How the contagion at links influences epidemic spreading

The reaction-diffusion (RD) model of epidemic spreading generally assume that contagion occurs only at the nodes of network, i.e., the links are used only for migration/diffusion of agents. However, in reality, we observe that contagion occurs also among the travelers staying in the same car, train or plane etc., which consist of the links of network. To reflect the contagious effect of links, we here present a traveling-contagion model where contagion occurs not only at nodes but also at links. Considering that the population density in transportation is generally much larger than that in districts, we introduce different infection rates for the nodes and links, respectively, whose two extreme cases correspond to the type-I and type-II reactions in the RD model [V. Colizza, R. Pastor-Satorras, A. Vespignani, Nat. Phys. 3, 276 (2007)]. Through studying three typical diffusion processes, we reveal both numerically and theoretically that the contagion at links can accelerate significantly the epidemic spreading. This finding is helpful in designing the controlling strategies of epidemic spreading.

[1]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[2]  Ming Tang,et al.  Epidemic spreading by objective traveling , 2009 .

[3]  A. F. Pacheco,et al.  Epidemic incidence in correlated complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  M. Serrano,et al.  Percolation and epidemic thresholds in clustered networks. , 2006, Physical review letters.

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

[6]  Ming Tang,et al.  An adaptive routing strategy for packet delivery in complex networks , 2007, ArXiv.

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

[8]  Zonghua Liu.  Effect of mobility in partially occupied complex networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  M. Newman,et al.  Epidemics and percolation in small-world networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Zonghua Liu,et al.  Influence of dynamical condensation on epidemic spreading in scale-free networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  M. Newman.  Threshold effects for two pathogens spreading on a network. , 2005, Physical review letters.

[12]  R. Pastor-Satorras,et al.  Bosonic reaction-diffusion processes on scale-free networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Alessandro Vespignani,et al.  Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: theory and simulations. , 2007, Journal of theoretical biology.

[14]  Alessandro Vespignani,et al.  Invasion threshold in heterogeneous metapopulation networks. , 2007, Physical review letters.

[15]  M. Kuperman,et al.  Small world effect in an epidemiological model. , 2000, Physical review letters.

[16]  Alessandro Vespignani,et al.  Reaction–diffusion processes and metapopulation models in heterogeneous networks , 2007, cond-mat/0703129.

[17]  S. Havlin,et al.  Epidemic threshold for the susceptible-infectious-susceptible model on random networks. , 2010, Physical review letters.

[18]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[19]  Pratik Mukherjee,et al.  Epidemiology of Travel-associated Pandemic (H1N1) 2009 Infection in 116 Patients, Singapore , 2010, Emerging infectious diseases.

[20]  Naoki Masuda,et al.  Effects of diffusion rates on epidemic spreads in metapopulation networks , 2010, 1004.2391.