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Stability and bifurcation of an SIS epidemic model with treatment

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  • Li, Xue-Zhi
  • Li, Wen-Sheng
  • Ghosh, Mini

Abstract

An SIS epidemic model with a limited resource for treatment is introduced and analyzed. It is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. 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

  • Li, Xue-Zhi & Li, Wen-Sheng & Ghosh, Mini, 2009. "Stability and bifurcation of an SIS epidemic model with treatment," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2822-2832.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2822-2832
    DOI: 10.1016/j.chaos.2009.04.024
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    References listed on IDEAS

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    1. Jiang, Zhichao & Wei, Junjie, 2008. "Stability and bifurcation analysis in a delayed SIR model," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 609-619.
    2. Sun, Chengjun & Lin, Yiping & Han, Maoan, 2006. "Stability and Hopf bifurcation for an epidemic disease model with delay," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 204-216.
    3. Niu, Ben & Wei, Junjie, 2008. "Stability and bifurcation analysis in an amplitude equation with delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1362-1371.
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    Cited by:

    1. Misra, A.K. & Mishra, S.N. & Pathak, A.L. & Srivastava, P.K. & Chandra, Peeyush, 2013. "A mathematical model for the control of carrier-dependent infectious diseases with direct transmission and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 41-53.
    2. Jana, Soovoojeet & Haldar, Palash & Kar, T.K., 2016. "Optimal control and stability analysis of an epidemic model with population dispersal," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 67-81.
    3. Ren, Jianguo & Yang, Xiaofan & Yang, Lu-Xing & Xu, Yonghong & Yang, Fanzhou, 2012. "A delayed computer virus propagation model and its dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 74-79.
    4. Kar, T.K. & Nandi, Swapan Kumar & Jana, Soovoojeet & Mandal, Manotosh, 2019. "Stability and bifurcation analysis of an epidemic model with the effect of media," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 188-199.
    5. Srivastav, Akhil Kumar & Ghosh, Mini, 2019. "Assessing the impact of treatment on the dynamics of dengue fever: A case study of India," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    6. Kuddus, Md Abdul & McBryde, Emma S. & Adekunle, Adeshina I. & Meehan, Michael T., 2022. "Analysis and simulation of a two-strain disease model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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