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The selection pressures induced non-smooth infectious disease model and bifurcation analysis

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  • Qin, Wenjie
  • Tang, Sanyi

Abstract

Mathematical models can assist in the design strategies to control emerging infectious disease. This paper deduces a non-smooth infectious disease model induced by selection pressures. Analysis of this model reveals rich dynamics including local, global stability of equilibria and local sliding bifurcations. Model solutions ultimately stabilize at either one real equilibrium or the pseudo-equilibrium on the switching surface of the present model, depending on the threshold value determined by some related parameters. Our main results show that reducing the threshold value to a appropriate level could contribute to the efficacy on prevention and treatment of emerging infectious disease, which indicates that the selection pressures can be beneficial to prevent the emerging infectious disease under medical resource limitation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:69:y:2014:i:c:p:160-171
    DOI: 10.1016/j.chaos.2014.09.014
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    References listed on IDEAS

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    1. Wenjie Qin & Sanyi Tang & Robert A. Cheke, 2013. "Nonlinear Pulse Vaccination in an SIR Epidemic Model with Resource Limitation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-13, December.
    2. Christina E. Mills & James M. Robins & Marc Lipsitch, 2004. "Transmissibility of 1918 pandemic influenza," Nature, Nature, vol. 432(7019), pages 904-906, December.
    3. Tang, Guangyao & Qin, Wenjie & Tang, Sanyi, 2014. "Complex dynamics and switching transients in periodically forced Filippov prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 13-23.
    4. 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.
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    1. 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.
    2. Dong, Cunjuan & Xiang, Changcheng & Xiang, Zhongyi & Yang, Yi, 2022. "Global dynamics of a Filippov epidemic system with nonlinear thresholds," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    3. 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.

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