المجلة الدولية للعلوم والتقنية

Deterministic models have played an important role in biology over the past few centuries, and continue to play. However, there is a need to introduce a random factor due to the nature of biological processes, which led to the emergence of stochastic models. To bridge the gap between deterministic and stochastic models, and in appreciation of the huge efforts made in deterministic models, which have played a fundamental role in understanding, predicting, and controlling the transmission dynamics of infectious diseases, this study aims to clarify a method for creating stochastic model for one of most vital and recent deterministic, that is Covid-19 model with two doses, which showed the effect of receiving both doses in containing the disease. To achieve this goal, the deterministic model was studied extensively before converting to corresponding stochastic. The deterministic and stochastic systems were solved numerically and represented using MATAB tools. ........... Keywords: ......Covid-19 deterministic model, stochastic model, next generation matrix method (NGMM), The diffusion matrix G.