Epidemics on a weighted network with tunable degree–degree correlation

• We propose a model for generating weighted graphs with tunable degree correlation.
• We study an epidemic model where infectivity depends on the edge weights.
• R0R0 increases (decreases) when the degree correlation increases (decreases).
• The effect magnitude depends on the relation among degrees, weights and infectivity.
• We show that further heterogeneities in the infectivity can lead to different results.

We propose a weighted version of the standard configuration model which allows for a tunable degree–degree correlation. A social network is modeled by a weighted graph generated by this model, where the edge weights indicate the intensity or type of contact between the individuals. An inhomogeneous Reed–Frost epidemic model is then defined on the network, where the inhomogeneity refers to different disease transmission probabilities related to the edge weights. By tuning the model we study the impact of different correlation patterns on the network and epidemics therein. Our results suggest that the basic reproduction number R0R0 of the epidemic increases (decreases) when the degree–degree correlation coefficient ρρ increases (decreases). Furthermore, we show that such effect can be amplified or mitigated depending on the relation between degree and weight distributions as well as the choice of the disease transmission probabilities. In addition, for a more general model allowing additional heterogeneity in the disease transmission probabilities we show that ρρ can have the opposite effect on R0R0.