Geodesic
Multiscale population dynamics in reproductive biology: singular perturbation reduction in deterministic and stochastic models
Celine Bonnet1 ; Keltoum Chahour2 ; Frédérique Clément3 ; Marie Postel4 ; Romain Yvinec5
1 CMAP, Ecole Polytechnique, Route de Saclay, 91128 Palaiseau cedex, France.
2 LERMA, Mohammadia Engineering School, Mohamed V University in Rabat, Morocco LJAD Université Côte d’Azur, Parc Valrose, 06108 Nice, France
3 Inria, Université Paris-Saclay, LMS, Ecole Polytechnique, CNRS, Université Paris-Saclay
4 Sorbonne Université, Université Paris-Diderot SPC, CNRS, Laboratoire Jacques-Louis Lions, LJLL
5 PRC, INRA, CNRS, IFCE, Université de Tours, 37380 Nouzilly, France
ESAIM. Proceedings, Tome 67 (2020), pp. 72-99.

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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.
DOI : 10.1051/proc/202067006

Celine Bonnet 1 ; Keltoum Chahour 2 ; Frédérique Clément 3 ; Marie Postel 4 ; Romain Yvinec 5

1 CMAP, Ecole Polytechnique, Route de Saclay, 91128 Palaiseau cedex, France.
2 LERMA, Mohammadia Engineering School, Mohamed V University in Rabat, Morocco LJAD Université Côte d’Azur, Parc Valrose, 06108 Nice, France
3 Inria, Université Paris-Saclay, LMS, Ecole Polytechnique, CNRS, Université Paris-Saclay
4 Sorbonne Université, Université Paris-Diderot SPC, CNRS, Laboratoire Jacques-Louis Lions, LJLL
5 PRC, INRA, CNRS, IFCE, Université de Tours, 37380 Nouzilly, France 
@article{EP_2020_67_a6,
     author = {Celine Bonnet and Keltoum Chahour and Fr\'ed\'erique Cl\'ement and Marie Postel and Romain Yvinec},
     title = {Multiscale population dynamics in reproductive biology: singular perturbation reduction in deterministic and stochastic models},
     journal = {ESAIM. Proceedings},
     pages = {72--99},
     publisher = {mathdoc},
     volume = {67},
     year = {2020},
     doi = {10.1051/proc/202067006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202067006/}
}
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Celine Bonnet; Keltoum Chahour; Frédérique Clément; Marie Postel; Romain Yvinec. Multiscale population dynamics in reproductive biology: singular perturbation reduction in deterministic and stochastic models. ESAIM. Proceedings, Tome 67 (2020), pp. 72-99. doi : 10.1051/proc/202067006. http://geodesic.mathdoc.fr/articles/10.1051/proc/202067006/

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