Joint Colloquium: Kim -- Bridging Agent-Based Models and PDEs: a Model of Cell Differentiation

Speaker: Dr. Peter Kim (Sydney). Link: 

http://www.maths.usyd.edu.au/u/pkim/

Time: Friday, Oct. 28, 2--3PM, 2011

Room: RC-4082, East Wing of the Red Centre 
Building, UNSW

Lunch: meet around 12:30 for lunch by the 
fig tree outside East Wing of the Red 
Centre Building

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Title: Bridging Agent-Based Models and PDEs: 
a Model of Cell Differentiation

Abstract: different modelling frameworks have been 
applied to cell differentiation, including partial 
differential equations (PDEs) and agent-based models 
(ABMs). ABMs simulate individual cell behaviour, 
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 begin building this connection, we present an 
ABM of blood cell differentiation proposed by Roeder 
et al. (Nat Med 2006) and formulate a PDE model that 
reproduces the behavior of the ABM.  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.  We discuss how 
this approach of introducing an intermediate system 
of difference equations could provide a method for 
constructing analogous PDE systems from other ABMs.

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One choice of commuting from Sydney: meet at Carslaw 
620 around 12 and we share taxi to UNSW. The round 
trip is covered by department colloquium fund.