A demographic scaling model for estimating the total number of COVID-19 infections

Bohk-Ewald, C.; Dudel, C.; Myrskyla, M.

Background: The total number of COVID-19 infections is critical information for decision makers when assessing the progress of the pandemic, its implications, and policy options. Despite efforts to carefully monitor the COVID-19 pandemic, the reported number of confirmed cases is likely to underestimate the actual number of infections. We aim to estimate the total number of COVID-19 infections in a straightforward manner using a demographic scaling approach based on life tables. Methods: We use data on total number of COVID-19 attributable deaths, population counts, and life tables as well as information on infection fatality rates as reported in Verity et al. (2020) for Hubei, China. We develop a scaling approach based on life tables and remaining life expectancy to map infection fatality rates between two countries to account for differences in their age structure, health status, and the health care system. The scaled infection fatality rates can be used in combination with COVID-19 attributable deaths to calculate estimates of the total number of infected. We also introduce easy to apply formulas to quantify the bias that would be required in death counts and infection fatality rates in order to reproduce a certain estimate of infections. Findings: Across the 10 countries with most COVID-19 deaths as of April 17, 2020, our estimates suggest that the total number of infected is approximately 4 times the number of confirmed cases. The uncertainty, however, is high, as the lower bound of the 95% prediction interval suggests on average twice as many infections than confirmed cases, and the upper bound 10 times as many. Country-specific variation is high. For Italy, our estimates suggest that the total number of infected is approximately 1 million, or almost 6 times the number of confirmed cases. For the U.S., our estimate of 1.4 million is close to being twice as large as the number of confirmed cases, and the upper bound of 3 million is more than 4 times the number of confirmed cases. For Germany, where testing has been comparatively extensive, we estimate that the total number of infected is only 1.2 times (upper bound: 3 times) than the number of confirmed cases. Comparing our results with findings from local seroprevalence studies and applying our bias formulas shows that some of their infection estimates would only be possible if just a small fraction of COVID-19 related deaths were recorded, indicating that these seroprevalence estimates might not be representative for the total population. Interpretation: As many countries lack population based seroprevalence studies, straightforward demographic adjustment can be used to deliver useful estimates of the total number of infected cases. Our results imply that the total number COVID-19 cases may be approximately 4 times (95%: 2 to 10 times) that of the confirmed cases. Although these estimates are uncertain and vary across countries, they indicate that the COVID-19 pandemic is much more broadly spread than what confirmed cases would suggest, and the number of asymptomatic cases or cases with mild symptoms may be high. In cases in which estimates from local seroprevalence studies or from simulation models exist, our approach can provide a simple benchmark to assess the quality of those estimates.