Abstract
Most real networks are characterized by connectivity patterns that evolve in time following complex, non-Markovian, dynamics. Here we investigate the impact of this ubiquitous feature by studying the Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Susceptible (SIS) epidemic models on activity driven networks with and without memory (i.e., Markovian and non-Markovian). We find that memory inhibits the spreading process in SIR models by shifting the epidemic threshold to larger values and reducing the final fraction of recovered nodes. On the contrary, in SIS processes memory reduces the epidemic threshold and, for a wide range of disease parameters, increases the fraction of nodes affected by the disease in the endemic state. The heterogeneity in tie strengths, and the frequent repetition of strong ties it entails, allows in fact less virulent SIS-like diseases to survive in tightly connected local clusters that serve as reservoir for the virus. We validate this picture by studying both processes on two real temporal networks.
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References
C. Butts, Science 325, 414 (2009)
M. Newman, Networks. An Introduction (Oxford University Press, 2010)
A. Barrat, M. Barthélemy, A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, 2008)
G. Caldarelli, Scale-Free Networks (Oxford University Press, 2007)
P. Holme, J. Saramäki, Phys. Rep. 519, 97 (2012)
P. Holme, Eur. Phys. J. B 88, 234 (2015)
C. Cattuto, W. Van den Broeck, A. Barrat, V. Colizza, J. Pinton, A. Vespignani, PloS One 5, e11596 (2010)
L. Isella, J. Stehlé, A. Barrat, C. Cattuto, J.F. Pinton, W.V. den Broeck, J. Theor. Biol. 271, 166 (2011)
A. Panisson, A. Barrat, C. Cattuto, W.V. den Broeck, G. Ruffo, R. Schifanella, Ad Hoc Networks 10, 1532 (2012)
L. Weng, J. Ratkiewicz, N. Perra, B. Goncalves, C. Castillo, F. Bonchi, R. Schifanella, F. Menczer, A. Flammini, The role of information diffusion in the evolution of social networks, in Proc. 19th ACM SIGKDD Conference on Knowledge Discovery and Data Mining KDD, 2013
A. Barrat, C. Cattuto, in Social Phenomena. From Data Analysis to Models (Springer International Publishing, 2015), pp. 37−57
A. Vespignani, Science 325, 425 (2009)
B. Gonçalves, N. Perra, Social Phenomena: From Data Analysis to Models (Springer, 2015)
M. Morris, Nature 365, 437 (1993)
M. Morris, in Sexually Transmitted Diseases, edited by K.K. Holmes et al. (McGraw-Hill, 2007)
A. Clauset, N. Eagle, Persistence and periodicity in a dynamic proximity network, in DIMACS Workshop on Computational Methods for Dynamic Interaction Networks, 2007, pp. 1−5
A. Vespignani, Nat. Phys. 8, 32 (2012)
L.E.C. Rocha, F. Liljeros, P. Holme, PLoS Comput. Biol. 7, e1001109 (2011)
J. Stehlé et al., BMC Medicine 9, 87 (2011)
M. Karsai, M. Kivelä, R.K. Pan, K. Kaski, J. Kertész, A.L. Barabási, J. Saramäki, Phys. Rev. E 83, 025102 (2011)
G. Miritello, E. Moro, R. Lara, Phys. Rev. E 83, 045102 (2011)
M. Kumar Kivela, R. Pan, K. Kaski, J. Kertesz, J. Saramaki, M. Karsai, J. Stat. Mech. 2012, 03005 (2012)
N. Fujiwara, J. Kurths, A. Díaz-Guilera, Phys. Rev. E 83, 025101 (2011)
R. Parshani, M. Dickison, R. Cohen, H.E. Stanley, S. Havlin, Europhys. Lett. 90, 38004 (2010)
P. Bajardi, A. Barrat, F. Natale, L. Savini, V. Colizza, PLoS One 6, e19869 (2011)
A. Baronchelli, A. Díaz-Guilera, Phys. Rev. E 85, 016113 (2012)
M. Starnini, A. Baronchelli, A. Barrat, R. Pastor-Satorras, Phys. Rev. E 85, 056115 (2012)
R. Pfitzner, I. Scholtes, A. Garas, C. Tessone, F. Schweitzer, Phys. Rev. Lett. 110, 19 (2013)
M. Karsai, N. Perra, A. Vespignani, Sci. Rep. 4, 4001 (2014)
T. Hoffmann, M. Porter, R. Lambiotte, Phys. Rev. E 86, 046102 (2012)
Z. Toroczkai, H. Guclu, Physica A 378, 68 (2007)
N. Perra, B. Gonçalves, R. Pastor-Satorras, A. Vespignani, Sci. Rep. 2, 469 (2012)
B. Ribeiro, N. Perra, A. Baronchelli, Sci. Rep. 3, 3006 (2013)
N. Perra, A. Baronchelli, D. Mocanu, B. Gonçalves, R. Pastor-Satorras, A. Vespignani, Phys. Rev. Lett. 109, 238701 (2012)
S. Liu, A. Baronchelli, N. Perra, Phys. Rev. E 87, 032805 (2013)
M. Starnini, R. Pastor-Satorras, Phys. Rev. E 87, 062807 (2013)
D. Mistry, Q. Zhang, N. Perra, A. Baronchelli, Phys. Rev. E 92, 042805 (2015)
S. Liu, M. Perra, N. Karsai, A. Vespignani, Phys. Rev. Lett. 112, 118702 (2014)
I. Scholtes, N. Wider, R. Pfitzner, A. Garas, C. Tessone, F. Schweitzer, Nat. Commun. 5, 5024 (2014)
G. Miritello, E. Moro, R. Lara, Phys. Rev. E 83, 045102 (2011)
M. Granovetter, Am. J. Sociol. 78, 1360 (1973)
S. Wasserman, K. Faust, Structural analysis in the social sciences, in Social Network Analysis: Methods and Applications, 1st edn. (Cambridge University Press, 1994), Vol. 8
R.I.M. Dunbar, J. Human Evol. 22, 469 (1992)
M. Rosvall, A. Esquivel, A. Lancichinetti, J. West, R. Lambiotte, Nat. Commun. 5, 4630 (2014)
A. Flache, M. Macy, J. Math. Sociol. 21, 3 (1996)
D.R. White, M. Houseman, Complexity 8, 72 (2002)
P. Dodds, R. Muhamad, D. Watts, Science 301, 827 (2003)
J.P. Onnela, J. Saramaki, J. Hyvonen, G. Szabo, D. Lazer, K. Kaski, J. Kertesz, A.L. Barabasi, Proc. Natl. Acad. Sci. USA 104, 7332 (2007)
X. Shi, L. Adamic, M. Strauss, Physica A 378, 33 (2007)
R. Xiang, J. Neville, M. Rogati, Modeling Relationship Strength in Online Social Networks, in Proceedings of the 19th International Conference on World Wide Web, WWW ’10 (ACM, New York, 2010), pp. 981–990
R. Lambiotte, V. Salnikov, M. Rosvall, J. Complex Networks 3, 177 (2015)
C.L. Vestergaard, M. Génois, A. Barrat, Phys. Rev. E 90, 042805 (2014)
A. Moinet, M. Starnini, R. Pastor-Satorras, Phys. Rev. Lett. 114, 108701 (2015)
M. Karsai, M. Kivelä, R.K. Pan, K. Kaski, J. Kertész, A.L. Barabási, J. Saramäki, Phys. Rev. E 83, 025102 (2011)
M. Karsai, K. Kaski, J. Kertész, PLoS One 7, e40612 (2012)
M. Keeling, P. Rohani, Modeling Infectious Disease in Humans and Animals (Princeton University Press, 2008)
S.C. Ferreira, C. Castellano, R. Pastor-Satorras, Phys. Rev. E 86, 044125 (2012)
C. Castellano, R. Pastor-Satorras, Phys. Rev. Lett. 105, 218701 (2010)
A.V. Goltsev, S.N. Dorogovtsev, J.G. Oliveira, J.F.F. Mendes, Phys. Rev. Lett. 109, 128702 (2012)
M. Starnini, R. Pastor-Satorras, Phys. Rev. E 89, 032807 (2014)
M. Boguña, C. Castellano, R. Pastor-Satorras, Phys. Rev. Lett. 111, 068701 (2013)
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Sun, K., Baronchelli, A. & Perra, N. Contrasting effects of strong ties on SIR and SIS processes in temporal networks. Eur. Phys. J. B 88, 326 (2015). https://doi.org/10.1140/epjb/e2015-60568-4
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DOI: https://doi.org/10.1140/epjb/e2015-60568-4