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Global stability of a delayed SEIRS epidemic model with saturation incidence rate

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Abstract

In this paper, an SEIRS epidemic model with a saturation incidence rate and a time delay describing a latent period is investigated. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is established. When the basic reproduction number is greater than unity, by means of an iteration technique, sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium. By comparison arguments, it is proved that if the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable. Numerical simulations are carried out to illustrate the main theoretical results.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, 050003, P.R. China

    Rui Xu

  2. Department of Applied Mathematics, Xi’an Jiaotong University, Xi’an, 710049, P.R. China

    Zhien Ma

Authors
  1. Rui Xu
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  2. Zhien Ma
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Correspondence to Rui Xu.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 10671209, 10531030) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

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Xu, R., Ma, Z. Global stability of a delayed SEIRS epidemic model with saturation incidence rate. Nonlinear Dyn 61, 229–239 (2010). https://doi.org/10.1007/s11071-009-9644-3

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  • DOI: https://doi.org/10.1007/s11071-009-9644-3

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