Low prevalence, quasi-stationarity and power-law behavior in a model of contagion spreading

While contagion (information, infection, etc.) spreading has been extensively studied recently, the role of active local agents has not been fully considered. Here, we propose and study a model of spreading which takes into account the strength or quality of contagions as well as the local probabilistic dynamics occurring at various nodes. Transmission occurs only after the quality-based fitness of the contagion has been evaluated by the local agent. We study such spreading dynamics on Erdos-Renyi as well as scale free networks. The model exhibits quality-dependent exponential time scales at early times leading to a slowly evolving quasi-stationary state. Low prevalence is seen for a wide range of contagion quality for arbitrary large networks. We also investigate the activity of nodes and find a power-law distribution with a robust exponent independent of network topology. These properties, while absent in standard theoretical models, are observed in recent empirical observations.

[1]  Alessandro Vespignani,et al.  Velocity and hierarchical spread of epidemic outbreaks in scale-free networks. , 2003, Physical review letters.

[2]  Tao Zhou,et al.  Optimal contact process on complex networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Lewi Stone,et al.  Unexpected epidemic thresholds in heterogeneous networks: the role of disease transmission. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  R. Pastor-Satorras,et al.  Generation of uncorrelated random scale-free networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Yamir Moreno,et al.  Dynamics of rumor spreading in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Michel L. Lapidus,et al.  Riemann zeros and phase transitions via the spectral operator on fractal strings , 2012, 1203.4828.

[8]  N. Mavromatos,et al.  LECT NOTES PHYS , 2002 .

[9]  Sergio Gómez,et al.  Nonperturbative heterogeneous mean-field approach to epidemic spreading in complex networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Peter Kenez,et al.  The birth of the propaganda state : Soviet methods of mass mobilization, 1917-1929 , 1985 .

[11]  A. Barabasi,et al.  Impact of non-Poissonian activity patterns on spreading processes. , 2006, Physical review letters.

[12]  R. Dickman,et al.  Nonequilibrium Phase Transitions in Lattice Models , 1999 .

[13]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[14]  Peter Kenez,et al.  The birth of the propaganda state : Soviet methods of mass mobilization, 1917-1929 , 1985 .

[15]  Wolfgang Kellerer,et al.  Outtweeting the Twitterers - Predicting Information Cascades in Microblogs , 2010, WOSN.

[16]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[17]  Claudio Castellano,et al.  Thresholds for epidemic spreading in networks , 2010, Physical review letters.

[18]  Norman T. J. Bailey,et al.  The Mathematical Theory of Infectious Diseases , 1975 .

[19]  Alessandro Vespignani,et al.  Absence of epidemic threshold in scale-free networks with degree correlations. , 2002, Physical review letters.

[20]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[21]  Claudius Gros,et al.  Complex and Adaptive Dynamical Systems: A Primer , 2008 .