Analysis and optimal control of a fractional-order model of a vector-borne disease

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Résumé

In this paper, a fractional-order model has been developed to study the transmission dynamics of a vector-borne disease. The use of fractional calculus, particularly through the Caputo derivative, provides a mathematical framework that accounts for memory effects and long-term dynamics often observed in vector-borne diseases. The difference between fractional-order and integer-order derivatives is reflected in the memory effect, which allows for greater accuracy in modeling real epidemiological dynamics. The basic reproduction number is calculated, and a qualitative stability analysis of the equilibria is provided. Two control strategies are applied, namely the rate of human protection and the rate of vector control interventions, with the aim of minimizing the number of infected individuals. Numerical simulations are carried out to illustrate the theoretical results obtained.

Mots-clés

Fractional order, Stability, Optimal Control, Vector-borne disease