Equation-free modelling of evolving diseases: coarse-grained computations with individual-based models
Authored by Simon A Levin, J Cisternas, CW Gear, IG Kisvrekidis
Date Published: 2004
DOI: 10.1098/rspa.2004.1300
Sponsors:
AFOSR
United States National Institutes of Health (NIH)
United States National Science Foundation (NSF)
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Abstract
We demonstrate how direct simulation of stochastic, individual-based
models can be combined with continuum numerical-analysis techniques to
study the dynamics of evolving diseases. Sidestepping the necessity of
obtaining explicit population-level models, the approach analyses the
(unavailable in closed form) `coarse' macroscopic equations, estimating
the necessary, quantities through appropriately initialized short
`bursts' of individual-based dynamic simulation. We illustrate this
approach by analysing a stochastic and discrete model for the evolution
of disease agents caused by point mutations within individual hosts.
Building up from classical susceptible-infected-recovered and
susceptible-infected-recovered-susceptible models, our example uses a
one-dimensional lattice for variant space, and assumes a finite number
of individuals. Macroscopic computational tasks enabled through this
approach include stationary-state computation., coarse projective
integration, parametric continuation and stability analysis.
Tags
Evolution
time
Differential-equations
Bifurcation-analysis
Molecular-dynamics
Traveling-waves
Optimal prediction
Influenza-a drift
Smooth landscape
Quasi-continuum