Auteurs : Fabien Campillo ¹; Mohsen Chebbi ²; Salwa Toumi ³

• 1 Mathématiques pour les Neurosciences
• 2 Ecole Nationale d'Ingénieurs de Tunis
• 3 Institut National des Sciences Appliquées et de Technologie - Carthage

The model AM2b is conventionally represented by a system of differential equations. However, this model is valid only in a large population context and our objective is to establish several stochastic models at different scales. At a microscopic scale, we propose a pure jump stochastic model that can be simulated exactly. But in most situations this exact simulation is not feasible, and we propose approximate simulation methods of Poisson type and of diffusive type. The diffusive type simulation method can be seen as a discretization of a stochastic differential equation. Finally, we formally present a result of law of large numbers and of functional central limit theorem which demonstrates the convergence of these stochastic models towards the initial deterministic models.