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In this study, we describe different modeling approaches for ovarian folliclepopulation dynamics, based on either ordinary (ODE), partial (PDE) orstochastic (SDE) differential equations, and accounting for interactionsbetween follicles. We put a special focus on representing the population-levelfeedback exerted by growing ovarian follicles onto the activation of quiescentfollicles. We take advantage of the timescale difference existing between thegrowth and activation processes to apply model reduction techniques in theframework of singular perturbations. We first study the linear versions of themodels to derive theoretical results on the convergence to the limit models. Inthe nonlinear cases, we provide detailed numerical evidence of convergence tothe limit behavior. We reproduce the main semi-quantitative featurescharacterizing the ovarian follicle pool, namely a bimodal distribution of thewhole population, and a slope break in the decay of the quiescent pool withaging.

Multiscale population dynamics in reproductive biology: singular perturbation reduction in deterministic and stochastic models