摘要
本文提出一类具有潜伏时滞和非线性疾病发生率的SEIRS传染病模型,通过分析对应的特征方程,运用时滞微分方程的稳定性理论得出:当基本再生数R_0<1时无病平衡点处的局部渐近稳定性,R_0> 1时地方病平衡点处的局部渐近稳定性.通过构造Lyapunov泛函,运用LaSalle's不变集原理得到:当基本再生数R_0≤1时无病平衡点处的全局渐近稳定性;通过比较方法得到R_0>
In this paper,an SEIRS epidemiological with nonlinear incidence rate and time delay representing a latent period of the disease is investigated.By analyzing the corresponding characteristic equations and using the stability theory of delay differential equations,when the basic reproduction number R0<1,the local stability of a disease-free equilibrium is obtained;the endemic equilibrium is locally asymptotically stable if R0>1.By Lyapunov functional and LaSalle’s invariant set principle,it is proved that if R0≤1,the disease-free equilibrium is globally asymptotically stable.By comparison,if R0>1,the system is uniformly persistent.
作者
魏泽萍
刘贤宁
WEI Ze-ping;LIU Xian-ning(School of Mathematics and Statistics,Southwest University,Chongqing 400715 China)
出处
《生物数学学报》
2019年第1期63-74,共12页
Journal of Biomathematics
基金
国家自然科学基金项目(11671327)
作者简介
魏泽萍(1993-),女,土家族,贵州湄潭县人,碩士研究生.E-mail:1311250342@qq.com;通讯作者:刘贤宁。
