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

Sepehr Elahi, Paula Mürmann, Patrick Thiran

TL;DR: We develop algorithms to learn the graph structure and control SIS epidemics, providing sample complexity bounds, strategy optimality, and experimental validation.

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.

Lay Summary: Imagine a contagious disease spreading through a population, but the contact network—who is infecting whom—remains completely hidden. Only who gets infected and when is observed, and a limited number of vaccines must be allocated to stop the outbreak as quickly as possible. Our work tackles exactly this: how to choose effective vaccinations when the contact network is hidden. We first develop an algorithm that reconstructs the hidden contact network using only observations of who gets sick and when. With the learned network in hand, we propose two vaccination strategies that determine who to vaccinate: one that’s mathematically optimal but slow to compute on big networks, and another that’s much quicker and almost as good. We show that our learn-to-vaccinate approach effectively controls simulated outbreaks across a range of settings, including real-world contact networks from flu epidemics. This early work paves the way for smarter, data-efficient vaccination strategies that can support faster, more effective outbreak response—even when the underlying contact network is unknown.

Link To Code: https://github.com/sepehr78/learn2vac

Primary Area: Probabilistic Methods->Structure Learning

Keywords: Structure learning, SIS models, Epidemics, Vaccinations, Spectral radius minimization, Bounded treewidth, Dynamic programming, Parameterized algorithms

Submission Number: 7300