Coarse-grained bifurcation analysis and detection of criticalities of an individual-based epidemiological network model with infection control

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Abstract

We present and discuss how the so called Equation-free approach for multi-scale computations can be used to systematically study certain aspects of the dynamics of detailed individual-based epidemiological simulators. As our illustrative example, we choose a simple individual-based stochastic epidemic model evolving on a fixed random regular network (RRN). We show how control policies based on the isolation of the infected population can dramatically influence the dynamics of the disease resulting to big-amplitude oscillations. We also address the development of a computational framework that enables detailed epidemiological simulators to converge to their coarse-grained critical points, which mark the onset of the emergent time-dependent solutions as well as to trace branches of coarse-grained unstable equilibria. Using the individual-based simulator we construct the coarse-grained bifurcation diagrams illustrating the dependence of the solutions on the disease characteristics. © 2009 Elsevier Inc. All rights reserved.

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Reppas, A. I., Tsoumanis, A. C., & Siettos, C. I. (2010). Coarse-grained bifurcation analysis and detection of criticalities of an individual-based epidemiological network model with infection control. Applied Mathematical Modelling, 34(3), 552–560. https://doi.org/10.1016/j.apm.2009.06.005

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