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

doi:10.13371/j.cnki.chin.q.j.m.2015.03.016

Chinese Quarterly Journal of Mathematics ›› 2015, Vol. 30 ›› Issue (3): 450-461.doi: 10.13371/j.cnki.chin.q.j.m.2015.03.016

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

1. School of Science, Chang'an University 2. School of Science, Xi'an Polytechnic University

Received:2015-01-02 Online:2015-09-30 Published:2020-11-23
About author: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.
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)；

Abstract

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

CLC Number:

O175

KANG Rui-ni, ZHANG Tai-lei, LIU Jun-li. A Non-autonomous SIR Epidemic Model of Prey-predator with Vaccination and Time Delay[J]. Chinese Quarterly Journal of Mathematics, 2015, 30(3): 450-461.

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

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