Individual and population approaches for calibrating division rates in population dynamics: Application to the bacterial cell cycle
Résumé
Modelling, analysing and inferring triggering mechanisms in population reproduction is fundamental in many biological applications. It is also an active and growing research domain in mathematical biology. In this chapter, we review the main results developed over the last decade for the estimation of the division rate in growing and dividing populations in a steady environment. These methods combine tools borrowed from PDE's and stochastic processes, with a certain view that emerges from mathematical statistics. A focus on the application to the bacterial cell division cycle provides a concrete presentation, and may help the reader to identify major new challenges in the field.
Mots clés
Cell division cycle
Bacterial growth
Inverse problem
Nonparametric statistical inference
Kernel density estimation
Gowth-fragmentation equation
Growth-fragmentation process
Renewal equation
Renewal process
Adder model
Incremental model
Asymptotic behaviour
Long-term dynamics
Eigenvalue problem
Malthusian parameter
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