Containing epidemic outbreaks by message-passing techniques
F. Altarelli, A. Braunstein, L. Dall'Asta, J.R. Wakeling, R., Zecchina

TL;DR
This paper introduces a message-passing algorithm for targeted network immunization that efficiently identifies near-optimal nodes to vaccinate, minimizing epidemic spread while balancing vaccination costs, applicable to various epidemic models.
Contribution
It develops a scalable message-passing method to optimize immunization strategies based on mean-field approximations for different epidemic models.
Findings
The algorithm scales linearly with network size.
It outperforms topological heuristics and greedy methods.
It effectively finds near-optimal immunization sets.
Abstract
The problem of targeted network immunization can be defined as the one of finding a subset of nodes in a network to immunize or vaccinate in order to minimize a tradeoff between the cost of vaccination and the final (stationary) expected infection under a given epidemic model. Although computing the expected infection is a hard computational problem, simple and efficient mean-field approximations have been put forward in the literature in recent years. The optimization problem can be recast into a constrained one in which the constraints enforce local mean-field equations describing the average stationary state of the epidemic process. For a wide class of epidemic models, including the susceptible-infected-removed and the susceptible-infected-susceptible models, we define a message-passing approach to network immunization that allows us to study the statistical properties of epidemic…
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