In this article, a stochastic model is introduced to describe the spread of coronavirus with considering several disease compartments related to different age groups. The presented model is based on observing safety protocols, such as quarantine and mask use, by people at different ages. In order to simulate the natural randomness, some white noises are added to five main parameters of the proposed model. Moreover, the existence and uniqueness of the solution for this stochastic model are proved. Finally, some numerical results are outlined by using the famous Euler method to investigate the effect of safety protocols on the prevalence of COVID-19.