Fractional-order Modeling and Optimal Control of Dengue-Malaria Co-infection with Local and Advanced Treatment Strategies

Abstract: This study presents a novel fractional-order co-infection model describing the joint transmission dynamics of dengue and malaria using the generalized fractional derivative. The total human population is divided into eight epidemiological compartments that account for single infections, co-infection, treatment stages, and recovery. The proposed framework incorporates memory effects and nonlocal behavior, offering a more realistic representation of disease progression compared to classical integer-order models. Local and advanced treatment strategies are introduced based on infection severity, allowing targeted intervention for both mild and co-infected cases. The fundamental mathematical properties of the model, including positivity, boundedness, existence, and uniqueness of solutions, are rigorously established. The basic reproduction number is derived, and both local and global stability of the disease-free equilibrium are analyzed using suitable Lyapunov functions. A statistical sensitivity analysis is performed to identify key parameters influencing disease transmission. Furthermore, optimal control strategies are formulated to minimize co-infection prevalence while reducing treatment and implementation costs. Numerical simulations validate the theoretical findings and demonstrate that fractional-order dynamics provide deeper insights into long-term disease behavior. The results offer valuable guidance for policymakers in designing effective and cost-efficient strategies to control dengue and malaria co-infection. Graphic Abstract: (Figure presented.) The