一类具有非线性发生率的SEIR传染病模型的全局稳定性分析

doi:10.13371/j.cnki.chin.q.j.m.2016.03.002

数学季刊 ›› 2016, Vol. 31 ›› Issue (3): 237-247.doi: 10.13371/j.cnki.chin.q.j.m.2016.03.002

一类具有非线性发生率的SEIR传染病模型的全局稳定性分析

School of Science,Xi’an Polytechnic University

收稿日期:2015-04-19 出版日期:2016-09-30 发布日期:2020-11-04
作者简介:JIA Ying(1990-), female, native of Hanzhong, Shannxi, a graduate student of Xi'an Polytechnic University, engages in differential equation and its application; LIU Jun-li(1981-), female, native of Puyang, Henan, an associate professor of Xi'an Polytechnic University, Ph.D., engages in biomathematics.
基金资助:
Supported by the National Natural Science Foundation of China(11101323)； Supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2014JQ1038)； Supported by the Xi’an Polytechnic University Innovation Fund for Graduate

Students(CX201608)；

Global Analysis of an SEIR Epidemic Model with Nonlinear Incidence Rates

School of Science,Xi’an Polytechnic University

Received:2015-04-19 Online:2016-09-30 Published:2020-11-04
About author:JIA Ying(1990-), female, native of Hanzhong, Shannxi, a graduate student of Xi'an Polytechnic University, engages in differential equation and its application; LIU Jun-li(1981-), female, native of Puyang, Henan, an associate professor of Xi'an Polytechnic University, Ph.D., engages in biomathematics.
Supported by:
Supported by the National Natural Science Foundation of China(11101323)； Supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2014JQ1038)； Supported by the Xi’an Polytechnic University Innovation Fund for Graduate Students(CX201608)；

摘要/Abstract

摘要： In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R₀ characterizes the disease transmission dynamics: if R₀≤ 1,the disease-free equilibrium is globally asymptotically stable and the disease always dies out,if R₀> 1 then there is a unique endemic equilibrium which is globally asymptotically stable and the disease persists.

关键词: SEIR model, nonlinear incidence rate, compound matrices, global stability

Abstract: In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R₀ characterizes the disease transmission dynamics: if R₀≤ 1,the disease-free equilibrium is globally asymptotically stable and the disease always dies out,if R₀> 1 then there is a unique endemic equilibrium which is globally asymptotically stable and the disease persists.

Key words: SEIR model, nonlinear incidence rate, compound matrices, global stability

中图分类号:

O175

贾滢, 刘俊利. 一类具有非线性发生率的SEIR传染病模型的全局稳定性分析[J]. 数学季刊, 2016, 31(3): 237-247.

JIA Ying, LIU Jun-li. Global Analysis of an SEIR Epidemic Model with Nonlinear Incidence Rates[J]. Chinese Quarterly Journal of Mathematics, 2016, 31(3): 237-247.

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一类具有非线性发生率的SEIR传染病模型的全局稳定性分析

Global Analysis of an SEIR Epidemic Model with Nonlinear Incidence Rates

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