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Rich Dynamics of an Epidemic Model with Saturation Recovery

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  • Hui Wan
  • Jing-an Cui

Abstract

A SIR epidemic model is proposed to understand the impact of limited medical resource on infectious disease transmission. The basic reproduction number is identified. Existence and stability of equilibria are obtained under different conditions. Bifurcations, including backward bifurcation and Hopf bifurcation, are analyzed. Our results suggest that the model considering the impact of limited medical resource may exhibit vital dynamics, such as bistability and periodicity when the basic reproduction number is less than unity, which implies that the basic reproductive number itself is not enough to describe whether the disease will prevail or not and a subthreshold number is needed. It is also shown that a sufficient number of sickbeds and other medical resources are very important for disease control and eradication. Considering the costs, we provide a method to estimate a suitable treatment capacity for a disease in a region.

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  • Hui Wan & Jing-an Cui, 2013. "Rich Dynamics of an Epidemic Model with Saturation Recovery," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, April.
    • Handle: RePEc:hin:jnljam:314958
    DOI: 10.1155/2013/314958
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    Cited by:

    1. Ebenezer Bonyah & Muhammad Altaf Khan & K O Okosun & Saeed Islam, 2017. "A theoretical model for Zika virus transmission," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-26, October.
    2. Li, Qian & Xiao, Yanni, 2023. "Analysis of a hybrid SIR model combining the fixed-moments pulse interventions with susceptibles-triggered threshold policy," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    3. Zhou, Weike & Zhao, Tingting & Wang, Aili & Tang, Sanyi, 2024. "Bifurcations and dynamics of a Filippov epidemic model with nonlinear threshold control policy and medical-resource constraints," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).

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