Abstract
An individual-based model of SIS epidemic propagation is considered on regular graphs. This model explicitly incorporates the adjacency matrix of the network enabling us to study the effect of network structure on the dynamic of the propagation process. Our goal in this paper is to understand how the one-dimensional approximation, called also mean-field equation, performs, depending on the main characteristics of the network. It turns out that for dense random regular graphs the approximation is excellent, while for sparse graphs a significant correction term is needed to obtain the proper time dependence of the prevalence (number of infected nodes in the network) based on solving only the mean-field model. Numerical evidence is shown that this correction term depends linearly on the mean distance in the network.