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 ( SIS ) dynamics on the network and the resulting spectrum of model be- haviour is explored via simulation and a pairwise model for dynamic networks. First, the dynamic network model is systematically analysed by considering link-type in- dependent and dependent network dynamics coupled with globally constrained link creation. Finally, a pairwise model is proposed and used to study the interplay be- tween SIS -type dynamics on the network and link-type dependent activation-deletion. Assumptions of the pairwise model are identiØed 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