Eur. Phys. J. B (2013) 86: 149
https://doi.org/10.1140/epjb/e2013-30914-9

Regular Article

How the contagion at links influences epidemic spreading

¹ Institute of Theoretical Physics and Department of Physics, East China Normal University, Shanghai 200062, P.R. China
² Web Science Center, University of Electronic Science and Technology of China, Chengdu 611731, P.R. China

^a e-mail: zhliu@phy.ecnu.edu.cn

Received: 9 October 2012
Received in final form: 19 January 2013
Published online: 10 April 2013

Abstract

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.