On SIR epidemic models with generally distributed infectious periods: Number of secondary cases and probability of infection

Abstract

Recently, Clancy [SIR epidemic models with general infectious period distribution, Statist. Prob. Lett. 85 (2014) 1–5] has shown how SIR epidemics in which individuals’ infection periods are not necessarily exponentially distributed may be modeled in terms of a piecewise-deterministic Markov process (PDMP). In this paper, we present a more detailed description of the underlying PDMP, from which we analyze the population transmission number and the infection probability of a certain susceptible individual.