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 θ_i: θ_i = 1 - ∏ _j∈N(i)(1 - λ_j), λ_j = min(1, λ₀ × (d_ij/min_k∈N(i)(d_ik))- ^β), where λ₀ is the average transmission rate of the virus, j is one of the infected neighbors (N(i))of susceptible individual i, λ_j is transmission rate of individual j, d_ij 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.