A storage model with random release rate for modeling exposure to food contaminants
-
1.
Modal'X - Université Paris X & CREST - LS, Universié Paris X, Bât. G, 200 avenue de la république, 92001 Nanterre
-
2.
LTCI - UMR 5141 Telecom Paris / CNRS & Mét@risk - INRA, Telecom Paris - TSI, rue Barrault, 75634 Paris Cedex 13
-
3.
Mét@risk - INRA & ISMT - HKUST, Hong Kong University of Science and Technology, ISMT, Clear Water Bay, HONG KONG
-
Received:
01 April 2007
Accepted:
29 June 2018
Published:
01 January 2008
-
-
MSC :
Primary: 60J25, 62P10; Secondary: 92B15.
-
-
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.
Citation: Patrice Bertail, Stéphan Clémençon, Jessica Tressou. A storage model with random release rate for modeling exposure to food contaminants[J]. Mathematical Biosciences and Engineering, 2008, 5(1): 35-60. doi: 10.3934/mbe.2008.5.35
-
Abstract
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.
-
-
-
-