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Global Dynamics of an Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate

Author

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  • Sanling Yuan
  • Bo Li

Abstract

We study an epidemic model with a nonlinear incidence rate which describes the psychological effect of certain serious diseases on the community when the ratio of the number of infectives to that of the susceptibles is getting larger. The model has set up a challenging issue regarding its dynamics near the origin since it is not well defined there. By carrying out a global analysis of the model and studying the stabilities of the disease-free equilibrium and the endemic equilibrium, it is shown that either the number of infective individuals tends to zero as time evolves or the disease persists. Computer simulations are presented to illustrate the results.

Suggested Citation

  • Sanling Yuan & Bo Li, 2009. "Global Dynamics of an Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate," Discrete Dynamics in Nature and Society, Hindawi, vol. 2009, pages 1-13, November.
    • Handle: RePEc:hin:jnddns:609306
    DOI: 10.1155/2009/609306
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    Cited by:

    1. Gupta, R.P. & Kumar, Arun, 2022. "Endemic bubble and multiple cusps generated by saturated treatment of an SIR model through Hopf and Bogdanov–Takens bifurcations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 1-21.
    2. Zhou, Baoquan & Jiang, Daqing & Han, Bingtao & Hayat, Tasawar, 2022. "Threshold dynamics and density function of a stochastic epidemic model with media coverage and mean-reverting Ornstein–Uhlenbeck process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 15-44.
    3. Xu, Rui, 2014. "Global dynamics of an SEIRI epidemiological model with time delay," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 436-444.

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