Stochastic modeling using Adomian method and fractionnal differential equations

In this paper, we propose a fractional differential equation of order one-half, to model the evolution through time of the dynamics of accumulation and elimination of the contaminant in human organism with a deficient immune system, during consecutive intakes of contaminated food. This process quantifies the exposure to toxins of subjects living with comorbidity (children not breast-fed, the elderly, pregnant women) to food-born diseases. The Adomian Decomposition Method and the fractional integration of Riemann Liouville are used in the modeling processes.