Inverse problem for cell division rate in population dynamics

Université de Lyon 1, UMR 5208, Institut Camille Jordan, INRIA Grenoble Rhône-Alpes-Dracula, France

^a e-mail: leon-matar.tine@univ-lyon1.fr

Abstract

In population dynamics, more precisely in cell structured population, experimental measures of the temporal dynamics of some parameters are often difficult or even impossible because of the lack of appropriate technology. It is the case of the division rate parameter for a structured population of cells. So theoretical and numerical approaches are needed to recover such parameters by indirect observation of the solution of the modeling system. In this work we present how to estimate the division rate from a growth-fragmentation type equation as done in the work of Doumic and Tine (see [1]) and following the work done in [2] and [3]. The estimation strategy is based on the observation of the long-term solution of the model for a size structured population when the growth and division rates are fully general. The issue of the theoretical and numerical results are discussed here.