  To better describe the spread of a disease, we extend a discrete time
stochastic SIR-type epidemic model of Tuckwell and Williams. We assume the
dependence on time of the number of daily encounters and include a parameter to
represent a possible quarantine of the infectious individuals. We provide an
analytic description of this Markovian model and investigate its dynamics. Both
a diffusion approximation and the basic reproduction number are derived.
Through several simulations, we show how the evolution of a disease is affected
by the distribution of the number of daily encounters and its dependence on
time.
