Abstract
The periodic behaviors and non-periodic behaviors of recurrent epidemic are discussed by building an SIS model with disease age structure and infectious delay. We formulate the model as an abstract non-densely defined Cauchy problem and derive the conditions for the existence of Hopf bifurcation under the condition where endemic equilibrium is unstable. It implies that the recurrent epidemics will switch between periodic behavior and non-periodic behavior as the parameter values changing when the disease persists in population. The numerical examples are provided to illustrate our theoretical results.
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Acknowledgements
We would like to thank the referees very much for the careful review and the valuable comments to this manuscript which improve it greatly. We also should say thanks to professor Jianquan Li, who gave us some helpful suggestions for revising this paper. This work is supported by National Natural Science Foundation of China (Grants 11301314, 11501443, 11671142, and 11371087), by Natural Science Foundation of Shaanxi Provincial Department of Education Grant 18JK0092, and by Natural Science Basic Research Plan in Shaanxi Province of China Grant 2019JM-081.
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Cao, H., Yan, D., Zhang, S. et al. Analysis of Dynamics of Recurrent Epidemics: Periodic or Non-periodic. Bull Math Biol 81, 4889–4907 (2019). https://doi.org/10.1007/s11538-019-00638-5
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DOI: https://doi.org/10.1007/s11538-019-00638-5