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The Effect of Graph Structure on Epidemic Spread in a Class of Modified Cycle Graphs

  • A. Szabó-Solticzky and P.L. Simon


In this paper, an SIS (susceptible-infected-susceptible)-type epidemic propagation is studied on a special class of 3-regular graphs, called modified cycle graphs. The modified cycle graph is constructed from a cycle graph with N nodes by connecting node i to the node i + d in a way that every node has exactly three links. Monte-Carlo simulations show that the propagation process depends on the value of d in a non-monotone way. A new theoretical model is developed to explain this phenomenon. This reveals a new relation between the spreading process and the average path length in the graph.


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[1] A. Barrat, M. Barthelemy, A. Vespignani. Dynamical Processes on Complex Networks. Cambridge University Press, Cambridge, 2008.
[2] Boguna, M., Pastor–Satorras, R.. Epidemic spreading in correlated complex networks. Phys. Rev. E., 66 (2002), 47104.
[3] L. Danon, A.P. Ford, T. House, C.P. Jewell, M.J. Keeling, G.O. Roberts, J.V. Ross, M.C. Vernon. Networks and the Epidemiology of Infectious Disease, Interdisciplinary Perspectives on Infectious Diseases. 2011:284909 special issue “Network Perspectives on Infectious Disease Dynamics”.
[4] Gleeson, J.P.. High-accuracy approximation of binary-state dynamics on networks. Phys. Rev. Letters, 107 (2011), 068701.
[5] House, T., Keeling, M. J.. Insights from unifying modern approximations to infections on networks. J. Roy. Soc. Interface, 8 (2011), 67-73.
[6] Keeling, M.J., Eames, K.T.D.. Networks and epidemic models. J. Roy. Soc. Interface, 2 (2005), 295-307.
[7] Nagy, N., Simon, P.L.. Monte-Carlo simulation and analytic approximation of epidemic processes on large networks. Central European Journal of Mathematics, 11 (4) (2013), 800-815.
[8] Newman, M. E. J.. The structure and function of complex networks. SIAM Review, 45 (2003), 167-256.
[9] Saramäki, J., Kaski, K.. Modelling development of epidemics with dynamic small-world networks. J. Theor. Biol., 234 (2005), 413-421.
[10] Simon, P.L., Taylor, M., Kiss, I.Z.. Exact epidemic models on graphs using graph automorphism driven lumping. J. Math. Biol., 62 (2010), 479-508.
[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., 64 (2012), 1021-1042.
[12] H.C. Tijms. A First Course in Stochastic Models. John Wiley and Sons, 2003.


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The Effect of Graph Structure on Epidemic Spread in a Class of Modified Cycle Graphs

  • A. Szabó-Solticzky and P.L. Simon


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