A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes

‎‎The rapid spread of ‎coronavirus ‎disease‎ (‎COVID-19) ‎has‎‎‎ increased the attention to the mathematical modeling of spreading the disease in the ‎world.‎ ‎The behavior of spreading ‎is ‎not ‎deterministic‎ ‎in ‎the ‎last ‎year‎. The purpose of this paper is to presents a stochastic differential equation for modeling the data sets of the COVID-19 involving ‎infected‎, recovered, and death cases. ‎At ‎first, ‎the ‎time ‎series‎ of the covid-19 ‎is modeling with the Ornstein-Uhlenbeck process and then using the Ito lemma and Euler approximation the analytical and numerical simulations for ‎the stochastic ‎differential equation are ‎achieved.‎‎ Parameters estimation is done using the maximum ‎likelihood estimator. Finally, numerical simulations are performed using reported data by ‎the world health ‎organization‎ for case studies of Italy and Iran. The numerical simulations and root mean square error criteria confirm the ‎accuracy and ‎efficiency of the findings of the present ‎study.‎‎‎