Links between deterministic and stochastic approaches for invasion in growth-fragmentation-death models.
Fiche publication
Date publication
décembre 2016
Journal
Journal of mathematical biology
Auteurs
Membres identifiés du Cancéropôle Est :
Dr CHAMPAGNAT Nicolas
Tous les auteurs :
Campillo F, Champagnat N, Fritsch C
Lien Pubmed
Résumé
We present two approaches to study invasion in growth-fragmentation-death models. The first one is based on a stochastic individual based model, which is a piecewise deterministic branching process with a continuum of types, and the second one is based on an integro-differential model. The invasion of the population is described by the survival probability for the former model and by an eigenproblem for the latter one. We study these two notions of invasion fitness, giving different characterizations of the growth of the population, and we make links between these two complementary points of view. In particular we prove that the two approaches lead to the same criterion of possible invasion. Based on Krein-Rutman theory, we also give a proof of the existence of a solution to the eigenproblem, which satisfies the conditions needed for our study of the stochastic model, hence providing a set of assumptions under which both approaches can be carried out. Finally, we motivate our work in the context of adaptive dynamics in a chemostat model.
Mots clés
Death, Models, Biological, Probability, Stochastic Processes, Survival Analysis
Référence
J Math Biol. 2016 12;73(6-7):1781-1821