TY - JOUR
T1 - Equation-free modelling of evolving diseases
T2 - Coarse-grained computations with individual-based models
AU - Cisternas, Jaime
AU - Gear, Charles William
AU - Levin, Simon Asher
AU - Kevrekidis, Yannis
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2004/10/8
Y1 - 2004/10/8
N2 - 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.
AB - 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.
KW - Equation-free
KW - Individual-based model
KW - Influenza A drift
KW - Multiscale analysis
KW - Travelling wave
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U2 - 10.1098/rspa.2004.1300
DO - 10.1098/rspa.2004.1300
M3 - Article
AN - SCOPUS:17144394892
SN - 1364-5021
VL - 460
SP - 2761
EP - 2779
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2050
ER -