Behavior of disease propagation with random long-distance spreading on complex networks

This paper proposed an epidemic model with the long-distance spreading.In this model,the infected nodes could propagate the virus to the non-adjacent nodes with a certain probability while infecting the adjacent nodes.It focused our attention on the SIRS model.For small-world networks and scale-free networks,integrated the long-distance infecting rate with rewiring probability-dependent and degree-dependent into the improved SIRS model respectively and got the accurately value of the epidemic threshold and the stationary infected density of the improved model in above two kinds of networks by the mean-field theory.Theoretical analysis and simulated results show that:for small-world networks,the rewiring probability has evident effect on stationary infected density and epidemic spreading velocity while the effective spreading rate changing in a range,however,the effect on the stationary infected density can be neglected once beyond the range,for scale-free networks,infected nodes'degree plays an significant role in altering stationary infected density and epidemic spreading velocity.