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Effects of Media Coverage on Global Stability Analysis and Optimal Control of an Age-Structured Epidemic Model with Multi-Staged Progression

Author

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  • Chao Liu

    (Institute of Systems Science, Northeastern University, Shenyang 110169, China
    School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Peng Chen

    (Institute of Systems Science, Northeastern University, Shenyang 110169, China
    School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Qiyu Jia

    (Sydney Smart Technology College, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Lora Cheung

    (Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada)

Abstract

In this paper, a hybrid SEIAM model for infectious disease with a continuous age structure is established, where combined dynamic effects of media coverage and multi-staged infected progression on threshold dynamics are discussed. Sufficient conditions for uniform persistence of the solution are studied by using the basic reproduction number. By constructing appropriate Lyapunov functions, the global stability analysis of endemic equilibrium is investigated based on Lyapunov–LaSalle’s stability theorem. In order to minimize costs incurred due to applied controls and infectious disease burden, an optimal cost-effective control strategy associated with disease treatment and media coverage is discussed. Numerical simulations are carried out to show consistency with theoretical analysis.

Suggested Citation

  • Chao Liu & Peng Chen & Qiyu Jia & Lora Cheung, 2022. "Effects of Media Coverage on Global Stability Analysis and Optimal Control of an Age-Structured Epidemic Model with Multi-Staged Progression," Mathematics, MDPI, vol. 10(15), pages 1-28, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2712-:d:877467
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    References listed on IDEAS

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    1. Zhang, Heting & Yang, Zhanwen & Pawelek, Kasia A & Liu, Shengqiang, 2020. "Optimal control strategies for a two-group epidemic model with vaccination-resource constraints," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    2. Zhang, Suxia & Guo, Hongbin, 2018. "Global analysis of age-structured multi-stage epidemic models for infectious diseases," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 214-233.
    3. Gashirai, Tinashe B. & Musekwa-Hove, Senelani D. & Lolika, Paride O. & Mushayabasa, Steady, 2020. "Global stability and optimal control analysis of a foot-and-mouth disease model with vaccine failure and environmental transmission," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Kumar, Anuj & Srivastava, Prashant K. & Dong, Yueping & Takeuchi, Yasuhiro, 2020. "Optimal control of infectious disease: Information-induced vaccination and limited treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
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