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Dynamics of an epidemic model with delays and stage structure

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Abstract

In this paper, dynamics of a stage-structured epidemic model with delays and nonlinear incidence rate is analyzed. Local stability and existence of Hopf bifurcation is discussed by choosing possible combination of the delays as the bifurcation parameter. It is proved that the unique endemic equilibrium is locally asymptotically stable when the delay is suitably small and a bifurcating periodic solution will be caused once the delay passes through the corresponding critical value of the delay. We make use of the normal form theory and center manifold theorem to obtain the explicit formulas for determining the properties of the Hopf bifurcation. Numerical simulations supporting our obtained findings are carried out in the end.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Bengbu University, Bengbu, 233030, China

    Juan Liu

  2. School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, 233030, China

    Kai Wang

Authors
  1. Juan Liu
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  2. Kai Wang
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Corresponding author

Correspondence to Juan Liu.

Additional information

Communicated by Maria do Rosário de Pinho.

This work was supported by Natural Science Foundation of the Higher Education Institutions of Anhui Province (KJ2015A144) and Anhui Provincial Natural Science Foundation (1508085QA13, 1708085MA17).

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Liu, J., Wang, K. Dynamics of an epidemic model with delays and stage structure. Comp. Appl. Math. 37, 2294–2308 (2018). https://doi.org/10.1007/s40314-017-0452-y

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  • DOI: https://doi.org/10.1007/s40314-017-0452-y

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