A Comparative Study of a Fractional-Order Rabies Model With MCMC Estimation Using Singular and Nonsingular Operators

Rabies remains a significant public health concern, particularly in regions with high dog-mediated transmission, and understanding its dynamics is crucial for effective control strategies. This study investigates the transmission dynamics of rabies by developing a deterministic human-dog model extended to fractional-order derivatives, incorporating three operators: Caputo, Caputo–Fabrizio (CF), and Atangana–Baleanu–Caputo (ABC), to capture memory and hereditary effects. Model parameters were estimated from field data using the Markov chain Monte Carlo (MCMC) method, and the effective reproduction number, Re, was derived via a graph-theory approach. Mathematical analysis establishes the positivity, boundedness, and stability of solutions. Comparative simulations indicate that fractional-order models capture slower disease progression compared to classical integer-order systems, with the ABC operator producing the most conservative epidemic projections, reflecting realistic epidemic inertia. The study highlights the critical impact of vaccination, culling, and postexposure prophylaxis (PEP) in controlling rabies. The novelty of this work lies in the comprehensive comparison of different fractional-order operators within the same modeling framework, providing new insights into the role of memory effects in rabies transmission and guiding more effective intervention strategies.