The mathematics of the reproduction number R for Covid-19: A primer for demographers

Abstract

The reproduction number R is a key indicator to monitor the dynamics of Covid-19 and to assess the effect of control strategies that frequently have high social and economic costs. Despite having an analog in demography’s “net reproduction rate” that has been routinely computed for a century, demographers may not be familiar with the concept and measurement of R in the context of Covid-19. This article intends to be a primer for understanding and estimating R in demography. We show that R can be estimated as a ratio between the numbers of new cases today divided by the weighted average of cases in previous days. We present two alternative derivations for these weights based on how risks change over time: constant vs. exponential decay. We provide estimates of these weights and demonstrate their use in calculating R to trace the course of the first pandemic year in several countries.