Exponential rate of epidemic spreading on complex networks

The initial phase of an epidemic is often characterized by an exponential increase in the number of infected individuals. In this paper, we predict the exponential spreading rate of an epidemic on a complex network. We first find an expression of the reproduction number for a network, based on the degree distribution, the network assortativity, and the level of clustering. We then connect this reproduction number and the disease infectiousness to the spreading rate. Our result holds for a broad range of networks, apart from networks with very broad degree distribution, where no clear exponential regime is present. Our theory bridges the gap between classic epidemiology and the theory of complex networks, with broad implications for model inference and policy making.