A fractional SEIVRB model for aquatic diseases dynamics with stability analysis and numerical solution

This research presents a fractional epidemiological model utilizing the standard incidence rate to characterize the transmission dynamics of aquatic infectious diseases like cholera. The framework incorporates a vaccinated compartment to assess preventive measures. We analytically derive both disease-free and endemic equilibrium states and compute the basic reproduction number. The human population is modeled as a time-dependent variable, and we construct a positively invariant domain for the solution space, demonstrating boundedness and nonnegativity of solutions. For the disease-free equilibrium, local asymptotic stability is verified through the Routh–Hurwitz criterion, while global stability is established using Lyapunov direct method. For the endemic equilibrium, global asymptotic stability is proven through a direct Lyapunov approach. In order to thoroughly test the proposed fractional model, real data was incorporated in the numerical simulation phase. Numerical simulation employs a computational scheme utilizing the piecewise Chebyshev cardinal functions, reducing the fractional system to an algebraic problem.