This study aims to analyze a stochastic epidemic system incorporating a relapse mechanism, which is correlated to a Brownian motion (Bm), capturing real-world disease dynamics with more accuracy. We establish the existence, uniqueness, and boundedness of the model’s positive solution, ensuring mathematical consistency. Using stochastic analysis, we derive the stochastic reproduction numbers, \(\mathfrak {R}_{0}^{s}\) and \(\bar{\mathfrak {R}}_{0}^{s}\) , which serves a key function in determining the dynamic behavior of the illness. Specifically, we demonstrate that the illness becomes extinct when \(\mathfrak {R}_{0}^{s} \le 1\) , highlighting conditions under which infection can be eradicated. Conversely, when \(\bar{\mathfrak {R}}_{0}^{s} > 1\) , the disease persists on average, indicating sustained transmission within the population. To further explore these theoretical results, we conduct numerical simulations that illustrate the model’s behavior under various parameter settings. These simulations provide a visual and quantitative validation of our analytical findings, offering insight into how stochastic effects influence disease progression. Our study emphasizes the significance of incorporating stochasticity in epidemic modeling, as it better reflects real-life uncertainties in disease spread. The results contribute to a deeper understanding of relapse-driven epidemics and provide a framework for developing effective control strategies in public health.