Optimal Containment of Epidemics in Temporal and Adaptive Networks

In this chapter, we focus on the problem of containing the spread of diseases taking place in both temporal and adaptive networks (i.e., networks whose structure `adapts' to the state of the disease). We specifically focus on the problem of finding the optimal allocation of containment resources (e.g., vaccines, medical personnel, traffic control resources, etc.) to eradicate epidemic outbreaks over the following three models of temporal and adaptive networks: (i) Markovian temporal networks, (ii) aggregated-Markovian temporal networks, and (iii) stochastically adaptive models. For each model, we present a rigorous and tractable mathematical framework to efficiently find the optimal distribution of control resources to eliminate the disease. In contrast with other existing results, our results are not based on heuristic control strategies, but on a disciplined analysis using tools from dynamical systems and convex optimization.