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Relaxation Oscillation and Canard Explosion for a SIRS Model with Nonlinear Incidence Rate

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Abstract

In this paper, we study a susceptible-infectious-recovered model with a nonlinear incidence rate. Assume that the infected individual has large immunity failure rate, then it becomes a slow–fast system. Using geometry singular perturbation theory, we revealed that it exhibits rich dynamics, such as supercritical Hopf bifurcation, canard explosion and relaxation oscillation.

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Acknowledgements

We thank the reviews for their valuable comments and suggestions that helped us to improve the presentation of our paper. This work supported by NNSF of China (No. 12071091) and the Natural Science Foundation of Guangdong Province, P.R. China (No. 2019A1515011885).

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  1. Wang Xiaoling and Li Shimin have equal contributions.

Authors and Affiliations

  1. School of Mathematics and Statistics, Guangdong University of Finance and Economics, 21 Luntou Road, Guangzhou, 510320, Asia, People’s Republic of China

    Wang Xiaoling

  2. School of Mathematics, Hangzhou Normal University, 2318 Yuhangtang Road, Hangzhou, 310036, Asia, People’s Republic of China

    Li Shimin

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  1. Wang Xiaoling
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  2. Li Shimin
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Correspondence to Li Shimin.

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Xiaoling, W., Shimin, L. Relaxation Oscillation and Canard Explosion for a SIRS Model with Nonlinear Incidence Rate. Qual. Theory Dyn. Syst. 21, 134 (2022). https://doi.org/10.1007/s12346-022-00663-1

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