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Qualitative Analysis of Delayed SIR Epidemic Model with a Saturated Incidence Rate

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  • Fathalla A. Rihan
  • M. Naim Anwar

Abstract

We consider a delayed SIR epidemic model in which the susceptibles are assumed to satisfy the logistic equation and the incidence term is of saturated form with the susceptible. We investigate the qualitative behaviour of the model and find the conditions that guarantee the asymptotic stability of corresponding steady states. We present the conditions in the time lag in which the DDE model is stable. Hopf bifurcation analysis is also addressed. Numerical simulations are provided in order to illustrate the theoretical results and gain further insight into the behaviour of this system.

Suggested Citation

  • Fathalla A. Rihan & M. Naim Anwar, 2012. "Qualitative Analysis of Delayed SIR Epidemic Model with a Saturated Incidence Rate," International Journal of Differential Equations, Hindawi, vol. 2012, pages 1-13, December.
    • Handle: RePEc:hin:jnijde:408637
    DOI: 10.1155/2012/408637
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    Cited by:

    1. George E. Chatzarakis & Tongxing Li, 2018. "Oscillation Criteria for Delay and Advanced Differential Equations with Nonmonotone Arguments," Complexity, Hindawi, vol. 2018, pages 1-18, April.
    2. Rihan, F.A. & Al-Mdallal, Q.M. & AlSakaji, H.J. & Hashish, A., 2019. "A fractional-order epidemic model with time-delay and nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 97-105.
    3. Li, Ning & Yan, Mengting, 2022. "Bifurcation control of a delayed fractional-order prey-predator model with cannibalism and disease," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).

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