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<p>This paper presents a comprehensive analysis of an optimal control model for spread of infection in infectious diseases utilizing the Fractal-Fractional derivative with an exponentially decaying type kernel. The next-generation matrix method is employed to calculate the reproduction number. The equilibrium points of the model are calculated, and the local and global stability of the disease-free equilibrium point is also examined. Sensitivity analysis is discussed to assess the significance of the parameters. The existence and uniqueness of the solution for the model are demonstrated. A numerical method for modeling infectious diseases is introduced, applying the Newton polynomial. Also, optimal strategies to minimize the prevalence of the disease are identified. Through numerical simulations performed applying MatLab, the impact of various control measures, including disseminating health recommendations via the media, vaccination and therapy, on the spread of infection is analyzed. In addition, the effect of the fractional order and fractal dimension on the transmission dynamics of infection is investigated. By utilizing the incremental cost-effectiveness ratio, the most cost-effective and efficient optimal control strategy is determined. The model designed in this paper is used for transmission of infection in various infectious diseases. Finally, for example, the outbreak of Cholera in Yemen in&#xa0;2017 is analyzed.</p>

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Optimal control strategies and cost-effectiveness analysis for infectious diseases under fractal-fractional derivative: a case study of Cholera outbreak

  • 期刊论文

  • 发表日期：

    2025年1月31日

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  • Behnam Mohammadaliee,
  • Mohammad Esmael Samei,
  • Vahid Roomi,
  • Shahram Rezapour

摘要

This paper presents a comprehensive analysis of an optimal control model for spread of infection in infectious diseases utilizing the Fractal-Fractional derivative with an exponentially decaying type kernel. The next-generation matrix method is employed to calculate the reproduction number. The equilibrium points of the model are calculated, and the local and global stability of the disease-free equilibrium point is also examined. Sensitivity analysis is discussed to assess the significance of the parameters. The existence and uniqueness of the solution for the model are demonstrated. A numerical method for modeling infectious diseases is introduced, applying the Newton polynomial. Also, optimal strategies to minimize the prevalence of the disease are identified. Through numerical simulations performed applying MatLab, the impact of various control measures, including disseminating health recommendations via the media, vaccination and therapy, on the spread of infection is analyzed. In addition, the effect of the fractional order and fractal dimension on the transmission dynamics of infection is investigated. By utilizing the incremental cost-effectiveness ratio, the most cost-effective and efficient optimal control strategy is determined. The model designed in this paper is used for transmission of infection in various infectious diseases. Finally, for example, the outbreak of Cholera in Yemen in 2017 is analyzed.