Existence and Sensitivity Analysis of a Caputo-Fabirizo Fractional Order Vector-Borne Disease model

In this study, we develop a mathematical model for vector-borne infections within a fractional-order framework, employing the Caputo-Fabrizio fractional derivative to enhance the analysis. The steady states of the system are examined, and the basic reproduction number $\mathcal{R}_0$ is derived using the next-generation matrix method. The existence and uniqueness of solutions are established through the application of the Banach fixed-point theorem. A detailed sensitivity analysis of $\mathcal{R}_0$ identifies the most critical parameters influencing the disease dynamics. Numerical simulations are performed to validate the theoretical findings and highlight key factors impacting the control and prevention of the infection. This work provides insights into the dynamics of vector-borne infections and offers a robust mathematical approach for optimizing intervention strategies.