title: Impact of constrained rewiring on network structure and node dynamics.
abstract: In this paper, we study an adaptive spatial network. We consider a susceptible-infected-susceptible (SIS) epidemic on the network, with a link or contact rewiring process constrained by spatial proximity. In particular, we assume that susceptible nodes break links with infected nodes independently of distance and reconnect at random to susceptible nodes available within a given radius. By systematically manipulating this radius we investigate the impact of rewiring on the structure of the network and characteristics of the epidemic. We adopt a step-by-step approach whereby we first study the impact of rewiring on the network structure in the absence of an epidemic, then with nodes assigned a disease status but without disease dynamics, and finally running network and epidemic dynamics simultaneously. In the case of no labeling and no epidemic dynamics, we provide both analytic and semianalytic formulas for the value of clustering achieved in the network. Our results also show that the rewiring radius and the network's initial structure have a pronounced effect on the endemic equilibrium, with increasingly large rewiring radiuses yielding smaller disease prevalence.
authors.affiliation: Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom.
authors.forename: P
authors.initials: P
authors.lastname: Rattana
authors.affiliation: Centre for Computational Neuroscience and Robotics, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom and Institute of Child Health, London, University College London, London WC1E 6BT, United Kingdom.
authors.forename: L
authors.initials: L
authors.lastname: Berthouze
authors.affiliation: Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom.
authors.forename: I Z
authors.initials: IZ
authors.lastname: Kiss