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

Kiss, I. Z. and Berthouze, L. and Simon L., Péter and Taylor, T. J. (2012) Modelling approaches for simple dynamic networks and applications to disease transmission models. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 468 (2141). pp. 1332-1355. ISSN 1364-5021

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Abstract

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.

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