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.
Feng Rao. "Dynamics Analysis of a Stochastic SIR Epidemic Model." Abstr. Appl. Anal. 2014 (SI01) 1 - 9, 2014. https://doi.org/10.1155/2014/356013