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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

IMPACT FACTOR 2015: 0.512

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Source Normalized Impact per Paper (SNIP) 2015: 1.233
Impact per Publication (IPP) 2015: 0.546

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Monte Carlo simulation and analytic approximation of epidemic processes on large networks

1Institute of Mathematics, Eötvös Loránd University, Pázmány P. s. 1/c, 1117, Budapest, Hungary

© 2013 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Open Mathematics. Volume 11, Issue 4, Pages 800–815, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-012-0162-z, January 2013

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Low dimensional ODE approximations that capture the main characteristics of SIS-type epidemic propagation along a cycle graph are derived. Three different methods are shown that can accurately predict the expected number of infected nodes in the graph. The first method is based on the derivation of a master equation for the number of infected nodes. This uses the average number of SI edges for a given number of the infected nodes. The second approach is based on the observation that the epidemic spreads along the cycle graph as a front. We introduce a continuous time Markov chain describing the evolution of the front. The third method we apply is the subsystem approximation using the edges as subsystems. Finally, we compare the steady state value of the number of infected nodes obtained in different ways.

MSC: 05C82; 37N25; 60J28; 90B15

Keywords: SIS epidemic; ODE approximation; Network process

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