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

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Résumé

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 R_0≤1, while a unique, globally stable endemic equilibrium exists if 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.

Mots-clés

Fractional-order mathematical model. General incidence function. Vaccination coverage. Lyapunov function. Graph theory.