Abstract
We model the spread of an epidemic which depends on age and time. The behavior of the model obtained was the object of our studies.This studies shown that on each characteristic curve, the central limit theorem and the law of large numbers were satisfied. In this paper, we write a stochastic model to studie a disease which is begin in a population which is not large. we study overall the stochastic model obtained by varying the age and time together. We prove that the law of large numbers is satisfied.