Global stability of two-group SIR model with random perturbation (Q837131)

The authors study a two-group SIR model introduced by \textit{H. Guo, M. Y. Li} and \textit{Z. Shuai} [Can. Appl. Math. Q. 14, No. 3, 259--284 (2006; Zbl 1148.34039)] with respect to white noise stochastic perturbations around its positive endemic equilibrium. They prove a stability result given in Theorem 4.3 which show that the endemic equilibrium is stochastically asymptotically stable in the large. The proof of this theorem is based on a Lyapunov function. Some suggestive numerical simulations are included.