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

2025-06-18

AI Summary

This paper addresses outbreak control of epidemics (or information diffusion) under an unknown propagation network, modeled via the SIS framework, with the objective of minimizing extinction time. Given only node infection-state observations, we jointly learn the underlying graph structure and design an optimal vaccination strategy. Methodologically, we (i) establish the first sample-complexity theory for inclusion–exclusion-based graph learning algorithms; (ii) propose a polynomial-time exact algorithm for bounded-treewidth graphs to minimize the spectral radius—the critical epidemic threshold; and (iii) develop a general-purpose greedy heuristic for arbitrary graphs. Experiments on synthetic and real-world networks demonstrate high structural recovery accuracy, substantial reduction in extinction time achieved by the learned vaccination policies, and computational efficiency sufficient for practical deployment.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Economics, Online Markets and Human Computation: Social networks and social learning

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.

Problem

• Minimize disease extinction time with unknown graph structure
• Develop graph learning and optimal vaccination strategies jointly
• Address NP-hard Spectral Radius Minimization for bounded treewidth graphs

Innovation

• Inclusion-exclusion-based graph learning algorithm
• Optimal vaccination via Spectral Radius Minimization
• Polynomial-time greedy heuristic for any graph