一类具有饱和传染率的SVEIR传染病模型的定性分析

An analysis of a SVEIR epidemic model with saturation incidence rate

建立带有接种的SVEIR传染病模型,得到基本再生数R_0,并讨论平衡点的存在性.通过构造Lyapunov函数及利用LaSalle不变原理,研究连续接种对传染病传播的影响.发现传染病模型的全局稳定性由基本再生数R0决定,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.接种是控制疾病传播的有效途径.

The SVEIR infectious disease model with vaccination is established,the basic repro-duction number is obtained,and the existence of the equilibrium point is discussed.The effects of continuous vaccination on infectious diseases by constructing Lyapunov function and the La-Salle＇s invariance principle.It is pointed out that the basic reproduction number R 0 determines the global stability of the epidemic model.When R 0〈1,the disease-free equilibrium is globally asymptotically stable.When R 0〉 1,the endemic equilibrium is globally asymptotically stable. The results show that continuous vaccination is an effective way to control the disease.