Stochastic modeling of the anaeorobic model AM2b: Models at different scales

International audienceThe AM28 model is conventionally represented, in large population, as a system of ordinary differential equations. Our goal is to build several models at different scales. At the microscopic scale (the scale of the individual), we propose a pure jump stochastic model. This model can be exactly simulated. However, when the size of the population is large that type of exact simulation is not feasible, hence we propose approximated simulation methods in discrete time, of the Pois-son type or of the diffusive type. The diffusive type of approximated simulation method can be seen as a discretization of a stochastic differential equation. Finally, we present informally a law of large numbers/central limit theorem of the functional type and how they can be used to provide models at different scales or hybrid models.Le modele AM2b est classiquement represente, en grande population, par un systeme d'equations differentielles. Notre objectif est d'etablir plusieurs modeles a differentes echelles. A I'echelle microscopique (individuelle), on propose un modele stochastique de saut pur. Ce modele peut 1!tre simule de fa~on exacte. Lorsque la taille de la population est grande ce genre de simulation n'est pas praticable, et nous proposons des methodes de simulation, apas de temps discret, de type poissonnien ou de type diffusive. La methode de simulation de type diffusive peut 1!tre vue comme une discretisation d'une equation differentielle stochastique. Nous presentons enfin de fa~on infor-melle un resultat de type loi des grands nombres/theoreme centrallimite fonctionnelle et comment ce resultat peut conduire ades modeles selon I'echelle consideree ou encore ades modeles hybrides