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In this paper, we study an adaptive spatial network. We consider an SIS(susceptible-infectedsusceptible) epidemic on the network, with a link/contactrewiring process constrained by spatial proximity. In particular, we assumethat susceptible nodes break links with infected nodes independently ofdistance, and reconnect at random to susceptible nodes available within a givenradius. By systematically manipulating this radius we investigate the impact ofrewiring 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 rewiringon the network structure in the absence of an epidemic, then with nodesassigned a disease status but without disease dynamics, and finally runningnetwork and epidemic dynamics simultaneously. In the case of no labelling andno epidemic dynamics, we provide both analytic and semi-analytic formulas forthe value of clustering achieved in the network. Our results also show that therewiring radius and the network's initial structure have a pronounced effect onthe endemic equilibrium, with increasingly large rewiring radiuses yieldingsmaller disease prevalence.

The impact of constrained rewiring on network structure and node dynamics