A Storage Model with Random Release Rate for Modeling Exposure to Food Contaminants

This paper is devoted to present and study a specific continuoustimepiecewise-deterministic Markov process for describing the temporal evolution ofexposure to a given food contaminant. The quantity X of food contaminant presentin the body evolves through its accumulation after repeated dietary intakes on theone hand and the pharmacokinetics behavior of the chemical on the other hand. Inthe dynamic modeling considered here, the accumulation phenomenon is modeled bya simple marked point process with positive i.i.d. marks and elimination in betweenintakes occurs at a random linear rate ?X, randomness of the coefficient ? accountingfor the variability of the elimination process due to metabolic factors. Via embeddedchain analysis, ergodic properties of this extension of the standard compound Poissondam with (deterministic) linear release rate are investigated, the latter being of crucialimportance for describing the long-term behavior of the exposure process (Xt)t=0and assessing values of quantities such as the proportion of time the body burdenin contaminant is over a certain threshold. The exposure process being not directlyobservable, simulation-based statistical methods for estimating steady-state or timedependentquantities are also investigated by coupling analysis. Finally, applicationsto methylmercury contamination data are considered.