| 一类潜伏期和染病期均传染的SEIQR流行病模型的稳定性 |
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| 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. |
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| 作者姓名： | 梁桂珍 郝林莉 |
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| 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 |
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| 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）. |
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| 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_01时,模型存在唯一的无病平衡点P_0,且P_0全局渐近稳定;当R_01时,模型存在两个平衡点,无病平衡点P_0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.
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| 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： | 2019/1/11 0:00:00 |
Stability of a SEIQR Epidemic Model with Infectious Incubation Period and Infectious Period |
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| 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),2020,45(3):1-9. |
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| Authors: | LIANG Gui-zhen HAO Lin-li |
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| Institution: | 1. Department of Mathematics and Information Science, Xinxiang University, Xinxiang Henan 453003, China;2. Department of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450000, China |
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| 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. |
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| Keywords: | incubation period insulate basic reproduction number locally asymptotic stability global asymptotic stability |
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