How does variability in cells aging and growth rates influence the malthus parameter?

Abstract : The aim of this study is to compare the growth speed of different populations of cells measured by their Malthus parameter. We focus on both the age-structured and size-structured equations. A first population (of reference) is composed of cells all aging or growing at the same rate $v¯$. A second population (with variability) is composed of cells each aging or growing at a rate v drawn according to a non-degenerated distribution $ρ$ with mean $v¯$. In a first part, analytical answers are provided for the age-structured model. In a second part, numerical answers based on stochastic simulations are derived for the size-structured model. It appears numerically that for experimentally plausible division rates the population with variability proliferates more slowly than the population of reference. The decrease in the Malthus parameter we measure, around 2% for distributions $ρ$ with realistic coefficients of variations around 15-20%, is determinant since it controls the exponential growth of the whole population.
Document type :
Journal articles
Complete list of metadatas

Cited literature [29 references]  Display  Hide  Download
Contributor : Adélaïde Olivier <>
Submitted on : Tuesday, February 28, 2017 - 11:01:52 AM
Last modification on : Monday, May 6, 2019 - 11:50:22 AM
Long-term archiving on: Monday, May 29, 2017 - 12:22:17 PM


Files produced by the author(s)



Adélaïde Olivier. How does variability in cells aging and growth rates influence the malthus parameter?. Kinetic and Related Models , AIMS, 2017, 10 (2), pp.481-512. ⟨10.3934/krm.2017019⟩. ⟨hal-01274529v2⟩



Record views


Files downloads