The contact structure between hosts – notably in terms of number and weight of contacts - affects disease spread. Yet network-based models used in epidemiology either tend to ignore heterogeneity in the weighting of network edges or largely rely on numerical simulations as analytical tools are still under development. We have recently presented a novel framework (PLoS Comput Biol 9: e1003352.) to estimate key epidemiological variables, such as the rate of early epidemic expansion r₀ and the basic reproductive ratio R₀, from joint probability distributions of number of partners (contacts) and number of interaction events between contacts (which are used to weight network edges). In addition, the framework also allows for a derivation of the full time course of epidemic prevalence and contact behaviour, particularly in risk groups. It quantifies how correlations between an individual’s number of contacts and the weight attributed to these contacts affect epidemic spread.

We extend these earlier analytical findings to networks in which we alleviate the assumption that individuals assign weight randomly to their contacts. Instead, we assume that contacts are specifically assigned to different activity classes. We focus on situations in which contacts show either high or low activity such as for example seen in stable and casual relationships in sexual contact networks. The analytical predictions allow us to identify the relative importance of stable and casual contacts for the epidemic expansion (through R₀) and prevalence. We show that the number and weight of casual contacts are major epidemic drivers and validate our approach with numerical simulations on networks. Finally, we apply the method to epidemic case studies on networks of sexual contacts derived from empirical data.

The framework provides new insights into epidemic spreading on networks with different weighting schemes, as seen in real transmission networks. In particular, it implies that the number of contacts and interaction events an individual maintains as well as the correlation between these values affect epidemic spread. For epidemic control, it is important to target individuals who maximise both casual contacts and interaction events per casual contact.