一类与环境有关的传染病模型的稳定性分析Stability Analysis of an SIQR Epidemic Model with Environmental Component
郭婷,滕志东
摘要(Abstract)：
研究了一类与环境有关的SIQR的传染病模型,得到了基本再生数R0.证明了当R0<1时无病平衡点全局渐近稳定,当R0>1时地方病平衡点全局渐近稳定.
关键词(KeyWords)： 传染病模型;基本再生数;无病平衡点;地方病平衡点;全局稳定性;Lyapunov函数
基金项目(Foundation): 国家自然科学基金(11271312,11201399)
作者(Author): 郭婷,滕志东
参考文献(References)：
- [1]李建全,王峰,马知恩.一类带有隔离的传染病模型[J].工程数学学报,2005,22(1):20-24.
- [2]陈军杰.几个具有隔离项的传染病模型的局部稳定性和全局稳定性[J].生物数学学报,2004,19(1):57-64.
- [3]徐文雄,张太雷.具有隔离仓室流行病传播数学模型的全局稳定性[J].西安交通大学学报,2005,39:210-213.
- [4]Liu X,Yang L.Stability analysis of an SEIQV epidemic model with saturated incidence rate[J].Nonlinear Anal RWA,2012,13:2671-2679.
- [5]Liao S,Wang J.Global stability analysis of epidemiological models based on Volterra-Lyapunov stable matrices[J].Chaos Solit Frac,2012,45:966-977.
- [6]Castillo-Chavez C,Feng Z,Huang W.On the computation of R0and its role on global stability[J].Mathematical approaches for emerging and reemerging infectious diseases,2002,125:229-250.
- [7]Li J,Xiao Y,Zhang F.An algebraic approach to proving the global stability of a class of epidemic models[J].Nonlinear Anal RWA,2012,13:2006-2016.
- [8]Diekman O,Heesterbeek J A P,Metz J A J.On the definition and the computation of the basic reproduction ratio R0in models for infectious diseases in heterogeneous population[J].J Math Biol,1990,28:365-382.