总人口变化的年龄结构SIQR传染病模型及稳定性  

Stability of age-structured SIQR epidemiological model with varying population size

作　　者：王改霞 刘纪轩 李学志[3] WANG Gai-xia;LIU Ji-xuan;LI Xue-zhi(College of Mathematics and Information,Xinyang University,Xinyang 464000,China;Basic Department,Aviation Maintenance NCO Academy of Air Force Engingeering University,Xinyang 464000,China;College of Mathematics and Physics,Anyang Institute of Techeology,Anyang 455000,China)

机构地区：[1]信阳学院数学与信息学院,河南信阳464000 [2]空军工程大学航空机务士官学校基础部,河南信阳464000 [3]安阳工学院数理学院,河南安阳455000

出　　处：《高校应用数学学报（A辑）》2018年第3期281-290,共10页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11271314);河南省科技创新人才计划(144200510021);河南省高等学校重点科研项目(17A110030)

摘　　要：讨论了总人口数量变化的年龄结构SIQR传染病模型,得到基本再生数R_0.并证明,若R_0<1,则无病平衡点局部渐近稳定;若R_0>1,则无病平衡点不稳定,此时还存在地方病平衡点,给出地方病平衡点的局部渐近稳定性条件.This article considers an age-structured SIQR epidemiological model with varing population size.The basic reproductive number R0 is gotten,and it is proved that if R0<1,the disease-free equilibrium is locally asymptotically stable;if R0>1,the disease-free equilibrium is unstable,at this time there is endemic equilibrium,and the locally asymptotic stability of the endemic equilibrium condition is given.

关 键 词：年龄结构 再生数 总人口变化 

分 类 号：O175.12[理学—数学]