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Open Mathematics

formerly Central European Journal of Mathematics

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

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Volume 11, Issue 4 (Apr 2013)


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

Noémi Nagy
  • Institute of Mathematics, Eötvös Loránd University, Pázmány P. s. 1/c, 1117, Budapest, Hungary
  • Email:
/ Péter Simon
  • Institute of Mathematics, Eötvös Loránd University, Pázmány P. s. 1/c, 1117, Budapest, Hungary
  • Email:
Published Online: 2013-01-29 | DOI: https://doi.org/10.2478/s11533-012-0162-z


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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About the article

Published Online: 2013-01-29

Published in Print: 2013-04-01

Citation Information: Open Mathematics, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-012-0162-z. Export Citation

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

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