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Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

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  • Eric Ávila-Vales
  • Erika Rivero-Esquivel
  • Gerardo Emilio García-Almeida

Abstract

We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate of the form , and it is shown that the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence of disease. Numerical simulations are performed using a nonlinear incidence rate to estimate the basic reproduction number and illustrate our analytical findings.

Suggested Citation

  • Eric Ávila-Vales & Erika Rivero-Esquivel & Gerardo Emilio García-Almeida, 2017. "Global Dynamics of a Periodic SEIRS Model with General Incidence Rate," International Journal of Differential Equations, Hindawi, vol. 2017, pages 1-14, November.
    • Handle: RePEc:hin:jnijde:5796958
    DOI: 10.1155/2017/5796958
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    Cited by:

    1. Aníbal Coronel & Fernando Huancas & Ian Hess & Esperanza Lozada & Francisco Novoa-Muñoz, 2020. "Analysis of a SEIR-KS Mathematical Model For Computer Virus Propagation in a Periodic Environment," Mathematics, MDPI, vol. 8(5), pages 1-20, May.

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