一类具有接种和治疗的传染病模型动力学分析  

Dynamic analysis of infectious disease model with vaccination and treatment

作　　者：吴梦媛[1] 孙法国[1] 陈瑶[1] 

机构地区：[1]西安工程大学理学院,西安710048

出　　处：《哈尔滨商业大学学报（自然科学版）》2017年第6期738-743,共6页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：陕西省教育厅自然科学专项基金资助项目(15JK1295)陕西省教育厅自然科学专项基金资助项目(2015JM1002)

摘　　要：假设被接种者获得的免疫会逐渐丧失,建立了一类具有接种和治疗的传染病模型,并对模型的稳定性进行了分析.通过构造Lyapunov函数以及利用判据和Lasalle不变原理,研究了模型的无病平衡点和地方病平衡点的稳定性,并找出影响传染病是否流行的阈值R_0.结论表明模型始终存在一个无病平衡点,且它在R_0<1时全局渐近稳定;R_0>1时还存在一个地方病平衡点,且它是全局渐近稳定的.The hypothesis is vaccination gain will gradually lose,established an epidemic model with vaccination and treatment,and the stability of the model was analyzed. By constructing a Lyapunov function and using the Bendixson criterion and Lasalle invariant principle,studied the stability of the disease-free equilibrium and the endemic equilibrium in infectious diseases,and found out the basic reproduction number that effect of infectious disease epidemic. The conclusion indicated that the model always had a disease-free equilibrium,and it was globally asymptotically stable when R_0 1; there was a endemic equilibrium when R_0 1,and it was globally asymptotically stable.

关 键 词：基本再生数 全局稳定性 连续接种 不完全治疗 

分 类 号：O175[理学—数学]