Risk models for food safety

Jessica Tressou (INRA) et Patrice Bertail (Paris-Ouest)

Food safety is now receiving increasing attention both in the public health community and in the scienti fic literature. Some food may indeed contain varying amounts of chemicals such as methylmercury (present in sea food), dioxins (in poultry, meat) or mycotoxins (in cereals, dried fruits, etc.), which may cause major health problems when accumulating inside the body in excessive doses. This topic naturally interfaces with various disciplines, such as biology, economics, nutritional medicine, toxicology and of course applied mathematics with the aim to develop rigorous methods for quantitative risk assessment.

The study of dietary exposure to food contaminants has raised many stimulating questions and motivated the use and/or the development of appropriate statistical methods for analyzing the data. Most recent works are mainly centered on static approaches for modelling the quantity X of a speci fic food contaminant ingested on a short period of time and computing the probability that X exceeds a maximum tolerable dose, eventually causing adverse e ffects on human health. This can be done either by using Monte-carlo type methods (for large risks) or extreme value theory.

However, it is essential for successful modelling to take appropriate account of the kinetics in man of the chemical of interest, when considering contaminants such as methylmercury, our running example in this course, with a half-life measured in weeks rather than days.

In this course, we will also present some variations over the traditional "ruin models" used in insurance which may be helpful for modeling the dynamic of the exposure. The amount of contaminant present in the body evolves through its accumulation after repeated intakes (food consumption) and according to the pharmacokinetics governing its elimination/excretion, so that its temporal evolution is described by a piecewise-deterministic Markov process (PDM process in abbreviated form): the accumulation process is modeled by a marked point process in a standard fashion, while the elimination phenomenon is described by a di fferential equation with random coefficients, randomness accounting for the variability of the rate at which the total contaminant body burden decreases in between intakes due to metabolic factors. Such a process slightly extends ruin models and storage models with general release rules widely used in operations research and engineering for dealing with problems such as water storage in dams, in that one allows here the (content dependent) release rate to be random, as strongly advocated by biological modeling, and inter-intake times are not required to be exponentially distributed. In some particular case (linear rate in the phamacokinetic elimination), these models may be seen as shot noise models.


The purpose of the course is to introduce the basic tools of ruin models in the framework of food risk assessments, as well as to emphasize the importance of developing new models and tools for analysing multivariate risks.

1. Food risk assessment: the static approach (3 hours)

 Introduction to food risk assessment

 Applications of extreme value theory: estimation of the Pareto index in the iid case 

Characterizing population at risk: a case study on Methyl-mercury

2. The basic dynamic models: Cramer-Lundberg (without and with barrier) and its generalisations (2 hours)

Spaare-Anderson model

Introducing dependence

3. KDEM Kinetic Dynamic Exposure Models (3 hours)

Probabilistic study of the model 

Statistical analysis

Date Course Place
28 Jan 2016 14:00 Risk models for food safety Université Paris Ouest Nanterre, Bâtiment G, Room 614
04 Feb 2016 14:00 Risk models for food safety Université Paris Ouest Nanterre, Bâtiment G, Room 511
11 Feb 2016 14:00 Risk models for food safety Université Paris Ouest Nanterre, Bâtiment G, Room 614