Global Analysis of an SEIR Epidemic Model with Nonlinear Incidence Rates

JIA Ying, LIU Jun-li

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

Chinese Quarterly Journal of Mathematics >

2016 , Vol. 31 >Issue 3: 237 - 247

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.03.002

Global Analysis of an SEIR Epidemic Model with Nonlinear Incidence Rates

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School of Science,Xi’an Polytechnic University

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.

Received date: 2015-04-19

Online published: 2020-11-04

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)；

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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

Cite this article

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

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