The effect of geographical distance on epidemic spreading

In this paper, we introduced the geographical effect into susceptible-infected-susceptible (SIS) model on a growing network proposed by Xie et al. [Phys. Rev. E 75 (2007) 036106] to investigate the effect of geographical distance on epidemic spreading. In our SIS model, the susceptible individual i can be infected by infectious neighbors with probability θi:θi=1−∏j∈N(i)(1−λj),λj=min(1,λ0×(dij/mink∈N(i)(dik))−β), where λ0 is the average transmission rate of the virus, j is one of the infected neighbors (N(i)) of susceptible individual i,λj is transmission rate of individual j, dij is Euclidean distance between individual i and j, and β is the tunable parameter. Simulation results show that the steady density of infected individuals monotonously decreases with the increment of β and the epidemic threshold emerges in the scale-free networks when the effect of geographical distance is taken into account. Moreover, when the network is star-like, the density of the infected individuals shows large amplitude oscillations.