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Effects of limited medical resource on a Filippov infectious disease model induced by selection pressure

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  • Qin, Wenjie
  • Tang, Sanyi
  • Xiang, Changcheng
  • Yang, Yali

Abstract

In reality, the outbreak of emerging infectious diseases including SARS, A/H1N1 and Ebola are accompanied by the common cold and flu. The selective treatment measure for mitigating and controlling the emerging infectious diseases should be implemented due to limited medical resources. However, how to determine the threshold infected cases and when to implement the selective treatment tactics are crucial for disease control. To address this, we derive a non-smooth Filippov system induced by selective treatment measure. The dynamic behaviors of two subsystems have been discussed completely, and the existence conditions for sliding segment, sliding mode dynamics and different types of equilibria such as regular equilibrium, pseudo-equilibrium, boundary equilibrium and tangent point have been provided. Further, numerical sliding bifurcation analyses show that the proposed Filippov system has rich sliding bifurcations. Especially, the most interesting results are those for the fixed parameter set as the bifurcation parameter varies, the sliding bifurcations occur sequentially: crossing → buckling → real/virtual equilibrium → buckling → crossing. The key factors which affect the selective treatment measures and the threshold value of infected cases for emerging infectious disease have been discussed in more detail.

Suggested Citation

  • Qin, Wenjie & Tang, Sanyi & Xiang, Changcheng & Yang, Yali, 2016. "Effects of limited medical resource on a Filippov infectious disease model induced by selection pressure," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 339-354.
    • Handle: RePEc:eee:apmaco:v:283:y:2016:i:c:p:339-354
    DOI: 10.1016/j.amc.2016.02.042
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    References listed on IDEAS

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    1. Laura Matrajt & M Elizabeth Halloran & Ira M Longini Jr, 2013. "Optimal Vaccine Allocation for the Early Mitigation of Pandemic Influenza," PLOS Computational Biology, Public Library of Science, vol. 9(3), pages 1-15, March.
    2. Qin, Wenjie & Tang, Sanyi, 2014. "The selection pressures induced non-smooth infectious disease model and bifurcation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 160-171.
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    Cited by:

    1. Sheng Bin & Gengxin Sun & Chih-Cheng Chen, 2019. "Spread of Infectious Disease Modeling and Analysis of Different Factors on Spread of Infectious Disease Based on Cellular Automata," IJERPH, MDPI, vol. 16(23), pages 1-16, November.
    2. Peipei Wang & Wenjie Qin & Guangyao Tang, 2019. "Modelling and Analysis of a Host-Parasitoid Impulsive Ecosystem under Resource Limitation," Complexity, Hindawi, vol. 2019, pages 1-12, January.
    3. Gómez-Corral, A. & Lopez-Herrero, M.J. & Taipe, D., 2023. "A Markovian epidemic model in a resource-limited environment," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    4. Qin, Wenjie & Tan, Xuewen & Tosato, Marco & Liu, Xinzhi, 2019. "Threshold control strategy for a non-smooth Filippov ecosystem with group defense," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    5. Yang, Jin & Chen, Zhuo & Tan, Yuanshun & Liu, Zijian & Cheke, Robert A., 2023. "Threshold dynamics of an age-structured infectious disease model with limited medical resources," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 114-132.
    6. Jiao, Xubin & Li, Xiaodi & Yang, Youping, 2022. "Dynamics and bifurcations of a Filippov Leslie-Gower predator-prey model with group defense and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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