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<p>This work presents a fractional-order mathematical model featuring a generalized incidence function, designed to encapsulate the inherent memory effects observed in biological systems. The model incorporates partial vaccination coverage and accounts for complex transmission pathways, thereby elucidating critical yet often neglected mechanisms that are essential for understanding and managing pathogen propagation effectively. A mathematical analysis is conducted to validate the biological soundness of the model and to characterize the asymptotic behavior of its solutions. The disease-free equilibrium is globally stable if <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {R}_0\le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, while a unique, globally stable endemic equilibrium exists if <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {R}_0&gt; 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, as rigorously proven via Lyapunov functions and graph theory. A sensitivity analysis ranks key parameters to guide public health interventions. Finally, the operational relevance of the model is illustrated and validated through numerical simulations calibrated with historical cholera outbreak data, confirming its utility for epidemic forecasting and the design of effective containment strategies.</p>

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Optimal control and global dynamics of a fractional-order model incorporating general incidence and vaccination coverage

  • 期刊论文

  • 发表日期：

    2026年1月30日

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  • Téwendé Emmanuel Nana,
  • Boureima Sangaré,
  • Abou Bakari Diabaté

摘要

This work presents a fractional-order mathematical model featuring a generalized incidence function, designed to encapsulate the inherent memory effects observed in biological systems. The model incorporates partial vaccination coverage and accounts for complex transmission pathways, thereby elucidating critical yet often neglected mechanisms that are essential for understanding and managing pathogen propagation effectively. A mathematical analysis is conducted to validate the biological soundness of the model and to characterize the asymptotic behavior of its solutions. The disease-free equilibrium is globally stable if \(\mathcal {R}_0\le 1\) R 0 ≤ 1 , while a unique, globally stable endemic equilibrium exists if \(\mathcal {R}_0> 1\) R 0 > 1 , as rigorously proven via Lyapunov functions and graph theory. A sensitivity analysis ranks key parameters to guide public health interventions. Finally, the operational relevance of the model is illustrated and validated through numerical simulations calibrated with historical cholera outbreak data, confirming its utility for epidemic forecasting and the design of effective containment strategies.