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

作　　者：孙丹丹 马丽[1] 胡秀燕 王宇强 唐青 王婷 Sun Dandan;Ma Li;Hu Xiuyan;Wang Yuqiang;Tang Qing;Wang Ting(College of Mathematical and Physical Science,Xinjiang Agricultural University,Urumqi 830052,China)

机构地区：[1]新疆农业大学数理学院,新疆乌鲁木齐830052

出　　处：《宁夏大学学报（自然科学版）》2020年第4期332-336,342,共6页Journal of Ningxia University(Natural Science Edition)

基　　金：新疆维吾尔自治区高校科研计划资助项目(XJEDU2018Y021);新疆农业大学大学生创新创业训练计划项目(dxscx2020517)。

摘　　要：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.

关 键 词：年龄依赖 基本再生数 稳定性 接种 

分 类 号：O175[理学—数学] O231.3[理学—基础数学]