具有年龄依赖的传染病模型定性分析

Global Stability of An Epidemic Model with Age-dependent

接种、恢复时期是影响传染病发展的较为重要的两个因素,为此建立一类具有年龄依赖的SVIR传染病模型.首先,验证了模型总存在无病平衡点,当且仅当基本再生数R0>1时正平衡点存在,并求得基本再生数.其次,确定了疾病的一致持续性.最后,得到当R0<1时无病平衡点E0全局渐近稳定,当R0>1时只存在全局渐近稳定的正平衡点E^*,并用数值模拟表示了接种的年龄依赖.

The period of vaccination and recovery are two important factors that affect infectious diseases.An SVIR epidemic model with age-dependent is established.Firstly,it is verified that there is always has a disease-free equilibrium,the positive equilibrium point always exist if R0>1 and the basic reproduction number R0 is identify.Secondly,the uniform persistence of the disease is proved.Finally,the disease-free equilibrium is globally asymptotically stable if R0<1,which if R0>1 the positive equilibrium is globally asymptotically stable,and the age dependence of vaccination is represented by numerical simulation.