Epidemics on Interacting Networks

Epidemic spreading is of great importance in public health, as well as in related fields such as infrastructure. While complex network models have been used with great success to analyze epidemic behavior on single networks, the reality is that our world is made up of a system of interacting networks that do not necessarily share common characteristics. I introduce a model for constructing interacting networks and show that the phase transtion depends on the parameters $\kappa_T, kappa_A$ and $\kappa_B$, where $\kappa_T = \langle k^2 \rangle / \langle k \rangle$ over the nodes in both networks, including internetwork links, and $\kappa_A$ and $\kappa_B$ are over the networks considered individually, with no internetwork links. For strongly interacting networks ($\kappa_T > \kappa_A and \kappa_B$), there exists only one phase transition, between a disease-free phase and an epidemic phase across both networks. For weakly interacting networks ($\kappa_T < \kappa_A$ or $\kappa_B$), a third, ``mixed,'' phase exists, where the disease enters an epidemic on one network alone. The analytic predictions are confirmed by Monte-Carlo simulations.