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Threshold dynamics of an age-structured infectious disease model with limited medical resources

Author

Listed:
  • Yang, Jin
  • Chen, Zhuo
  • Tan, Yuanshun
  • Liu, Zijian
  • Cheke, Robert A.

Abstract

In this paper, an age-structured infectious disease dynamical model that considers two diseases simultaneously but with limited medical resources is proposed and analyzed. The asymptotic smoothness and persistence of the solution semi-flow are investigated. Then conditions for the existence of a global attractor are derived, which means that disease persists when ℜ0>1. By using a Lyapunov function, it is shown that the infection-free equilibrium is globally asymptotically stable if ℜ0<1 and the infection equilibrium is globally asymptotically stable if ℜ0>1. In the presence of limited medical resources, the results suggest that equitable distribution for the limited medical resources is significant when treating low-risk and high-risk diseases and that keeping a resource sharing coefficient at a moderate level helps to eliminate the disease.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:214:y:2023:i:c:p:114-132
    DOI: 10.1016/j.matcom.2023.07.003
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    References listed on IDEAS

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    1. Mishra, A.M. & Purohit, S.D. & Owolabi, K.M. & Sharma, Y.D., 2020. "A nonlinear epidemiological model considering asymptotic and quarantine classes for SARS CoV-2 virus," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. 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.
    3. Abidemi, Afeez & Owolabi, Kolade M. & Pindza, Edson, 2022. "Modelling the transmission dynamics of Lassa fever with nonlinear incidence rate and vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    4. 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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