Dynamics Analysis of a Stochastic SIR Epidemic Model

Abstract EN

We investigate an SIR epidemic model with stochastic perturbations.

We assume that stochastic perturbations are of a white noise type which is directly proportional to the distances of three variables from the steady-state values, respectively.

By constructing suitable Lyapunov functions and applying Itô’s formula, some qualitative properties are obtained, such as the existence of global positive solutions, stochastic boundedness, and permanence.

A series of numerical simulations to illustrate these mathematical findings are presented.