A singular limit for an age structured mutation problem

Jacek Banasiak; Aleksandra Falkiewicz

doi:10.3934/mbe.2017002

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2017, Volume 14, Issue 1: 17-30. Doi: 10.3934/mbe.2017002

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A singular limit for an age structured mutation problem

Jacek Banasiak^1,2, and
Aleksandra Falkiewicz^2,

1.
Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa
2.
Institute of Mathematics, Technical University of Łódź, Łódź, Poland

Received: October 30, 2015

Accepted: March 09, 2016

Published: September 2017

The paper was presented at the conference Micro and Macro Systems in Life Sciences, B¸edlewo, 8-13 June 2015 and was supported by the statutory grant of the Institute of Mathematics of Łódź University of Technology. Participation of A. F. was sponsored by the organizers of the conference.

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Abstract

The spread of a particular trait in a cell population often is modelled by an appropriate system of ordinary differential equations describing how the sizes of subpopulations of the cells with the same genome change in time. On the other hand, it is recognized that cells have their own vital dynamics and mutations, leading to changes in their genome, mostly occurring during the cell division at the end of its life cycle. In this context, the process is described by a system of McKendrick type equations which resembles a network transport problem. In this paper we show that, under an appropriate scaling of the latter, these two descriptions are asymptotically equivalent.

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Mathematics Subject Classification: Primary: 34E15, 92D25; Secondary: 34E13.

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