Journal
AUTOMATICA
Volume 48, Issue 1, Pages 121-131Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2011.09.044
Keywords
Stochastic SIR model; Disease-free equilibrium; Endemic equilibrium; Stationary distribution; Ergodicity
Funding
- Ministry of Education of China [109051]
- Foundation of Ministry of China [200918]
- NSFC of China [10971021]
- NENU [09SSXT117]
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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.
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