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

## TL;DR

This paper explores multiscale modeling of ovarian follicle population dynamics using differential equations and singular perturbation techniques, revealing key population features and convergence behaviors.

## Contribution

It introduces a unified approach applying singular perturbation reduction to both deterministic and stochastic models of follicle dynamics, highlighting population feedback effects.

## Key findings

- Convergence of models to limit behaviors demonstrated.
- Reproduction of bimodal population distribution.
- Identification of a slope break in follicle decay with age.

## Abstract

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.