<p>This paper studies the global dynamics and stochastic stability of an SEIR epidemic model that describes infectious disease transmission. The population is partitioned into four compartments: susceptible, exposed, infectious, and recovered. Interactions and transitions among the segments are referred to by a system of deterministic differential equations. To incorporate real-world variability and inherent randomness of disease transmission, stochastic elements are added to this through Brownian motion. Global stability of both the disease-free and endemic equilibrium points is evaluated under deterministic and stochastic conditions with the use of Lyapunov functions. The stability of the system in the presence of random fluctuations is analyzed with stochastic perturbations. A global sensitivity analysis is run to evaluate the robustness of the model. Theoretical results are validated through numerical simulations delineating the effects of key parameters on disease spread and the efficacy of interventions in containing outbreaks.</p>