数学季刊 >

2015 , Vol. 30 >Issue 3: 450 - 461

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.03.016

一类具有接种和时滞的非自治捕食-食饵的SIR传染病模型

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  • 1. School of Science, Chang'an University  2. School of Science, Xi'an Polytechnic University
KANG Rui-ni(1989-), female, native of Xianyang, Shannxi, a graduate student of Chang'an University, engages in differential equation and its application; ZHANG Tai-lei(1980-), male, native of Songzi County, Hubei, a professor of Chang'an University, engages in differential equation and its application.

收稿日期: 2015-01-02

  网络出版日期: 2020-11-23

基金资助

Supported by the National Natural Science Foundation of China(11101323)； Supported by the Fundamental Research Funds for the Central Universities(310812152002)； Supported by the Project Supported by Natural Science Basic Research Plan in Shaanxi Province(2014JQ1018,2014JQ1038)；

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A Non-autonomous SIR Epidemic Model of Prey-predator with Vaccination and Time Delay

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  • 1. School of Science, Chang'an University  2. School of Science, Xi'an Polytechnic University
KANG Rui-ni(1989-), female, native of Xianyang, Shannxi, a graduate student of Chang'an University, engages in differential equation and its application; ZHANG Tai-lei(1980-), male, native of Songzi County, Hubei, a professor of Chang'an University, engages in differential equation and its application.

Received date: 2015-01-02

  Online published: 2020-11-23

Supported by

Supported by the National Natural Science Foundation of China(11101323)； Supported by the Fundamental Research Funds for the Central Universities(310812152002)； Supported by the Project Supported by Natural Science Basic Research Plan in Shaanxi Province(2014JQ1018,2014JQ1038)；

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摘要

A non-autonomous SIR epidemic model of prey-predator with vaccination and time delay is investigated in this paper. And an infectious disease is only considered to spread among the prey population. By using comparison principle and Lyapunov functional methods, we obtain the sufficient criteria for the permanence, extinction of infectious disease and the global attractively of the model. Furthermore, some numerical simulations illustrate that the vaccination has a better effect for disease controlling of infective prey.

关键词： vaccination; time delay; permanence; extinction

本文引用格式

康瑞妮, 张太雷, 刘俊利 . 一类具有接种和时滞的非自治捕食-食饵的SIR传染病模型[J]. 数学季刊, 2015 , 30(3) : 450 -461 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.03.016

Abstract

A non-autonomous SIR epidemic model of prey-predator with vaccination and time delay is investigated in this paper. And an infectious disease is only considered to spread among the prey population. By using comparison principle and Lyapunov functional methods, we obtain the sufficient criteria for the permanence, extinction of infectious disease and the global attractively of the model. Furthermore, some numerical simulations illustrate that the vaccination has a better effect for disease controlling of infective prey.

Key words： vaccination; time delay; permanence; extinction

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