Model reduction and quasi-steady state approximation
This work develops a rigorous reduction approach for 2 time scale nonlinear systems of ordinary differential equations. The result is a higher order extension of the Tikhonov singular perturbation theorem for infinite intervals. The application to a model of stem cell dynamics is demonstrated.
A. Marciniak-Czochra, A. Mikelic, T. Stiehl, "Renormalization group second order approximation for singularly perturbed nonlinear ordinary differential equations", Math. Methods in Applied Sciences 41: 5691-5710, 2018.
Multi-scale modeling of mammalian follicular development
This work introduces a stochastic individual-based model of the first stages of follicular development. It considers cell populations that are structured with respect to age and space. Molecular feedbacks between the oocyte and granulosa cells are included. The model can reproduce follicle phenotypes of wild type sheep and important mutants.
F. Clement, P. Michel, D. Monniaux, T. Stiehl, "Coupled Somatic Cell Kinetics and Germ Cell Growth: Multiscale Model-Based Insight on Ovarian Follicular Development", SIAM Multiscale Model. Simul. 11: 719-746, 2013.