To model the evolution of diseases with extended latency periods like vari-
cella, 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
R 0 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.

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• On a stochastic epidemic SEIHR model and its diffusion approximation