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The impact of constrained rewiring on network structure and node dynamics

In this paper, we study an adaptive spatial network. We consider an SIS (susceptible-infectedsusceptible) epidemic on the network, with a link/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 labelling and no epidemic dynamics, we provide both analytic and semi-analytic 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.