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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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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DOI: https://doi.org/10.1007/s12346-022-00663-1