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Equation-free modeling of evolving diseases: Coarse-grained computations with individual-based models | | Jaime Cisternas
; C. William Gear
; Simon Levin
; Ioannis G. Kevrekidis
; | | Date: |
9 Oct 2003 | | Subject: | Adaptation and Self-Organizing Systems; Populations and Evolution | nlin.AO q-bio.PE | | 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 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. | | Source: | arXiv, nlin.AO/0310011 | | Services: | Forum | Review | PDF | Favorites | |
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