question: This work is devoted to a stochastic model on the spread and control of corona virus (COVID-19), in which the total population of a corona infected area is divided into susceptible, infected, and recovered classes In reality, the number of individuals who get disease, the number of deaths due to corona virus, and the number of recovered are stochastic, because nobody can tell the exact value of these numbers in the future The models containing these terms must be stochastic Such numbers are estimated and counted by a random process called a Poisson process (or birth process) We construct an SIR-type model in which the above numbers are stochastic and counted by a Poisson process To understand the spread and control of corona virus in a better way, we first study the stability of the corresponding deterministic model, investigate the unique nonnegative strong solution and an inequality managing of which leads to control of the virus After this, we pass to the stochastic model and show the existence of a unique strong solution Next, we use the supermartingale approach to investigate a bound managing of which also leads to decrease of the number of infected individuals Finally, we use the data of the COVOD-19 in USA to calculate the intensity of Poisson processes and verify our results [ABSTRACT FROM AUTHOR] Copyright of Advances in Difference Equations is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission However, users may print, download, or email articles for individual use This abstract may be abridged No warranty is given about the accuracy of the copy Users should refer to the original published version of the material for the full abstract (Copyright applies to all Abstracts )