Optimal Control For A Crossover Cholera Mathematical Model Using Fractal (Variable-Fractional) Ψ-Caputo Derivative With Nonstandard Kernel

This paper introduces an optimal control strategy for cholera’s crossover mathematical model. The proposed model integrates Ψ-Caputo fractal variable-order derivatives, fractal fractional-order derivatives, and integer-order derivatives across three distinct time intervals, utilizing a simple non-standard kernel function Ψ( t ). A comprehensive stability analysis of the model’s steady states is conducted. The model’s results are compared with real-world data from the cholera outbreak in Yemen. Following this, an optimal control problem is formulated within the crossover framework. To numerically solve the resulting optimality system, a discretized non-standard -finite difference method is developed. Numerical simulations and comparative studies are presented to demonstrate the method’s applicability and the efficiency of the approximation approach. The key finding of this study highlights that the crossover-controlled system proves to be the most effective approach for mitigating and controlling the spread of cholera.