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.
