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Complex dynamics in a discrete SIS epidemic model with Ricker-type recruitment and disease-induced death

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Abstract

In this paper, we investigate the complex dynamics in a discrete SIS epidemic model with Ricker-type recruitment and disease-induced death. It is shown that the model has a unique disease-free equilibrium if the basic reproduction number \({\mathcal {R}}_{0}\le 1\) and a unique endemic equilibrium if \({\mathcal {R}}_{0}> 1\). Sufficient conditions for the locally asymptotic stability of the equilibria are obtained. A detailed bifurcation analysis at the endemic equilibrium reveals that the model undergoes a sequence of bifurcations, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation, as the parameters vary. Various numerical simulations, including bifurcation diagrams, phase portraits, maximum Lyapunov exponents and feasible sets, are carried out to present complex periodic windows, period-28 points, multiple chaotic bands, fractal basin boundaries, chaotic attractors and the coexistence of period points and three invariant tori, which not only illustrate the theoretical results but also demonstrate more complex dynamical behaviors of the model.

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Acknowledgements

The third author wishes to thank Professor Zhujun Jing for her helpful discussions and suggestions. The authors also would like to thank the editor and referees whose comments and suggestions have led to improvements in the manuscript.

Funding

The work of Jicai Huang was partially supported by NSFC (No. 11871235) and the Fundamental Research Funds for the Central Universities (CCNU19TS030). The work of Shigui Ruan was partially supported by NSFC (No. 11771168).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, Hubei, P. R. China

    Lei Xiang, Yuyue Zhang & Jicai Huang

  2. Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA

    Shigui Ruan

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  1. Lei Xiang
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  2. Yuyue Zhang
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  3. Jicai Huang
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  4. Shigui Ruan
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Correspondence to Jicai Huang.

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Xiang, L., Zhang, Y., Huang, J. et al. Complex dynamics in a discrete SIS epidemic model with Ricker-type recruitment and disease-induced death. Nonlinear Dyn 104, 4635–4654 (2021). https://doi.org/10.1007/s11071-021-06444-w

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  • DOI: https://doi.org/10.1007/s11071-021-06444-w

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