Cost-Optimal Switching Protection Strategy in Adaptive Networks

TL;DR

This paper develops a framework for controlling spreading processes in adaptive networks by optimizing edge switching strategies to minimize costs while effectively controlling infection spread.

Contribution

It introduces a novel cost-optimization approach for network adaptation laws in arbitrary initial topologies, using convex optimization techniques.

Findings

Optimal switching laws can be derived via convex optimization.

The framework applies to arbitrary initial network topologies.

Numerical simulations validate the effectiveness of the proposed method.

Abstract

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.