Dynamics of a multigroup SIR epidemic model with stochastic perturbation

In this paper, we introduce stochasticity into a multigroup SIR (susceptible, infective, and recovered) model. The stochasticity in the model is introduced by parameter perturbation, which is a standard technique in stochastic population modeling. In the deterministic models, the basic reproduction number R-0 is a threshold which completely determines the persistence or extinction of the disease. We carry out a detailed analysis on the asymptotic behavior of the stochastic model, also regarding of the value of R-0. If R-0 <= 1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model, whereas, if R-0 > 1, there is a stationary distribution, which means that the disease will prevail. (C) 2011 Elsevier Ltd. All rights reserved.