We study numerically the variability of the outbreak of diseases on complex networks. We use a susceptible-infected model to simulate the disease spreading at short times in homogeneous and in scale-free networks. In both cases, we study the effect of initial conditions on the epidemic dynamics and its variability. The results display a time regime during which the prevalence exhibits a large sensitivity to noise. We also investigate the dependence of the infection time of a node on its degree and its distance to the seed. In particular, we show that the infection time of hubs have non-negligible fluctuations which limit their reliability as early detection stations. Finally, we discuss the effect of the multiplicity of paths between two nodes on the infection time. In particular, we demonstrate that the existence of even long paths reduces the average infection time. These different results could be of use for the design of time-dependent containment strategies.

• Received 14 September 2005

DOI:https://doi.org/10.1103/PhysRevE.73.046131