Mathematical Biology Seminar
Peter Kim
University of Sydney
Wednesday, November 16th, 2011
1:00pm in LCB 215
"Bridging agent-based models and PDEs: A model of cell differentiation"
Different modeling frameworks have been applied to cell differentiation, including partial differential equations (PDEs) and agent-based models (ABMs). ABMs simulate individual cell behavior, while PDEs model spatial dynamics at a population level. Also, ABMs directly capture randomness and variability, but PDEs are faster to evaluate numerically and more conducive to mathematical analysis. Because of the advantages of each modeling strategy, it is valuable to form bridges between them to benefit from both and understand their similarities and differences.
To begin building this connection, we present an ABM of blood cell differentiation proposed by Roeder et al. (Nature Medicine 2006) and formulate a PDE model that reproduces the behavior of the ABM for a variety of parameters. We then show how to obtain the PDE model by translating the ABM to a system of difference equations that suggests a numerical scheme for a PDE system. In conclusion, we point out that this approach of introducing an intermediate system of difference equations could provide a general method for constructing analogous PDE systems from other ABMs.
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