Kermack-McKendrick epidemic model revisited

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 Nt that solves the Engelbert–Schmidt stochastic differential equation (??). The model is given by the stochastic differential equation (M2) or equivalently by the ordinary differential equation (M3) whose coefficients depend on the size Nt. Theorems on a unique strong and weak existence of the solution to (M2) are proved and computer simulations performed.