| Abstract: |
| We consider structured population models in which the population is subdivided into states according to a certain feature of the individuals. We consider various rules allowing individuals to move between the states -- it may be physical migration between geographical patches, or the change of the genotype by mutation during mitosis. Such models are often referred to as piecewise deterministic but at the level of densities, depending on the migration rule, they may vary from a system of nonlocally coupled McKendrick equations to a system of transport equations on a graph. We address the well-posedness of such problems, classical in the first case and more challenging in the second. The main interest, however, is the asymptotic state aggregation that, in the presence of different time scales of the processes driving the evolution, allows for a significant simplification of the equations. Interestingly, the aggregated equations vary widely, from a scalar transport equation to systems of ordinary differential equations. |
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