Kybernetika

This paper proposes a stochastic diffusion model for the spread of a susceptible-infective-removed Kermack--McKendric epidemic (M1) in a population which size is a martingale $N_t$ that solves the Engelbert--Schmidt stochastic differential equation \eqref{eq:9}. The model is given by the stochastic differential equation (M2) or equivalently by the ordinary differential equation (M3) whose coefficients depend on the size $N_t$. Theorems on a unique strong and weak existence of the solution to (M2) are proved and computer simulations performed.