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Individual and population approaches for calibrating division rates in population dynamics: Application to the bacterial cell cycle

Doumic, Marie; Hoffmann, Marc (2021), Individual and population approaches for calibrating division rates in population dynamics: Application to the bacterial cell cycle. https://basepub.dauphine.psl.eu/handle/123456789/22274

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-03328781
Date
2021
Series title
Cahier de recherche du CEREMADE
Pages
82
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Author(s)
Doumic, Marie
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Hoffmann, Marc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.
Subjects / Keywords
Long-term dynamics; Asymptotic behaviour; Incremental model; Adder model; Renewal process; Renewal equation; Growth-fragmentation process; Gowth-fragmentation equation; Kernel density estimation; Nonparametric statistical inference; Inverse problem; Bacterial growth; Cell division cycle; Eigenvalue problem; Malthusian parameter