New equation for infection spread in a finite population is found. Description of the epidemic COVID-19 by days corresponds to the obtained statistical reports and is an important factor for understanding of the spread and prevalence of infectious diseases. The developed model for a free epidemic based on four natural parameters: the size of population, the number of dangerous contacts of one infected person per day, the probability to obtain infection due to dangerous contact and the duration of the disease. The generalization of the obtained equation for the accounting of quarantine measures requires the inclusion of some function of external influence, which is determined phenomenologically on the basis of the official statistical data.