On a stochastic epidemic SEIHR model and its diffusion approximation

To model the evolution of diseases with extended latency periods like varicella, we generalise a simple discrete time stochastic SIR-type epidemic model of Tuckwell and Williams. We include both latent periods as well as the presence of quarantine areas, to capture the evolutionary dynamics of such diseases. Analytical results of the proposed Markovian model are provided. The basic reproduction number R0 of the former and new models as well as a diffusion approximation are derived, leading to a stochastic differential equation with multiple delays in a natural way.