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In many epidemiological and ecological contexts, there is a trade-off between infections and interaction. This arises because the links between individuals capable of spreading infections are also often associated with beneficial activities. Here, we consider how the presence of explicit network structure changes the optimal solution of a class of infection-interaction trade-offs. In order to do this, we develop and analyse a low-dimensional dynamical system approximating the network SIS epidemic. We find that network structure in the form of heterogeneous numbers of contacts can have a significant impact on the optimal number of contacts that comes out of a trade-off model., Comment: 16 pages; 5 figures