Dynamics of a Multigroup SIR Epidemic Model with Nonlinear Incidence and Stochastic Perturbation

摘要

We introduce stochasticity into a multigroup SIR model with nonlinear incidence. We prove that when the intensity of white noise is small, the solution of stochastic system converges weakly to a singular measure (i.e., a distribution) ifℛ0≤1and there exists an invariantdistribution which is ergodic ifℛ0>1. This is the same situation as the corresponding deterministiccase. When the intensity of white noise is large, white noise controls this system. This means thatthe disease will extinct exponentially regardless of the magnitude ofℛ0.