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This paper presents a stochastic model for COVID-19 that takes into account factors such as incubation times, vaccine effectiveness, and quarantine periods in the spread of the virus in symptomatically contagious populations. The paper outlines the conditions necessary for the existence and uniqueness of a global solution for the stochastic model. Additionally, the paper employs nonlinear analysis to demonstrate some results on the ergodic aspect of the stochastic model. The model is also simulated and compared to deterministic dynamics. To validate and demonstrate the usefulness of the proposed system, the paper compares the results of the infected class with actual cases from Iraq, Bangladesh, and Croatia. Furthermore, the paper visualizes the impact of vaccination rates and transition rates on the dynamics of infected people in the infected class. • Stochastic modeling of COVID-19 with the effect of vaccination, transition parameters and incubation period. • Existence and uniqueness of global solution. • Ergodic features and Extinction analysis of the stochastic model. • Comparison of deterministic and stochastic model. • Validation of the results with real data from some countries. [ABSTRACT FROM AUTHOR]