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To better describe the spread of a disease, we extend a discrete timestochastic SIR-type epidemic model of Tuckwell and Williams. We assume thedependence on time of the number of daily encounters and include a parameter torepresent a possible quarantine of the infectious individuals. We provide ananalytic description of this Markovian model and investigate its dynamics. Botha diffusion approximation and the basic reproduction number are derived.Through several simulations, we show how the evolution of a disease is affectedby the distribution of the number of daily encounters and its dependence ontime.

Time-dependent non-homogeneous stochastic epidemic model of SIR type