Fractional nonlinear dynamics and forward bifurcation in a memory-based cholera model.

This study explores the use of fractional-order epidemic models to capture the memory-dependent and nonlinear behaviors inherent in cholera transmission. We present a fractional-order susceptible-infected-recovered-individuals adopting preventive measures-bacteria model that integrates preventive behavior and environmental feedback. By applying the Caputo derivative, we demonstrate the existence, uniqueness, and boundedness of the model's solutions and derive an analytical expression for the basic reproduction number R0. Our stability and bifurcation analyses show how memory influences the system's transition from a disease-free to an endemic state via a forward bifurcation. We also design a fractional optimal control strategy that synthesizes health education, protection, and sanitation measures. Numerical simulations indicate that the fractional dynamics help suppress infection peaks by extending transient memory effects, which enhances the system's resilience to epidemics and lowers environmental contamination. These results underscore the profound impact of fractional-order memory and nonlinear coupling on both epidemic thresholds and the effectiveness of control measures, providing new perspectives on the dynamics of waterborne diseases.