirus 2 in controlling the corona virus disease 2019 epidemic. World J Clin Cases 8(4): 652-7.
Rogers K, Jakes L, et al. (2020). Trump Calls It the ‘Chinese Virus.’ Critics Say That’s Racist and
Provocative. New York Times. New York, A.G. Sulzberger: 11.
Rolfes MA, Foppa IM, et al. (2018). Annual estimates of the burden of seasonal influenza in the United
States: A tool for strengthening influenza surveillance and preparedness. Influenza Other Respir
Viruses 12(1): 132-7.
Seydel J, Kramer A, et al. (1994). Backcalculation of the number infected with human immunodeficiency
virus in Germany. J Acquir Immune Defic Syndr 7(1): 74-8.
Shi Y (2003). Stochastic dynamic model of SARS spreading. Chinese Science Bulletin 48: 1287-92.
Small M, Shi P, et al. (2003). Plausible models for propagation of the SARS virus. Trans Fundam
Electron, Commun Comput Sci E87-A.
. CC-BY-ND 4.0 International licenseIt is made available under a
author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the(which was not peer-reviewed) The copyright holder for this preprint .https://doi.org/10.1101/2020.03.28.20036715doi: medRxiv preprint
Knut M. Wittkowski: Two epidemics of COVID-19 (2020-03-28) -21-
Svoboda T, Henry B, et al. (2004). Public health measures to control the spread of the severe acute
respiratory syndrome during the outbreak in Toronto. N Engl J Med 350(23): 2352-61.
Wittkowski KM (1992). Estimates of HIV prevalence in Germany and the U.S. – Sensitivity to assumptions
concerning reporting delays and incubation time. VIII International Conference on AIDS / III STD World
Congress, Amsterdam, NL, Congrex Holland.
Wittkowski KM (1995a). Entwicklung der HIV-Epidemie bei Hämophilen anhand der Zahlen des Robert-
Koch-Instituts (Berlin). 25 Hämophilie-Symposion, Hamburg 1994. I Scharrer and W Schramm. Berlin,
D, Springer: 20-8.
Wittkowski KM (1995b). [Epidemiology of HIV in Germany]. Gesundheitswesen 57(5): 291-8.
Wittkowski KM (1996). [Epidemiology of HIV in Germany (status: 30 June 1995)--transmission among
heterosexuals and value of HIV screening programs]. Gesundheitswesen 58(4): 229-33.
Woolhouse M, Gaunt E (2007). Ecological origins of novel human pathogens. Crit Rev Microbiol 33(4):
231-42.
Yeh SH, Wang HY, et al. (2004). Characterization of severe acute respiratory syndrome coronavirus
genomes in Taiwan: molecular epidemiology and genome evolution. Proc Natl Acad Sci U S A 101(8):
2542-7.
Zhou G, Yan G (2003). Severe acute respiratory syndrome epidemic in Asia. Emerg Infect Dis 9(12):
1608-10.
. CC-BY-ND 4.0 International licenseIt is made available under a
author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the(which was not peer-reviewed) The copyright holder for this preprint .https://doi.org/10.1101/2020.03.28.20036715doi: medRxiv preprint
