Epidemics on a weighted network with tunable degree-degree correlation.

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 R0 of the epidemic increases (decreases) when the degree-degree correlation coefficient ρ 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 ρ can have the opposite effect on R0.