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. 2022 Jan 20:9:648545.
doi: 10.3389/fpubh.2021.648545. eCollection 2021.

A Method for Estimating the Number of Infections From the Reported Number of Deaths

Åke Brännström  1   2 , Henrik Sjödin  3 , Joacim Rocklöv  3
Affiliations

A Method for Estimating the Number of Infections From the Reported Number of Deaths

Åke Brännström et al. Front Public Health. .

Abstract

At the outset of an epidemic, available case data typically underestimate the total number of infections due to insufficient testing, potentially hampering public responses. Here, we present a method for statistically estimating the true number of cases with confidence intervals from the reported number of deaths and estimates of the infection fatality ratio; assuming that the time from infection to death follows a known distribution. While the method is applicable to any epidemic with a significant mortality rate, we exemplify the method by applying it to COVID-19. Our findings indicate that the number of unreported COVID-19 infections in March 2020 was likely to be at least one order of magnitude higher than the reported cases, with the degree of underestimation among the countries considered being particularly high in the United Kingdom.

Keywords: COVID-19; estimating; infectives; nowcasting; surveillance.

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Conflict of interest statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Figures

Figure 1
Figure 1
Not accounting for the standard deviation in time can lead to large estimation error. The blue curve shows the estimated number of infectives assuming that the time from infection to death is lognormally distributed with mean 21 days and standard deviation given by the horizontal axis. The heuristic estimate using Equation 1, shown as the red curve, underestimates the actual number up to four times. Other parameters: exponential doubling time T = 4, number of deaths d = 100, and infection fatality ratio p = 0.01 (i.e., 1%).
Figure 2
Figure 2
Estimated number of infections assuming exponential growth is robust to small variations in key parameters. How the estimated number of infections depends on (A) doubling time, (B) infection fatality ratio, and (C) average time from infection to death. Parameters not varied are doubling time T = 4, number of deaths d = 100, and infection fatality ratio p = 0.01 (i.e., 1%). Time from infection to death is assumed lognormally distributed with mean 21 days and standard deviation 8 days, except for the right panel where the mean time is given by the horizontal axis.
Figure 3
Figure 3
Predicted number of COVID-19 cases based on the reported number of deaths. The predicted cumulative number of COVID-19 cases (solid line) depending on the number of reported deaths, with 95% indicative confidence intervals (dashed line), here based on a doubling time of 4 days and an infectious fatality ratio of 0.8%. Two letter country codes indicate the country's reported deaths and cases based on European Center for Disease Prevention and Control data from March 25.
See this image and copyright information in PMC

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