Exponential rate of epidemic spreading on complex networks

TL;DR

This paper develops a theoretical framework to predict the exponential spreading rate of epidemics on complex networks by relating network properties to disease transmission dynamics.

Contribution

It introduces a new expression for the reproduction number based on network degree distribution, assortativity, and clustering, linking network structure to epidemic spread.

Findings

The model accurately predicts exponential growth in most network types.

Networks with very broad degree distributions do not exhibit clear exponential regimes.

The theory connects epidemiology with complex network analysis, aiding policy decisions.

Abstract

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.