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 postexposure 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, R-0, 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 diseasefree 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 R-0 < 1 and , R-0< 1respectively. 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.