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      Herd immunity – estimating the level required to halt the COVID-19 epidemics in affected countries

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          Abstract

          Dear Editor , Previous workers have attempted to predict the cumulative number of cases of Coronavirus Disease 2019 (COVID-19) in China. 1 However, since then, the epidemic has rapidly evolved into a pandemic affecting multiple countries worlwide. 2 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. 3 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, 4 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), 5 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. 6 As of 13 March 2020, there were 32 countries outside China with over 100 COVID-19 cases. 7 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, 7 ), 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. 6 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. 8 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. 9 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, 10 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. 3

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          Most cited references 2

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          Simulating and forecasting the cumulative confirmed cases of SARS-CoV-2 in china by Boltzmann function-based regression analyses

          Highlights • Cumulative confirmed cases in China were well fitted with Boltzmann function. • Potential total numbers of confirmed cases in different regions were estimated. • Key dates indicating minimal daily number of new confirmed cases were estimated. • Cumulative confirmed cases of 2003 SARS-CoV were well fitted to Boltzmann function. • The Boltzmann function was, for the first time, applied to epidemic analysis.
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            Clinical characteristics of 24 asymptomatic infections with COVID-19 screened among close contacts in Nanjing

             Z Hu,  C. Song,  C XU (2020)
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              Author and article information

              Contributors
              Journal
              J Infect
              J. Infect
              The Journal of Infection
              The British Infection Association. Published by Elsevier Ltd.
              0163-4453
              1532-2742
              21 March 2020
              21 March 2020
              Affiliations
              [a ]JC School of Public Health and Primary Care, The Chinese University of Hong Kong, Hong Kong Special Administrative Region, China
              [b ]Department of Cardiovascular Sciences, University of Leicester, United Kingdom
              [c ]Respiratory Sciences, Clinical Microbiology, University of Leicester, 5/F Sandringham Building, Leicester Royal Infirmary, Leicester LE1 5WW, United Kingdom
              Author notes
              Article
              S0163-4453(20)30154-7
              10.1016/j.jinf.2020.03.027
              7151357
              32209383
              © 2020 The British Infection Association. Published by Elsevier Ltd. All rights reserved.

              Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.

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              Infectious disease & Microbiology

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