A Fractional-Order Model for Chikungunya Virus Transmission with Optimal Control and Artificial Neural Network Validation

In this study, a fractional-order epidemic compartmental model is formulated using the Caputo derivative to account for the memory effects of the chikungunya virus. Based on Banach contractions, fixed-point theorems are used to prove existence and uniqueness, and fundamental properties such as positivity and boundedness are established. Normalized forward sensitivity indices are employed to evaluate the relative impact of model parameters on the transmission dynamics and control of the disease. To reduce the spreading of infection, an optimal control problem is formulated by introducing time-dependent control measures with four control strategies that include public health prevention, treatment enhancement, and vector-control measures. Necessary conditions for optimality are derived using Pontryagin’s Maximum Principle. The predictor–corrector Adams–Bashforth–Moulton scheme is applied across different fractional orders and effectively reduces infection levels. The influence of the fractional order ξ on the epidemic dynamics is investigated, showing that lower values of ξ slow disease progression through a memory effect inherent in the Caputo operator. Moreover, an artificial neural network (ANN) trained via the Levenberg–Marquardt algorithm independently validates the numerical solutions.