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A discrete epidemic model with stage structure

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  • Li, Xiuying
  • Wang, Wendi

Abstract

A discrete SIS epidemic model with stage structure is proposed that a disease spreads among mature individuals. A basic reproduction number R0 of the model is formulated, which is more complicated to calculate than that of differential equation models because the attractor of the model in disease free space may compose of equilibria, period cycles, even strange attractors. If the recruitment rate is of Beverton–Holt type, when R0<1 and recovery rate is equal to 0, the disease free equilibrium is globally stable, and R0 is monotone for any parameter of the system. When the recruitment rate is of Richer’s type, it is shown that the existence and extinction of the disease can emerge alternately with the change of intrinsic growth rate. The method for finding basic reproduction number can be applied to other discrete epidemic models.

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  • Li, Xiuying & Wang, Wendi, 2005. "A discrete epidemic model with stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 947-958.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:3:p:947-958
    DOI: 10.1016/j.chaos.2005.01.063
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    Cited by:

    1. Zhang, Tailei, 2015. "Permanence and extinction in a nonautonomous discrete SIRVS epidemic model with vaccination," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 716-729.
    2. Pang, Guoping & Chen, Lansun, 2007. "A delayed SIRS epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1629-1635.
    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. Begoña Cantó & Carmen Coll & Maria Jesús Pagán & Joan Poveda & Elena Sánchez, 2021. "A Mathematical Model to Control the Prevalence of a Directly and Indirectly Transmitted Disease," Mathematics, MDPI, vol. 9(20), pages 1-15, October.
    5. Salman, S.M. & Ahmed, E., 2018. "A mathematical model for Creutzfeldt Jacob Disease (CJD)," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 249-260.
    6. Zhang, Tailei & Liu, Junli & Teng, Zhidong, 2009. "Bifurcation analysis of a delayed SIS epidemic model with stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 563-576.
    7. 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.

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