A storage model with random release rate for modeling exposure to food contaminants
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,...
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| Format: | Article |
| Language: | English |
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AIMS Press
2007-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.35 |
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| author | Patrice Bertail Stéphan Clémençon Jessica Tressou |
| author_facet | Patrice Bertail Stéphan Clémençon Jessica Tressou |
| author_sort | Patrice Bertail |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-df428a944e20459d93a6a9a42bd4d736 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-df428a944e20459d93a6a9a42bd4d7362025-01-24T01:57:50ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-12-0151356010.3934/mbe.2008.5.35A storage model with random release rate for modeling exposure to food contaminantsPatrice Bertail0Stéphan Clémençon1Jessica Tressou2Modal'X - Université Paris X & CREST - LS, Universié Paris X, Bât. G, 200 avenue de la république, 92001 NanterreModal'X - Université Paris X & CREST - LS, Universié Paris X, Bât. G, 200 avenue de la république, 92001 NanterreModal'X - Université Paris X & CREST - LS, Universié Paris X, Bât. G, 200 avenue de la république, 92001 NanterreThis 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.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.35simulation methodpiecewise-deterministic markovprocessfood safetystability analysis.dietary contaminationpharmacokinetics model |
| spellingShingle | Patrice Bertail Stéphan Clémençon Jessica Tressou A storage model with random release rate for modeling exposure to food contaminants Mathematical Biosciences and Engineering simulation method piecewise-deterministic markovprocess food safety stability analysis. dietary contamination pharmacokinetics model |
| title | A storage model with random release rate for modeling exposure to food contaminants |
| title_full | A storage model with random release rate for modeling exposure to food contaminants |
| title_fullStr | A storage model with random release rate for modeling exposure to food contaminants |
| title_full_unstemmed | A storage model with random release rate for modeling exposure to food contaminants |
| title_short | A storage model with random release rate for modeling exposure to food contaminants |
| title_sort | storage model with random release rate for modeling exposure to food contaminants |
| topic | simulation method piecewise-deterministic markovprocess food safety stability analysis. dietary contamination pharmacokinetics model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.35 |
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