In this research article, we investigated a coronavirus (COVID-19) epidemic model with random perturbations, which was mainly constituted of five major classes: the susceptible population, the exposed class, the infected population, the quarantine class, and the population that has recovered. We studied the problem under consideration in order to derive at least one, and only one, nonlocal solution within the positive feasible region. The Lyapunov function was used to develop the necessary result of existence for ergodic stationary distribution and the conditions for the disease's extinction. According to our findings, the influence of Brownian motion and noise effects on epidemic transmission were powerful. The infection may diminish or eradicate if the noise is excessive. To illustrate our proposed scheme, we numerically simulated all classes' findings.