From heterogeneous network to homogeneous network: the influence of structure on synergistic epidemic spreading

Synergistic epidemic-like spreading phenomena in networked system occur in various forms in nature and human society. The networks' structure characterized by its structural heterogeneity affects the synergistic spreading process dramatically. It was believed that the synergistic epidemic spreading follows a continuous transition on heterogeneous networks, but an explosive one on homogeneous networks. In this work, we adopt the model that interpolates between homogeneous and heterogeneous networks to generate a series of networks. By continuously changing the ratio of homogeneous structure alpha of the network, we numerically show that the interplay between the spreading transition and the structural heterogeneity of network is much more complicated. Although the explosive epidemic transition is likely to be hindered by structural heterogeneity, it could occur on completely heterogeneous network as long as the synergistic strength is sufficiently strong. The predictions of heterogeneous mean-field analysis agree with the numerical results, thus helping to understand the role of structural heterogeneity in affecting synergistic epidemic spreading.