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一类潜伏期和染病期均传染的SEIQR流行病模型的稳定性
引用本文:梁桂珍,郝林莉. 一类潜伏期和染病期均传染的SEIQR流行病模型的稳定性[J]. 西南师范大学学报(自然科学版), 2020, 45(3): 1-9
作者姓名:梁桂珍  郝林莉
作者单位: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
基金项目: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R0.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R0<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*...

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
收稿时间:2019-01-11

Stability of a SEIQR Epidemic Model with Infectious Incubation Period and Infectious Period
LIANG Gui-zhen,HAO Lin-li. Stability of a SEIQR Epidemic Model with Infectious Incubation Period and Infectious Period[J]. Journal of southwest china normal university(natural science edition), 2020, 45(3): 1-9
Authors:LIANG Gui-zhen  HAO Lin-li
Affiliation:1. Department of Mathematics and Information Science, Xinxiang University, Xinxiang Henan 453003, China;2. Department of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450000, China
Abstract: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.
Keywords:incubation period  insulate  basic reproduction number  locally asymptotic stability  global asymptotic stability
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