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

Abstract

BACKGROUNDThe reproduction number R is a key indicator to characterize the dynamics of the Covid-19 pandemic and to assess the effect of control strategies that frequently have extremely high social and economic costs. Despite having an analog in demography’s net reproduction rate, demographers may not be familiar with the concept and measurement of R in the context of Covid-19. OBJECTIVETo provide a primer for demographers for understanding and estimating R for Covid-19. METHODSIn order to demystify the complexities of estimating this important indicator, we present a simple method for its calculation, following well-known procedures in demography, a discipline in which an analog of R -- the net reproduction rate -- has been routinely computed for a century. RESULTSWe show that R can be estimated as a quotient 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 Covid-19 pandemic in several countries. CONTRIBUTIONThis primer for demographers demonstrates a method for estimating the reproductive number R for the Covid-19 pandemic derived using familiar demographic techniques. The strengths of the proposed approach are the transparency of the assumptions and the simplicity of the procedure.