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Periodically forced discrete-time SIS epidemic model with disease induced mortality

  • Received: 01 February 2010 Accepted: 29 June 2018 Published: 01 April 2011
  • MSC : Primary: 37G15, 37G35; Secondary: 39A11, 92B05.

  • We use a periodically forced SIS epidemic model with disease induced mortality to study the combined effects of seasonal trends and death on the extinction and persistence of discretely reproducing populations. We introduce the epidemic threshold parameter, $R_0$, for predicting disease dynamics in periodic environments. Typically, $R_0<1$ implies disease extinction. However, in the presence of disease induced mortality, we extend the results of Franke and Yakubu to periodic environments and show that a small number of infectives can drive an otherwise persistent population with $R_0>1$ to extinction. Furthermore, we obtain conditions for the persistence of the total population. In addition, we use the Beverton-Holt recruitment function to show that the infective population exhibits period-doubling bifurcations route to chaos where the disease-free susceptible population lives on a 2-cycle (non-chaotic) attractor.

    Citation: John E. Franke, Abdul-Aziz Yakubu. Periodically forced discrete-time SIS epidemic model with diseaseinduced mortality[J]. Mathematical Biosciences and Engineering, 2011, 8(2): 385-408. doi: 10.3934/mbe.2011.8.385

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  • We use a periodically forced SIS epidemic model with disease induced mortality to study the combined effects of seasonal trends and death on the extinction and persistence of discretely reproducing populations. We introduce the epidemic threshold parameter, $R_0$, for predicting disease dynamics in periodic environments. Typically, $R_0<1$ implies disease extinction. However, in the presence of disease induced mortality, we extend the results of Franke and Yakubu to periodic environments and show that a small number of infectives can drive an otherwise persistent population with $R_0>1$ to extinction. Furthermore, we obtain conditions for the persistence of the total population. In addition, we use the Beverton-Holt recruitment function to show that the infective population exhibits period-doubling bifurcations route to chaos where the disease-free susceptible population lives on a 2-cycle (non-chaotic) attractor.


  • This article has been cited by:

    1. Zhidong Teng, Lei Wang, Linfei Nie, Global attractivity for a class of delayed discrete SIRS epidemic models with general nonlinear incidence, 2015, 38, 01704214, 4741, 10.1002/mma.3389
    2. Qiaoling Chen, Zhidong Teng, Lei Wang, Haijun Jiang, The existence of codimension-two bifurcation in a discrete SIS epidemic model with standard incidence, 2013, 71, 0924-090X, 55, 10.1007/s11071-012-0641-6
    3. Najat Ziyadi, Abdul-Aziz Yakubu, 2013, Chapter 15, 978-1-4614-4177-9, 411, 10.1007/978-1-4614-4178-6_15
    4. Najat Ziyadi, Abdul-Aziz Yakubu, Predator-induced and mating limitation-induced Allee effects in a discrete-timeSIMSepidemic model, 2013, 66, 08981221, 2196, 10.1016/j.camwa.2013.08.002
    5. Yueli Luo, Shujing Gao, Dehui Xie, Yanfei Dai, A discrete plant disease model with roguing and replanting, 2015, 2015, 1687-1847, 10.1186/s13662-014-0332-3
    6. Xiaolin Fan, Lei Wang, Zhidong Teng, Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence, 2016, 2016, 1687-1847, 10.1186/s13662-016-0846-y
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  • © 2011 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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