Modeling and analysis of cell population dynamics : application to the early development of ovarian follicles.

Summary This thesis aims at designing and analyzing population dynamics models dedicated to the dynamics of somatic cells during the early stages of ovarian follicle growth. The behavior of the models is analyzed by theoretical and numerical approaches, and the parameter values are calibrated by proposing maximum likelihood strategies adapted to our specific dataset. A non-linear stochastic model, which takes into account the joint dynamics between two cell types (precursor and proliferative), is dedicated to the activation of follicular growth. A rigorous finite state projection approach is used to characterize the state of the system at extinction and to calculate the extinction time of the precursor cells. A multi-type linear age-structured model, applied to the proliferative cell population, is dedicated to early follicular growth. The different types correspond here to the spatial positions of the cells. This model is decomposable and the transitions are unidirectional from the first to the last type. We prove the convergence in long time of the stochastic Bellman-Harris model and of the McKendrick-VonFoerster multi-type equation. We adapt existing results to the case where the Perron-Frobenius theorem does not apply, and we obtain explicit analytical formulas for the asymptotic moments of the cell numbers and the stationary age distribution. We also study the well-posedness of the inverse problem associated with the deterministic model.