An effective degree model for epidemics on dynamic networks

In this paper we present a new ODE based framework for modelling disease transmission on dynamic contact networks. We adapt and extend the effective degree model for a static network to account for the random creation and deletion of links between individuals. The resulting set of ODEs is solved numerically and results are compared to those obtained using individual-based stochastic network simulations. We show that the ODEs display excellent agreement for the evolution of both the disease and the network, and is able to accurately capture the epidemic threshold for a wide range of parameters. Using the proposed model we show that mild epidemics can be controlled while keeping the contact network well connected, and this is in contrast with severe epidemics, where successful control via link removal leads to a disconnected network.

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