Global Properties of a Fractional Order Model of a Vector-Borne Disease

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Résumé

We present here a fractional model in the sense of Caputo of a vector-borne disease with insecticide resistance genes. This study is important because it contributes to our understanding of vector-borne disease transmission dynamics using the notion of dif- ferential operators. The use of fractional derivatives in the model provides a memory efect and long-term dynamics often observed in infectious diseases. An epidemic must be able to decline slowly because of the memory of previous contacts. A detailed proof for the existence and uniqueness of the solution of the model is presented. The basic reproduction number R0 is derived, and a stability analysis of the equilibrium points is established. Numerical simulations are provided to prove the usefulness of the theoretical results. We simulated each model compartment at various fractional orders and compared them with integer-order simulation to show the efectiveness of fractional derivatives. Sensitivity analysis of the parameters is conducted, and the most sensitive pa- rameters are identifed.

Mots-clés

fractional differential equation, Lyapunov function, stability, vector-borne disease