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<p>In this study, we develop a fractional-order mathematical model to investigate the transmission dynamics of monkeypox disease using the Caputo derivative. To ensure that the model accurately represents the epidemiological patterns of monkeypox cases in the USA, some parameters are estimated from available demographic and literature data, while others are obtained using the least-squares curve-fitting method. From a dynamical systems perspective, we established the existence and uniqueness of solutions, along with their non-negativity and boundedness. The basic reproduction number is computed using the next generation matrix approach, and the influence of model parameters on this threshold is illustrated graphically. A normalized sensitivity analysis is performed to identify the most influential parameters affecting <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>. Furthermore, stability conditions for both the disease-free equilibrium and the endemic equilibrium are derived and validated through numerical simulations and graphical analysis. To control the spread of the disease, three intervention strategies are incorporated into the model using optimal control theory: public awareness, vaccination of susceptible individuals, and treatment of infected individuals. Numerical simulations are carried out to compare the disease dynamics with and without these control measures, demonstrating their effectiveness in reducing infection levels. Finally, a cost-effectiveness analysis is conducted using the Infections Averted Ratio (IAR) to determine the most economically efficient strategy for mitigating the spread of monkeypox.</p>

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Dynamical analysis and optimal control of fractional monkeypox transmission model

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Jatin Bansal,
  • Anoop Kumar

摘要

In this study, we develop a fractional-order mathematical model to investigate the transmission dynamics of monkeypox disease using the Caputo derivative. To ensure that the model accurately represents the epidemiological patterns of monkeypox cases in the USA, some parameters are estimated from available demographic and literature data, while others are obtained using the least-squares curve-fitting method. From a dynamical systems perspective, we established the existence and uniqueness of solutions, along with their non-negativity and boundedness. The basic reproduction number is computed using the next generation matrix approach, and the influence of model parameters on this threshold is illustrated graphically. A normalized sensitivity analysis is performed to identify the most influential parameters affecting \(R_{0}\) R 0 . Furthermore, stability conditions for both the disease-free equilibrium and the endemic equilibrium are derived and validated through numerical simulations and graphical analysis. To control the spread of the disease, three intervention strategies are incorporated into the model using optimal control theory: public awareness, vaccination of susceptible individuals, and treatment of infected individuals. Numerical simulations are carried out to compare the disease dynamics with and without these control measures, demonstrating their effectiveness in reducing infection levels. Finally, a cost-effectiveness analysis is conducted using the Infections Averted Ratio (IAR) to determine the most economically efficient strategy for mitigating the spread of monkeypox.