Mathematical Biology Seminar

Time scale separation in life-long ovarian follicles population dynamics model

Speaker(s): Romain Yvinec (INRAE, Physiologie de la Reproduction)
In this talk, we will detail population dynamics approach to study the aging of the ovarian follicle population. We revisit compartmental population dynamics model for ovarian follicles development [1] by adding follicles interaction that result (directly or indirectly) from the control exerted onto their growth and death rates by reproductive hormones. The shape of the follicle population distribution through time is obtained thanks to a time scale difference between follicle activation and follicle growth [2]. We obtain rigorously a limit model [3] that enable to study the effect of the growing follicle pool onto the quiescent one. Finally, we show how to calibrate such compartmental models on mice using published population count data and several perturbation scenarios [4]. References [1] M. Faddy, E. Jones, and R. Edwards, An analytical model for ovarian follicle dynamics, J. Exp. Zool., 197:173–185, 1976. [2] C. Bonnet, K. Chahour, F. Clément, M. Postel, and R. Yvinec, Multiscale population dynamics in reproductive biology : Singular perturbation reduction in deterministic and stochastic models, ESAIM Proc. Surveys, 67:72–99, 2020. [3] G. Ballif, F. Clément and R. Yvinec, Averaging of a Stochastic Slow-Fast Model for Population Dy- namics: Application to the Development of Ovarian Follicles, SIAM J. Appl. Maths., 82(1):359–380, 2022. [4] G. Ballif, F. Clément and R. Yvinec, nonlinear compartmental modeling to monitor ovarian follicle population dynamics on the whole lifespan, hal-03739205.

Physics 119