一类潜伏期和染病期均传染的SEIQR流行病模型的稳定性  

Stability of a SEIQR Epidemic Model with Infectious Incubation Period and Infectious Period

作　　者：梁桂珍 郝林莉 LIANG Gui-zhen;HAO Lin-li(Department of Mathematics and Information Science,Xinxiang University,Xinxiang Henan 453003,China;Department of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450000,China)

机构地区：[1]新乡学院数学与信息科学学院,河南新乡453003 [2]郑州大学数学与统计学院,郑州450000

出　　处：《西南师范大学学报（自然科学版）》2020年第3期1-9,共9页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11871238);河南省科技厅科技攻关项目(132102310482);河南省高等学校重点科研项目(20B110014);新乡学院科技创新项目(12ZB17).

摘　　要：研究了一类潜伏期和染病期均传染的SEIQR流行病模型,定义了基本再生数R 0.并运用Routh-Hurtwiz判据、Lyapunov函数及LaSalle不变集原理和第二加性复合矩阵证明了当R 0<1时,模型存在唯一的无病平衡点P0,且P0全局渐近稳定;当R0>1时,模型存在两个平衡点,无病平衡点P0不稳定,地方病平衡点P*全局渐近稳定.最后进行了数值模拟.In this paper,a SEIQR epidemic model of a class of diseases with infectious incubation period and infectious period has been studied,the basic regeneration number R0 been defined,and the Routh-hurtwiz criterion,Lyapunov function,LaSalle invariant set principle and second additive complex matrix been used to prove that,when R0<1,the model has a unique disease-free equilibrium point P0,and P0 is globally asymptotically stable;and when R0>1,there are two equilibrium points in the model.Endemic equilibrium P*is global asymptotic stability.And at the end of the article are numerically simulated.

关 键 词：潜伏期 隔离 基本再生数 局部渐近稳定 全局渐近稳定 

分 类 号：O175[理学—数学]