Dear Editor
,
Previous workers have attempted to predict the cumulative number of cases of Coronavirus
Disease 2019 (COVID-19) in China.
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However, since then, the epidemic has rapidly evolved into a pandemic affecting multiple
countries worlwide.
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There have been serious debates about how to react to the spread of this disease,
particularly by European countries, such as Italy, Spain, Germany, France and the
UK, e.g. from closing schools and universities to locking down entire cities and countries.
An alternative strategy would be to allow the causal virus (SARS-CoV-2) to spread
to increase the population herd immunity, but at the same time protecting the elderly
and those with multiple comorbidities, who are the most vulnerable to this virus.
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Before initiating either of these strategies, we need to estimate the basic reproductive
number (R0), or the more ‘real-life’ effective reproductive number (Rt) for a given
population. R0 is the number of secondary cases generated by the presence of one infected
individual in an otherwise fully susceptible, well-mixed population. Rt is a more
practical real-life version of this, which uses real-life data (from diagnostic testing
and/or clinical surveillance) to estimate the reproductive number for an ongoing epidemic.
For this anaylsis, we will estimate Rt, and we can do this by applying the exponential
growth method,
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using data on the daily number of new COVID-19 cases, together with a recent estimate
of the serial interval (mean = 4.7 days, standard deviation = 2.9 days),
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at a 0.05 significance level, with the mathematical software R (v3.6.1.).
Using these values of Rt, we can then calculate the minimum (‘critical’) level of
population immunity, Pcrit, acquired via vaccination or naturally-induced (i.e. after
recovery from COVID-19), to halt the spread of infection in that population, using
the formula: Pcrit= 1-(1/Rt). So, for example, if the value of Rt = 3 then Pcrit= 0.67,
i.e. at least two-thirds of the population need to be immune.
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As of 13 March 2020, there were 32 countries outside China with over 100 COVID-19
cases.
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The seven countries with the highest number of infections were: the United States
(n = 2294), France (n = 3671), Germany (n = 3675), Spain (n = 5232), Korea (n = 8086),
Iran (n = 11,364) and Italy (n = 17,660). The number of confirmed cases in the other
25 countries were less than 1200 (Table 1
).
Table 1
Estimates of SARS-CoV-2 effective reproduction number (Rt) of 32 study countries (as
of 13 March 2020,
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), and the minimum proportion (Pcrit, as% of population) needed to have recovered
from COVID-19 with subsequent immunity, to halt the epidemic in that population.
Table 1
Study countries
Population infected by COVID-19
Estimates of effective reproduction number (Rt) (95% CI), (n = 32)
Minimum proportion (%) of total population required to recover from COVID-19 to confer
immunity (Pcrit)
Rt >4
Bahrain
210
6.64 (5.20, 8.61)
85.0
Slovenia
141
6.38 (4.91, 8.38)
84.3
Qatar
320
5.38 (4.59, 6.34)
81.4
Spain
5232
5.17 (4.98, 5.37)
80.7
Denmark
804
5.08 (4.60, 5.62)
80.3
Finland
155
4.52 (3.72, 5.56)
77.9
Rt (2–4)
Austria
504
3.97 (3.56, 4.42)
74.8
Norway
996
3.74 (3.47, 4.04)
73.3
Portugal
112
3.68 (2.86, 4.75)
72.8
Czech Republic
141
3.57 (2.88, 4.45)
72.0
Sweden
814
3.44 (3.20, 3.71)
70.9
The United States
2294
3.29 (3.15, 3.43)
69.6
Germany
3675
3.29 (3.18, 3.40)
69.6
Switzerland
1139
3.26 (3.05, 4.78)
69.3
Brazil
151
3.26 (2.99, 3.55)
69.3
Netherlands
804
3.25 (3.02, 3.51)
69.2
Greece
190
3.12 (2.67, 3.67)
67.9
France
3661
3.09 (2.99, 3.19)
67.6
Israel
143
3.02 (2.56, 3.59)
66.9
The United Kingdom
798
2.90 (2.72, 3.10)
65.5
Italy
17,660
2.44 (2.41, 2.47)
59.0
Canada
198
2.30 (2.07, 2.57)
56.5
Iceland
134
2.28 (1.90, 2.75)
56.1
Rt (1–2)
Iran
11,364
2.00 (1.96, 2.03)
50.0
Australia
199
1.86 (1.71, 2.03)
46.2
Belgium
559
1.75 (1.55, 1.97)
42.9
Malaysia
197
1.74 (1.61, 1.88)
42.5
Iraq
101
1.67 (1.41,1.97)
40.1
Japan
734
1.49 (1.44, 1.54)
32.9
Korea
8086
1.43 (1.42, 1.45)
30.1
Singapore
200
1.13 (1.06, 1.19)
11.5
Kuwait
100
1.06 (0.89, 1.26)
5.66
Exploring these parameters and their implications further, the difference between
R0 and Rt is related to the proportion of individuals that are already immune (either
by vaccination or natural infection) to that pathogen in that population. So another
way of calculating Rt for a pathogen in a given population is by multiplying R0 by
the proportion of that population that is non-immune (i.e. susceptible) to that pathogen.
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Hence, R0 will only equal Rt when there are no immune individuals in the population
(i.e. when all are susceptible). This means that any partial, pre-existing immunity
to the infecting agent can reduce the number of expected secondary cases arising.
Although SARS-CoV-2 is a new coronavirus, one source of possible partial immunity
to is some possible antibody cross-reactivity and partial immunity from previous infections
with the common seasonal coronaviruses (OC43, 229E, NL63, HKU1) that have been circulating
in human populations for decades, as was noted for SARS-CoV.
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This could also be the case for SARS-CoV-2 and might explain why some individuals
(perhaps those who have recently recovered from a seasonal coronavirus infection)
have milder or asymptomatic infections.
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Finally, returning to the concept of enhancing herd immunity to control the COVID-19
epidemic, given that the case fatality rate (CFR) of COVID-19 can be anything between
0.25–3.0% of a country's population,
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the estimated number of people who could potentially die from COVID-19, whilst the
population reaches the Pcrit herd immunity level, may be difficult to accept.
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