Brief paper: Dynamics of a multigroup SIR epidemic model with stochastic perturbation

Authors:
Chunyan Ji;Daqing Jiang;Qingshan Yang;Ningzhong Shi
Affiliations:
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, PR China and Department of Mathematics, Changshu Institute of Technology, Changshu 215500, Jiangsu, PR C ...;School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, PR China;School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, PR China;School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, PR China
Venue:
Automatica (Journal of IFAC)
Year:
2012

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Abstract

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"01, there is a stationary distribution, which means that the disease will prevail.