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Global stability of two-group SIR model with random perturbation. (English) Zbl 1184.34064

The authors study a two-group SIR model introduced by H. Guo, M. Y. Li and 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.

MSC:
34F05ODE with randomness
34D23Global stability of ODE
92D30Epidemiology