A Caputo Fractional‐Order Model for Dog Rabies Transmission With Vaccination: A Case Study of Ulanga District, Tanzania

Abstract

Dog rabies remains a major public health concern in many regions, including Ulanga District, Morogoro, Tanzania. This study develops a fractional‐order compartmental model employing Caputo derivatives to incorporate memory effects, providing a more realistic representation of rabies transmission dynamics. We establish the positivity and boundedness of solutions, and prove the existence of both disease‐free equilibrium (DFE) and endemic equilibrium (EE) points. The basic reproduction number, , is derived using a graph‐theoretic approach and characterizes the system’s global stability: the DFE is locally stable when , and an EE exists when . Hyers–Ulam stability analysis confirms the model’s robustness under small perturbations, reinforcing the validity of the fractional‐order framework. The model is calibrated using Bayesian Markov Chain Monte Carlo (MCMC) techniques with field data. Numerical simulations indicate that strong memory effects (i.e., lower values of the fractional order ϕ ) significantly reduce infection levels in dog populations and influence the long‐term behavior of the vaccinated class. Further simulations under varying vaccination coverage levels show a substantial decline in the susceptible population, while also revealing the necessity for complementary control measures to effectively reduce the infections.