Mathematical Model of Canine Rabies Transmission Dynamics with Combined Pre and Post Exposure Vaccination

Canine rabies remains an important public health concern, and mathematical modeling provides a useful framework for understanding its transmission dynamics and evaluating vaccination strategies. This study develops a deterministic mathematical model for canine rabies transmission incorporating pre- and post-exposure vaccination. The positivity and boundedness of the model solutions are established, the rabies-free equilibrium is determined, and the effective reproduction number is derived. The rabies-free equilibrium is shown to be locally asymptotically stable whenever and unstable whenever The condition for the existence of an endemic equilibrium is established, and sensitivity analysis indicates that increases with the transmission contact rate , whereas increasing the disease-induced death rate reduces Numerical simulations are conducted to examine the effects of pre- and post-exposure vaccine effectiveness on rabies transmission dynamics. The results show that increasing the effectiveness of both vaccination strategies reduces rabies transmission and increases the number of protected dogs. However, pre-exposure vaccination has a greater effect on the protected dog population than post-exposure vaccination.