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Viral infection model with periodic lytic immune response

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  • Wang, Kaifa
  • Wang, Wendi
  • Liu, Xianning

Abstract

Dynamical behavior and bifurcation structure of a viral infection model are studied under the assumption that the lytic immune response is periodic in time. The infection-free equilibrium is globally asymptotically stable when the basic reproductive ratio of virus is less than or equal to one. There is a non-constant periodic solution if the basic reproductive ratio of the virus is greater than one. It is found that period doubling bifurcations occur as the amplitude of lytic component is increased. For intermediate birth rates, the period triplication occurs and then period doubling cascades proceed gradually toward chaotic cycles. For large birth rate, the period doubling cascade proceeds gradually toward chaotic cycles without the period triplication, and the inverse period doubling can be observed. These results can be used to explain the oscillation behaviors of virus population, which was observed in chronic HBV or HCV carriers.

Suggested Citation

  • Wang, Kaifa & Wang, Wendi & Liu, Xianning, 2006. "Viral infection model with periodic lytic immune response," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 90-99.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:1:p:90-99
    DOI: 10.1016/j.chaos.2005.05.003
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    Cited by:

    1. Dehghan, Mehdi & Nasri, Mostafa & Razvan, Mohammad Reza, 2007. "Global stability of a deterministic model for HIV infection in vivo," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1225-1238.
    2. Cai, Liming & Li, Xuezhi, 2009. "Stability and Hopf bifurcation in a delayed model for HIV infection of CD4+T cells," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 1-11.
    3. Yang, Junyuan & Zhang, Fengqin & Li, Xuezhi, 2009. "Epidemic model with vaccinated age that exhibits backward bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1721-1731.
    4. San Martín, Jesús & Moscoso, Ma José & González Gómez, A., 2009. "The universal cardinal ordering of fixed points," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1996-2007.
    5. Wen, Luosheng & Yang, Xiaofan, 2008. "Global stability of a delayed SIRS model with temporary immunity," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 221-226.
    6. Ji, Yu & Min, Lequan & Zheng, Yu & Su, Yongmei, 2010. "A viral infection model with periodic immune response and nonlinear CTL response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2309-2316.
    7. Xie, Falan & Shan, Meijing & Lian, Xinze & Wang, Weiming, 2017. "Periodic solution of a stochastic HBV infection model with logistic hepatocyte growth," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 630-641.
    8. Pang, Guoping & Wang, Fengyan & Chen, Lansun, 2009. "Analysis of a viral disease model with saturated contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 17-27.
    9. Jin, Yu & Wang, Wendi & Xiao, Shiwu, 2007. "An SIRS model with a nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1482-1497.
    10. Gao, Ting & Wang, Wendi & Liu, Xianning, 2011. "Mathematical analysis of an HIV model with impulsive antiretroviral drug doses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 653-665.
    11. Bai, Zhenguo & Zhou, Yicang, 2012. "Dynamics of a viral infection model with delayed CTL response and immune circadian rhythm," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1133-1139.
    12. Zhang, Zhonghua & Peng, Jigen & Zhang, Juan, 2009. "Melnikov method to a bacteria-immunity model with bacterial quorum sensing mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 414-420.
    13. Cai, Liming & Wu, Jingang, 2009. "Analysis of an HIV/AIDS treatment model with a nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 175-182.
    14. Jiang, Xiaowu & Zhou, Xueyong & Shi, Xiangyun & Song, Xinyu, 2008. "Analysis of stability and Hopf bifurcation for a delay-differential equation model of HIV infection of CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 447-460.

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