Canard Phenomenon in an SIRS Epidemic Model with Nonlinear Incidence Rate

Author:

Zhang Yingying1ORCID,Zhou Yicang1,Tang Biao2

Affiliation:

1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, P. R. China

2. Laboratory for Industrial and Applied Mathematics, York University, Toronto, Ontario M3J 1P3, Canada

Abstract

In this paper, we propose an SIRS epidemic model with a new complex nonlinear incidence rate, which describes the psychological effect of some diseases on the community as the number of infective individuals increases, including linear and nonlinear hazards of infection. The canard phenomenon for the model is analyzed, and its epidemiological meaning is discussed. By using geometrical singular perturbation theory and blow up technique, we investigate the relaxation oscillation of the model with the special fold point [Formula: see text]. The unique existence of the limit cycle is proved. We verify the existence of the canard cycle without head by using singular perturbation theory and analyze the cyclicity of the limit cycle. The detailed formula for slow divergence integral of the model is presented. We also discuss and prove the existence of the canard cycle with head. Numerical simulations are done to demonstrate our theoretical results.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Cited by 11 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3