DYNAMICS OF A WATERBORNE DISEASE MODEL IN POROUS MEDIA USING CAPUTO FRACTIONAL VARIABLE ORDER DERIVATIVE

In this study, we incorporate the Caputo Fractional Variable Order Derivative (CFVOD) to account for memory effects and nonlocal interactions, improving the mathematical description of the transmission of water-based diseases. Understanding fluid and contaminant movement requires a more complex description of the dynamic processes occurring with inporous media, which is made possible by the application of CFVOD. We prove Ulam–Hyers (UH) stability and investigate the existence and uniqueness of solutions for the model to guarantee robustness against small perturbations. The Euler approach is applied to numerical simulations in order to investigate the temporal spread of illnesses. The incorporation of CFVOD exhibits enhanced precision in capturing disease dynamics, underscoring its possible use in forecasting and controlling waterborne infections inporous settings.