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Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment

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  • Yakui Xue
  • Junfeng Wang

Abstract

An epidemic model with infectious force in infected and immune period and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infective on the disease spread. It is assumed that treatment rate is proportional to the number of infective below the capacity and is constant when the number of infective is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also the capacity for treatment of infective. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.

Suggested Citation

  • Yakui Xue & Junfeng Wang, 2012. "Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:647853
    DOI: 10.1155/2012/647853
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    References listed on IDEAS

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    1. Li, Guihua & Jin, Zhen, 2005. "Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1177-1184.
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    Cited by:

    1. Yakui Xue & Tiantian Li, 2013. "Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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