The article discusses a probability model of the spread of an epidemic in which the elimination of sick persons (through death, immunity, or isolation) is taken into account. The authors find a limit distribution for the magnitude of the epidemic, $\nu$, on the assumption that $n\to\infty$, where n is the original number of susceptible persons, and $\frac{\mu}{\lambda n}\to 1$, where $\lambda$ and $\mu$ are the coefficient of infection and the coefficient of elimination, respectively.