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


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


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


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.
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

Zhichuan Zhu, Bo Yu, Li Yang. Globally convergent homotopy method for designing piecewise linear deterministic contractual function. Journal of Industrial and Management Optimization, 2014, 10 (3) : 717-741. doi: 10.3934/jimo.2014.10.717


Vincent Renault, Michèle Thieullen, Emmanuel Trélat. Optimal control of infinite-dimensional piecewise deterministic Markov processes and application to the control of neuronal dynamics via Optogenetics. Networks and Heterogeneous Media, 2017, 12 (3) : 417-459. doi: 10.3934/nhm.2017019


Sze-Bi Hsu, Christopher A. Klausmeier, Chiu-Ju Lin. Analysis of a model of two parallel food chains. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 337-359. doi: 10.3934/dcdsb.2009.12.337


C. Burgos, J.-C. Cortés, L. Shaikhet, R.-J. Villanueva. A delayed nonlinear stochastic model for cocaine consumption: Stability analysis and simulation using real data. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1233-1244. doi: 10.3934/dcdss.2020356


Soliman A. A. Hamdallah, Sanyi Tang. Stability and bifurcation analysis of Filippov food chain system with food chain control strategy. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1631-1647. doi: 10.3934/dcdsb.2019244


Ana I. Muñoz, José Ignacio Tello. Mathematical analysis and numerical simulation of a model of morphogenesis. Mathematical Biosciences & Engineering, 2011, 8 (4) : 1035-1059. doi: 10.3934/mbe.2011.8.1035


Rebeccah E. Marsh, Jack A. Tuszyński, Michael Sawyer, Kenneth J. E. Vos. A model of competing saturable kinetic processes with application to the pharmacokinetics of the anticancer drug paclitaxel. Mathematical Biosciences & Engineering, 2011, 8 (2) : 325-354. doi: 10.3934/mbe.2011.8.325


Rolf Rannacher. A short course on numerical simulation of viscous flow: Discretization, optimization and stability analysis. Discrete and Continuous Dynamical Systems - S, 2012, 5 (6) : 1147-1194. doi: 10.3934/dcdss.2012.5.1147


Veysel Fuat Hatipoğlu. A novel model for the contamination of a system of three artificial lakes. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2261-2272. doi: 10.3934/dcdss.2020176


Maciek D. Korzec, Hao Wu. Analysis and simulation for an isotropic phase-field model describing grain growth. Discrete and Continuous Dynamical Systems - B, 2014, 19 (7) : 2227-2246. doi: 10.3934/dcdsb.2014.19.2227


Ruchika Sehgal, Aparna Mehra. Worst-case analysis of Gini mean difference safety measure. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1613-1637. doi: 10.3934/jimo.2020037


Wei Feng, Nicole Rocco, Michael Freeze, Xin Lu. Mathematical analysis on an extended Rosenzweig-MacArthur model of tri-trophic food chain. Discrete and Continuous Dynamical Systems - S, 2014, 7 (6) : 1215-1230. doi: 10.3934/dcdss.2014.7.1215


Chao Xing, Jiaojiao Pan, Hong Luo. Stability and dynamic transition of a toxin-producing phytoplankton-zooplankton model with additional food. Communications on Pure and Applied Analysis, 2021, 20 (1) : 427-448. doi: 10.3934/cpaa.2020275


Xianlong Fu, Dongmei Zhu. Stability results for a size-structured population model with delayed birth process. Discrete and Continuous Dynamical Systems - B, 2013, 18 (1) : 109-131. doi: 10.3934/dcdsb.2013.18.109


Ajay Jasra, Kody J. H. Law, Yaxian Xu. Markov chain simulation for multilevel Monte Carlo. Foundations of Data Science, 2021, 3 (1) : 27-47. doi: 10.3934/fods.2021004


Ismail Abdulrashid, Abdallah A. M. Alsammani, Xiaoying Han. Stability analysis of a chemotherapy model with delays. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 989-1005. doi: 10.3934/dcdsb.2019002


Stelian Ion, Gabriela Marinoschi. A self-organizing criticality mathematical model for contamination and epidemic spreading. Discrete and Continuous Dynamical Systems - B, 2017, 22 (2) : 383-405. doi: 10.3934/dcdsb.2017018


Weihua Ruan. Markovian strategies for piecewise deterministic differential games with continuous and impulse controls. Journal of Dynamics and Games, 2019, 6 (4) : 337-366. doi: 10.3934/jdg.2019022


Yulan Lu, Minghui Song, Mingzhu Liu. Convergence rate and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 695-717. doi: 10.3934/dcdsb.2018203


Kuo-Shou Chiu. Periodicity and stability analysis of impulsive neural network models with generalized piecewise constant delays. Discrete and Continuous Dynamical Systems - B, 2022, 27 (2) : 659-689. doi: 10.3934/dcdsb.2021060

2018 Impact Factor: 1.313


  • PDF downloads (34)
  • HTML views (0)
  • Cited by (12)

[Back to Top]