Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Open Mathematics

formerly Central European Journal of Mathematics

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

1 Issue per year

IMPACT FACTOR 2016 (Open Mathematics): 0.682
IMPACT FACTOR 2016 (Central European Journal of Mathematics): 0.489

CiteScore 2016: 0.62

SCImago Journal Rank (SJR) 2016: 0.454
Source Normalized Impact per Paper (SNIP) 2016: 0.850

Mathematical Citation Quotient (MCQ) 2016: 0.23

Open Access
See all formats and pricing
More options …
Volume 11, Issue 4 (Apr 2013)


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

Noémi Nagy / Péter Simon
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

  • [1] Barrat A., Barthélemy M., Vespignani A., Dynamical Processes on Complex Networks, Cambridge University Press, Cambridge, 2008 http://dx.doi.org/10.1017/CBO9780511791383CrossrefGoogle Scholar

  • [2] Bollobás B., Random Graphs, 2nd ed., Cambridge Stud. Adv. Math., 73, Cambridge University Press, Cambridge, 2001 http://dx.doi.org/10.1017/CBO9780511814068CrossrefGoogle Scholar

  • [3] Brauer F., van den Driessche P., Wu J. (Eds.), Mathematical Epidemiology, Lecture Notes in Math., 1945, Math. Biosci. Subser., Springer, Berlin-Heidelberg, 2008 Google Scholar

  • [4] Danon L., Ford A.P., House T., Jewell C.P., Keeling M.J., Roberts G.O., Ross J.V., Vernon M.C., Networks and the epidemiology of infectious disease, Interdisciplinary Perspectives on Infectious Diseases, 2011, #284909 Google Scholar

  • [5] Gleeson J.P., High-accuracy approximation of binary-state dynamics on networks, Phys. Rev. Lett., 2011, 107(6), #068701 http://dx.doi.org/10.1103/PhysRevLett.107.068701Google Scholar

  • [6] House T., Keeling M.J., Insights from unifying modern approximations to infections on networks, Journal of the Royal Society Interface, 2011, 8(54), 67–73 http://dx.doi.org/10.1098/rsif.2010.0179Web of ScienceCrossrefGoogle Scholar

  • [7] Keeling M.J., Eames K.T.D., Networks and epidemic models, Journal of the Royal Society Interface, 2005, 2(4), 295–307 http://dx.doi.org/10.1098/rsif.2005.0051Web of ScienceCrossrefGoogle Scholar

  • [8] Nåsell I., The quasi-stationary distribution of the closed endemic SIS model, Adv. in Appl. Probab., 1996, 28(3), 895–932 http://dx.doi.org/10.2307/1428186CrossrefGoogle Scholar

  • [9] Sharkey K.J., Deterministic epidemic models on contact networks: Correlations and unbiological terms, Theoretical Population Biology, 2011, 79(4), 115–129 http://dx.doi.org/10.1016/j.tpb.2011.01.004Web of ScienceCrossrefGoogle Scholar

  • [10] Simon P.L., Taylor M., Kiss I.Z., Exact epidemic models on graphs using graph-automorphism driven lumping, J. Math. Biol., 2010, 62(4), 479–508 http://dx.doi.org/10.1007/s00285-010-0344-xCrossrefWeb of ScienceGoogle Scholar

  • [11] Taylor M., Simon P.L., Green D.M., House T., Kiss I.Z., From Markovian to pairwise epidemic models and the performance of moment closure approximations, J. Math. Biol., 2012, 646(6), 1021–1042 http://dx.doi.org/10.1007/s00285-011-0443-3CrossrefWeb of ScienceGoogle Scholar

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. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Christoforos Hadjichrysanthou and Kieran J. Sharkey
Journal of Theoretical Biology, 2015, Volume 365, Page 84
A. Szabó-Solticzky, P.L. Simon, J.M. Hyman, F. Milner, and J. Saldaña
Mathematical Modelling of Natural Phenomena, 2014, Volume 9, Number 2, Page 89
Robert R. Wilkinson and Kieran J. Sharkey
Physical Review E, 2014, Volume 89, Number 2

Comments (0)

Please log in or register to comment.
Log in