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John Nardini, Department of Applied Mathematics, University of Colorado Boulder

Biochemical activity-structured population models

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Structured partial differential equation models are widespread in math biology.听 For age- and size-听structuring,听these features tend to increase over time. We extend previous results from these two types of structures to investigate a scenario where the added structural dimension may also decrease over time. This is particularly applicable to cell populations with internal biochemical signaling cascades that can activate and deactivate over time in response to the cell population's environment. We apply our results to the well-studied Fisher's Equation and investigate how an added biochemical activity structure can influence traveling wave solutions.