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.
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Sabbar et al. (2025) studied this question.
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