Cost-Optimal Switching Protection Strategy in Adaptive Networks

In this paper, we study a model of network adaptation mechanism to control spreading processes over switching contact networks, called adaptive susceptible-infected-susceptible model. The edges in the network model are randomly removed or added depending on the risk of spread through them. By analyzing the joint evolution of the spreading dynamics "in the network" and the structural dynamics "of the network", we derive conditions on the adaptation law to control the dynamics of the spread in the resulting switching network. In contrast with the results in the literature, we allow the initial topology of the network to be an arbitrary graph. Furthermore, assuming there is a cost associated to switching edges in the network, we propose an optimization framework to find the cost-optimal network adaptation law, i.e., the cost-optimal edge switching probabilities. Under certain conditions on the switching costs, we show that the optimal adaptation law can be found using convex optimization. We illustrate our results with numerical simulations.