An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal
Authored by Ioannis G Kevrekidis, R Erban, HG Othmer
Date Published: 2006
DOI: 10.1016/j.physd.2006.01.008
Sponsors:
United States National Institutes of Health (NIH)
United States National Science Foundation (NSF)
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Abstract
The movement of many organisms can be described as a random walk at
either or both the individual and population level. The rules for this
random walk are based on complex biological processes and it may be
difficult to develop a tractable, quantitatively-accurate, individual-level model. However, important problems in areas ranging
from ecology to medicine involve large collections of individuals, and a
further intellectual challenge is to model population-level behavior
based on a detailed individual-level model. Because of the large number
of interacting individuals and because the individual-level model is
complex, classical direct Monte Carlo simulations can be very slow, and
often of little practical use. In this case, an equation-free approach
{[}I.G. Kevrekidis, C.W. Gear, J.M. Hyman, P. Kevrekidis, O. Runborg, K.
Theodoropoulos, Equation-free, coarse-grained multiscale computation:
enabling microscopic simulators to perform system-level analysis, Commun. Math. Sci. 1 (4) (2003) 715-762] may provide effective methods
for the analysis and simulation of individual-based models. In this
paper we analyze equation-free coarse projective integration. For
analytical purposes, we start with known partial differential equations
describing biological random walks and we study the projective
integration of these equations. In particular, we illustrate how to
accelerate explicit numerical methods for solving these equations. Then
we present illustrative kinetic Monte Carlo simulations of these random
walks and show that a decrease in computational time by as much as a
factor of a thousand can be obtained by exploiting the ideas developed
by analysis of the closed form PDEs. The illustrative biological example
here is chemotaxis, but it could be any random walker that biases its
movement in response to environmental cues. (c) 2006 Elsevier B.V. All
rights reserved.
Tags
Simulations
systems
Bacterial chemotaxis
Integration
Differential-equations
Escherichia-coli
Monte-carlo
Molecular-dynamics
Dictyostelium-discoideum
Adaptive mesh