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  • 标题:Dynamics of deterministic and stochastic multi-group MSIRS epidemic models with varying total population size
  • 本地全文:下载
  • 作者:Zhigang Wang ; Xiaoming Fan ; Fuquan Jiang
  • 期刊名称:Advances in Difference Equations
  • 印刷版ISSN:1687-1839
  • 电子版ISSN:1687-1847
  • 出版年度:2014
  • 卷号:2014
  • 期号:1
  • 页码:270
  • DOI:10.1186/1687-1847-2014-270
  • 语种:English
  • 出版社:Hindawi Publishing Corporation
  • 摘要:In this paper, we extend the deterministic single-group MSIRS epidemic model to a multi-group model, and we also extend the deterministic multi-group framework to a stochastic one and formulate it as a stochastic differential equation. In the deterministic multi-group model, the basic reproduction number R 0 is a threshold that completely determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show that if R 0 > 1 , then the disease will prevail, the infective condition persists and the endemic state is asymptotically stable in a feasible region. If R 0 ⩽ 1 , then the infective condition disappears and the disease dies out. For the stochastic version, we perform a detailed analysis on the asymptotic behavior of the stochastic model, which also depends on the value of R 0 , when R 0 > 1 , we determine the asymptotic stability of the endemic equilibrium by measuring the difference between the solution and the endemic equilibrium of the deterministic model in time-averaged data. Numerical methods are used to illustrate the dynamic behavior of the model and to solve the systems.
  • 关键词:multi-group MSIRS model ; stochastic perturbation ; graph theory ; Brownian motion
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