Multigroup SIR epidemic model with stochastic perturbation

作者：Ji, Chunyan; Jiang, Daqing^*; Shi, Ningzhong

来源：Physica A: Statistical Mechanics and Its Applications , 2011, 390(10): 1747-1762.

DOI：10.1016/j.physa.2010.12.042

• Stochastic multigroup SIR model
• Disease-free equilibrium
• Endemic equilibrium
• Stochastic Lyapunov function
• Asymptotically stable in the large
• Persistent in mean

In this paper, we discuss a multigroup SIR model with stochastic perturbation. We deduce the globally asymptotic stability of the disease-free equilibrium when R-0 <= 1, which means the disease will die out. On the other hand, when R-0 > 1, we derive the disease will prevail, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model in time average. Furthermore, we prove the system is persistent in the mean which also reflects the disease will prevail. The key to our analysis is choosing appropriate Lyapunov functions. Finally, we illustrate the dynamic behavior of the model with n = 2 and their approximations via a range of numerical experiments.

• 出版日期2011-5-15
• 单位常熟理工学院; 东北师范大学