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2013 | 11 | 4 | 800-815
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Monte Carlo simulation and analytic approximation of epidemic processes on large networks

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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.
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Bibliografia
  • [1] Barrat A., Barthélemy M., Vespignani A., Dynamical Processes on Complex Networks, Cambridge University Press, Cambridge, 2008 http://dx.doi.org/10.1017/CBO9780511791383
  • [2] Bollobás B., Random Graphs, 2nd ed., Cambridge Stud. Adv. Math., 73, Cambridge University Press, Cambridge, 2001 http://dx.doi.org/10.1017/CBO9780511814068
  • [3] Brauer F., van den Driessche P., Wu J. (Eds.), Mathematical Epidemiology, Lecture Notes in Math., 1945, Math. Biosci. Subser., Springer, Berlin-Heidelberg, 2008
  • [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
  • [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.107.068701
  • [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.2010.0179
  • [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.2005.0051
  • [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/10.2307/1428186
  • [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.2011.01.004
  • [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-x
  • [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/s00285-011-0443-3
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Bibliografia
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bwmeta1.element.doi-10_2478_s11533-012-0162-z
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