A Caputo fractional-order model with MCMC for rabies transmission dynamics

Abstract

Rabies continues to pose a severe public health threat, particularly in regions with high interactions between humans and infected dog populations. This study develops a fractional-order mathematical model using the Caputo derivative to capture the memory and hereditary effects in rabies transmission dynamics. The model incorporates key intervention strategies, including public health education, treatment, and culling of stray and infected dogs, to evaluate their effectiveness in controlling rabies outbreaks. The Markov Chain Monte Carlo (MCMC) method is utilized for parameter estimation, enhancing model precision and predictive accuracy. Stability analysis demonstrates that the disease-free equilibrium is locally asymptotically stable when effective reproduction number $R_e<1$. Numerical simulations reveal that fractional-order model provides a more flexible and realistic representation of rabies spread compared to classical integer-order model. The results highlight the significant impact of public health education, treatment and targeted culling in reducing infection rates. The findings offer crucial insights for policymakers and public health officials in designing optimal intervention strategies to achieve sustainable rabies control.