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A singular limit for an age structured mutation problem

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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  • 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.

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


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