We show how epidemics in which individuals’ infectious periods are not necessarily exponentially distributed may be naturally modelled as piecewise deterministic Markov processes. For the standard susceptible–infective–removed (SIR) model, we exhibit a family of martingales which may be...

We consider a general class of piecewise-deterministic Markov processes with multiple time-scales. In line with recent results on the stochastic averaging principle for these processes, we obtain a description of their law through an asymptotic expansion. We further study the fluctuations around...