  In this study, we describe different modeling approaches for ovarian follicle
population dynamics, based on either ordinary (ODE), partial (PDE) or
stochastic (SDE) differential equations, and accounting for interactions
between follicles. We put a special focus on representing the population-level
feedback exerted by growing ovarian follicles onto the activation of quiescent
follicles. We take advantage of the timescale difference existing between the
growth and activation processes to apply model reduction techniques in the
framework of singular perturbations. We first study the linear versions of the
models to derive theoretical results on the convergence to the limit models. In
the nonlinear cases, we provide detailed numerical evidence of convergence to
the limit behavior. We reproduce the main semi-quantitative features
characterizing the ovarian follicle pool, namely a bimodal distribution of the
whole population, and a slope break in the decay of the quiescent pool with
aging.
