Recruitment Effects on the Evolution of Epidemics in a Simple SIR Model

Abstract

We analyse the patterns of the current epidemic evolution in various countries with the help of a simple SIR model. We consider two main effects: climate induced seasonality and recruitment. The latter is introduced as a way to palliate for the absence of a spatial component in the SIR model. In our approach we mimic the spatial evolution of the epidemic through a gradual introduction of susceptible individuals. We apply our model to the case of France and Australia and explain the appearance of two temporally well-separated epidemic waves. We examine also Brazil and the USA, which present patterns very different from those of the European countries. We show that with our model it is possible to reproduce the observed patterns in these two countries thanks to simple recruitment assumptions. Finally, in order to show the power of the recruitment approach, we simulate the case of the 1918 influenza epidemic reproducing successfully the, by now famous, three epidemic peaks.