Modelling approaches for simple dynamic networks and applications to disease transmission models

In this paper a random link activation–deletion (RLAD) model is proposed that gives rise to a stochastically evolving network. This dynamic network is then coupled to a simple susceptible-infectious-suceptible (SIS) dynamics on the network, and the resulting spectrum of model behaviour is explored via simulation and a novel pairwise model for dynamic networks. First, the dynamic network model is systematically analysed by considering link-type independent and dependent network dynamics coupled with globally constrained link creation. This is done rigorously with some analytical results and we highlight where such analysis can be performed and how these simpler models provide a benchmark to test and validate full simulations. The pairwise model is used to study the interplay between SIS-type dynamics on the network and link-type- dependent activation–deletion. Assumptions of the pairwise model are identified and their implications interpreted in a way that complements our current understanding. Furthermore, we also discuss how the strong assumptions of the closure relations can lead to disagreement between the simulation and pairwise model. Unlike on a static network, the resulting spectrum of behaviour is more complex with the prevalence of infections exhibiting not only a single steady state, but also bistability and oscillations.