Transmission dynamics of rabies through stochastic analysis with the effect of vaccination in dogs population

Each year, approximately 55,000 people die from the rabies virus, which is transmitted by dogs. Since deterministic approaches ignore effect randomness, such as different environmental factors that affect the rabies process dynamics. In this study, the stochastic epidemic model with the impact of vaccination for dogs is considered to investigate the transmission dynamics of rabies in the population with white noise effect. Firstly, we demonstrate the existence of a global solution and its positive impact. The basic stochastic reproduction number is then computed as a threshold that determines the persistence or extinction of the disease. If \(R_{0}^{s} < 1\) then the disease will be extinct from the population. And if \(R_{0}^{s}> 1\) the disease continues to persist in the population. Finally, we perform the numerical simulation to examine the impact of various parameters on the propagation of disease. The numerical simulation shows that vaccination plays a critical role in the control of the disease. In contrast, the disease spreads when infected dogs met susceptible humans and dogs.