On the stochastic modeling and forecasting of the $\mathcal{S}\mathcal{V}\mathcal{I}\mathcal{R}$ epidemic dynamic model under environmental white noise

This study introduced a novel $\mathcal{S}\mathcal{V}\mathcal{I}\mathcal{R}$ epidemic model incorporating environmental white noise to account for stochastic fluctuations in disease transmission. The model was analyzed to determine conditions for disease persistence and extinction, with outcomes linked to the basic reproduction number. A numerical approach was employed to facilitate computational analysis, and simulations were conducted using data from existing literature to generate realistic predictions. The stochastic model was further evaluated against its deterministic counterpart to assess predictive accuracy. The results highlight the significant role of randomness in epidemiological dynamics, providing valuable insights into disease spread and control strategies.