### Mathematical Biosciences and Engineering

2017, Issue 1: 17-30. doi: 10.3934/mbe.2017002

# A singular limit for an age structured mutation problem

• Received: 31 October 2015 Accepted: 10 March 2016 Published: 01 February 2017
• MSC : Primary: 34E15, 92D25; Secondary: 34E13

• 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.

Citation: Jacek Banasiak, Aleksandra Falkiewicz. A singular limit for an age structured mutation problem[J]. Mathematical Biosciences and Engineering, 2017, 14(1): 17-30. doi: 10.3934/mbe.2017002

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• 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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