American Institute of Mathematical Sciences

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2008, 5(1): 35-60. doi: 10.3934/mbe.2008.5.35

A storage model with random release rate for modeling exposure to food contaminants

Patrice Bertail 1, , Stéphan Clémençon 2, and  Jessica Tressou 3,

1. 

Modal'X - Université Paris X & CREST - LS, Universié Paris X, Bât. G, 200 avenue de la république, 92001 Nanterre, France
2. 

LTCI - UMR 5141 Telecom Paris / CNRS & Mét@risk - INRA, Telecom Paris - TSI, rue Barrault, 75634 Paris Cedex 13, France
3. 

Mét@risk - INRA & ISMT - HKUST, Hong Kong University of Science and Technology, ISMT, Clear Water Bay, HONG KONG, China

Received  April 2007 Revised  October 2007 Published  January 2008

This paper presents the study of a continuous-time piecewisedeterministic Markov process for describing the temporal evolution of exposure to a given food contaminant. The quantity X of food contaminant present in the body evolves through its accumulation after repeated dietary intakes on the one hand, and the pharmacokinetics behavior of the chemical on the other hand. In the dynamic modeling considered here, the accumulation phenomenon is modeled by a simple marked point process with positive i.i.d. marks, and elimination in between intakes occurs at a random linear rate θX, randomness of the coefficient θ accounting for the variability of the elimination process due to metabolic factors. Via embedded chain analysis, ergodic properties of this extension of the standard compound Poisson dam with (deterministic) linear release rate are investigated, the latter being of crucial importance in describing the long-term behavior of the exposure process (Xt)t≥0 and assessing values such as the proportion of time the contaminant body burden is over a certain threshold. We also highlight the fact that the exposure process is generally not directly observable in practice and establish a validity framework for simulation-based statistical methods by coupling analysis. Eventually, applications to methyl mercury contamination data are considered.
Keywords: simulation method, piecewise-deterministic Markov process, food safety, stability analysis., dietary contamination, pharmacokinetics model.
Mathematics Subject Classification: Primary: 60J25, 62P10; Secondary: 92B1.
Citation: Patrice Bertail, Stéphan Clémençon, Jessica Tressou. A storage model with random release rate for modeling exposure to food contaminants. Mathematical Biosciences & Engineering, 2008, 5 (1) : 35-60. doi: 10.3934/mbe.2008.5.35
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