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Bifurcation analysis of an SIS epidemic model with nonlinear birth rate

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  • Liu, Junli
  • Zhang, Tailei

Abstract

This paper deals with an SIS epidemic model with delay. By regarding p as the bifurcation parameter and analyzing the characteristic equation of the linearized system of the original system at the positive equilibrium, the stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. The explicit formulae determining the direction of the bifurcations, the stability and other properties of the bifurcating periodic solutions are given by using the normal form theory and center manifold theorem. Some numerical simulations are also included.

Suggested Citation

  • Liu, Junli & Zhang, Tailei, 2009. "Bifurcation analysis of an SIS epidemic model with nonlinear birth rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1091-1099.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1091-1099
    DOI: 10.1016/j.chaos.2007.08.082
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    References listed on IDEAS

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    1. 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.
    2. Yang, Hong-Yong & Tian, Yu-Ping, 2005. "Hopf bifurcation in REM algorithm with communication delay," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1093-1105.
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    Cited by:

    1. Sharma, Sandeep & Singh, Fateh, 2021. "Bifurcation and stability analysis of a cholera model with vaccination and saturated treatment," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    3. Guo, Zun-Guang & Sun, Gui-Quan & Wang, Zhen & Jin, Zhen & Li, Li & Li, Can, 2020. "Spatial dynamics of an epidemic model with nonlocal infection," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    4. Liu, Xinzhi & Stechlinski, Peter, 2014. "SIS models with switching and pulse control," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 727-742.
    5. Chen, Wei & Teng, Zhidong & Zhang, Long, 2021. "Global dynamics for a drug-sensitive and drug-resistant mixed strains of HIV infection model with saturated incidence and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    6. Ru Wang & Wandong Cai & Bo Shen, 2016. "The study of the dynamic model on KAD network information spreading," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 63(3), pages 371-379, November.

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