Modeling Cholera Transmission Dynamics with Vaccination Using Caputo-Fabrizio Fractional Derivatives

Abstract

We develop a fractional-order mathematical model for cholera transmission dynamics incorporating vaccination and memory effects via the Caputo-Fabrizio(CF) derivative. In the model, we capture the waning efficacy of vaccines and heterogeneous disease progression. We derive equilibrium states, compute the basic reproduction number ( ˜ R0), and analyze local/global stability using Lyapunov theory. Numerical simulations highlight the role of fractional order ,q, and vaccine waning on disease dynamics. Results demonstrate that higher q−values accelerate convergence to equilibria, while increased waning elevates R0, extending endemicity. The model suggests revaccination every 2.083 years to sustain herd immunity. This work advances cholera modeling by integrating fractional calculus to improve realism in public health interventions.