A Compartmental Model for the Transmission Dynamics of Rabies Disease in Dog Population

Dogs are the main source of more than 90% of human rabies infections that pose a significant threat to public health, primarily in Africa and Asia. However, it is also one of the viral diseases that can be prevented by vaccination that affects both warm-blooded animals and humans. There are two types of rabies vaccines: pre-exposure prophylaxis and post-exposure prophylaxis (PEP). Mathematical models can be valuable tools for predicting and controlling the spread of rabies disease. Thus, we introduce an SEIV (Susceptible-Exposed-Infected-Vaccinated) model incorporate vaccination control strategy to examine the transmission dynamics of rabies disease in dog population. The basic reproduction number, , positively invariant and attracting region, steady states, and the stability analysis of the model are investigated. We find that there are two equilibria exist in the model, i.e., disease-free and endemic equilibria. To prove the global stability of disease-free and endemic equilibria, the theory of asymptotic autonomous system and geometric approach have been applied, respectively. Hence, we find that the disease-free and endemic equilibria are globally asymptotically stable if and , respectively. Numerical simulations are performed to depict the dynamics of the model. As a conclusion, we will be able to control the disease effectively if the vaccination rate is sufficiently large.