A storage model with random release rate for modeling exposure to food contaminants - Patrice Bertail; Stéphan Clémençon; Jessica Tressou (Mathematical Biosciences and Engineering)
This paper presents the study of a continuous-time piecewisedeterministicMarkov process for describing the temporal evolution of exposureto a given food contaminant. The quantity X of food contaminantpresent in the body evolves through its accumulation after repeated dietaryintakes on the one hand, and the pharmacokinetics behavior of the chemicalon the other hand. In the dynamic modeling considered here, the accumulationphenomenon is modeled by a simple marked point process with positivei.i.d. marks, and elimination in between intakes occurs at a random linearrate θX, randomness of the coefficient θ accounting for the variability of theelimination process due to metabolic factors. Via embedded chain analysis,ergodic properties of this extension of the standard compound Poisson damwith (deterministic) linear release rate are investigated, the latter being of crucialimportance in describing the long-term behavior of the exposure process(Xt)t≥0 and assessing values such as the proportion of time the contaminantbody burden is over a certain threshold. We also highlight the fact that theexposure process is generally not directly observable in practice and establisha validity framework for simulation-based statistical methods by couplinganalysis. Eventually, applications to methyl mercury contamination data areconsidered.