Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2003-10-09
Nonlinear Sciences
Adaptation and Self-Organizing Systems
16 pages, 8 figures
Scientific paper
10.1098/rspa.2004.1300
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 analyzes 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 analyzing a stochastic and discrete model for the evolution of disease agents caused by point mutations within individual hosts. % Building up from classical SIR and SIRS 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.
Cisternas Jaime
Gear William C.
Kevrekidis Ioannis G.
Levin Simon
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