具有三次接种的SVIR传染病模型的稳定性分析

Stability Analysis of an Infectious Model of SVIR with Three Vaccinations

研究一类具有心理因素影响的传染率函数、有医疗限制的治疗函数和具有三次疫苗接种的SVIR传染病模型。讨论模型平衡点的存在性以及计算基本再生数,通过Hurwitz判据得到无病平衡点和地方病平衡点的局部稳定性,用构造Lyapunov函数的方法证明无病平衡点的全局稳定性。

A class of infectivity function with psychological factor influence,treatment function with medical limitation and SVIR epidemic model with three vaccinations were studied.Firstly,the existence of the model equilibrium point and the basic regeneration number are discussed.The local stability of disease-free equilibrium point and endemic equilibrium point is obtained by Hurwitz criterion.The global stability of disease-free equilibrium point is proved by constructing Lyapunov function.