Learn to Vaccinate: Combining Structure Learning and Effective Vaccination for Epidemic and Outbreak Control

TL;DR

This paper addresses the challenge of minimizing epidemic extinction time by developing a combined approach for learning unknown contact networks and selecting effective vaccination strategies, validated through experiments.

Contribution

It introduces a novel graph learning algorithm with proven sample complexity and an efficient vaccination strategy for unknown networks, bridging a gap in epidemic control methods.

Findings

The graph learning algorithm accurately recovers network structure from infection data.

The vaccination strategies significantly reduce outbreak extinction time.

The methods are effective on both synthetic and real-world datasets.

Abstract

The Susceptible-Infected-Susceptible (SIS) model is a widely used model for the spread of information and infectious diseases, particularly non-immunizing ones, on a graph. Given a highly contagious disease, a natural question is how to best vaccinate individuals to minimize the disease's extinction time. While previous works showed that the problem of optimal vaccination is closely linked to the NP-hard Spectral Radius Minimization (SRM) problem, they assumed that the graph is known, which is often not the case in practice. In this work, we consider the problem of minimizing the extinction time of an outbreak modeled by an SIS model where the graph on which the disease spreads is unknown and only the infection states of the vertices are observed. To this end, we split the problem into two: learning the graph and determining effective vaccination strategies. We propose a novel inclusion-exclusion-based learning algorithm and, unlike previous approaches, establish its sample complexity for graph recovery. We then detail an optimal algorithm for the SRM problem and prove that its running time is polynomial in the number of vertices for graphs with bounded treewidth. This is complemented by an efficient and effective polynomial-time greedy heuristic for any graph. Finally, we present experiments on synthetic and real-world data that numerically validate our learning and vaccination algorithms.