Analysis On an SEIRS Epidemic Model with Pulse Vaccination and Two Time Delays

GAO Jian-zhong, ZHANG Tai-lei

doi:10.13371/j.cnki.chin.q.j.m.2019.01.009

Chinese Quarterly Journal of Mathematics >

2019 , Vol. 34 >Issue 1: 75 - 87

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2019.01.009

Analysis On an SEIRS Epidemic Model with Pulse Vaccination and Two Time Delays

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School of Science, Chang’an University

GAO Jian-zhong(1991-), male, native of Yulin, Shannxi, a graduate student of Chang'an University, engages in di®erential equation and its application; ZHANG Tai-lei(1980-), male, native of Songzi County, Hubei, a professor of Chang'an University, engages in di®erential equation and its application.

Accepted date: 2018-07-29

Online published: 2020-10-07

Supported by

The Natural Science Basic Research Plan in Shaanxi Province of China(2018JM1011)； Natural Science Basic Research Plan in Shaanxi Province of China(2017JQ1014)； NSF of China(11701041)；

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Abstract

In this paper, an SEIRS epidemic model with pulse vaccination and two time delays is proposed. By using stroboscopic map and comparison principle, the disease-free periodic solution(DFPS for short) is obtained and the global asymptotic stability of the DFPS is proved. The sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results.

Key words： impulsive vaccination; time delay; threshold values; global stability; permanence

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GAO Jian-zhong, ZHANG Tai-lei . Analysis On an SEIRS Epidemic Model with Pulse Vaccination and Two Time Delays[J]. Chinese Quarterly Journal of Mathematics, 2019 , 34(1) : 75 -87 . DOI: 10.13371/j.cnki.chin.q.j.m.2019.01.009

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