Enhanced Analysis of General Noncontinuous Stochastic Epidemic Model With Vaccination: A Novel Framework and Practical Application to COVID-19 in Saudi Arabia

This paper introduces an enhanced analysis of a stochastic epidemic model that integrates vaccination and discontinuities. Our methodology initiates with formulating a perturbed model incorporating dual general incidence functions and a thorough distribution for jump components. After confirming the well-posed nature of this model, we proceed to establish a global threshold criterion that discerns between the persistence and eradication of the infection. The accuracy of this threshold is scrutinized through numerical simulations utilizing real data related to COVID-19 in Saudi Arabia. A distinctive feature of our approach is its departure from previous studies, as we provide a comprehensive framework and pinpoint optimal conditions for the model.