A Caputo–Fabrizio fractional-order model with MCMC estimation for rabies transmission dynamics in a multi-host population

Rabies is a fatal zoonotic disease that remains a major public health concern, especially in low- and middle-income countries where control measures are often inadequate. Despite vaccination campaigns, the persistence of rabies is exacerbated by complex transmission involving humans, domestic animals, and wildlife. This study proposes a Caputo–Fabrizio fractional-order model to capture the memory-dependent nature of rabies transmission in a multi-host setting. Mathematical analysis is conducted to establish the existence, uniqueness, and stability of solutions using fixed-point theory and the Routh–Hurwitz criterion. The effective reproduction number is derived through a graph-theoretic approach. Parameter estimation is performed using Markov Chain Monte Carlo methods applied to real and synthetic data. Numerical simulations reveal that memory effects introduced by the fractional-order operator significantly influence the dynamics of disease transmission. The results show that incorporating fractional dynamics leads to more realistic predictions compared to classical models, particularly in evaluating the timing and intensity of outbreaks. Moreover, targeted control strategies, especially vaccination and culling, substantially reduce infection levels under fractional-order dynamics. These findings underscore the importance of accounting for memory and non-local effects in infectious disease modeling.