Mathematical Analysis of a Stochastic SEIARV Model for COVID-19 Disease Transmission with Intervention

This study presents a stochastic SEIARV model for analysing COVID-19 transmission and vaccination intervention. The model incorporates symptomatic and asymptomatic infectious individuals, demographic recruitment and mortality, disease-induced mortality, incomplete vaccine protection, and stochastic fluctuations in epidemic dynamics. The basic reproduction number, $R_0$, is derived using the next-generation matrix approach, and the disease-free and endemic equilibria are analysed. The stochastic model is solved numerically using the Euler--Maruyama method, and multiple sample paths are generated to examine uncertainty in epidemic trajectories. Numerical results show that vaccination reduces both the reproduction number and the peak infectious population. In particular, increasing the vaccination rate from the baseline level to five times its value reduces $R_0$ below unity and substantially decreases the epidemic peak. The results demonstrate the importance of vaccination in reducing COVID-19 transmission and highlight the value of stochastic modelling in capturing variability and uncertainty in epidemic outcomes.