Estimating the prevalence of the COVID-19 infection, with an application to Italy

Knowing the prevalence of the COVID-19 infection in a population of interest, and how it changes over time and across space, is of fundamental importance for public health. Unfortunately, the fraction of cases who turn out to be positive in a test provides a distorted picture of the prevalence of the infection because the tested cases are not a random sample of the population. Since random testing of the population is costly and complicated to carry out, in this note we show how to use the available information, in conjunction with credible assumptions about unknown quantities, to obtain a range of plausible values for the prevalence of the infection. We then apply our method to the Italian data.