Modeling of proliferation of gene mutations in aged structured populations

One of the basic methods in modeling the proliferation of gene mutations is by the systems of ordinary differential equations expressing appropriate conservation principles.  Another possibility is to use a model containing more information about the micro parameters such as the age population density.  This approach is provided by the transport equations on network. We will prove the existence, find the form of solution to such problems and explain in what sense the transport model on a network can be regarded as a generalization of a model of population balance. Our work answers the question when it is reasonable to use a macro model for describing cells’ mutations and when the micro information essentially changes the long time behavior of the system.
(References: A singular limit for an age structured mutation problem, J. Banasiak, A. Falkiewicz, submitted to MATHEMATICAL BIOSCIENCES AND ENGINEERING)