Containing epidemic outbreaks by message-passing techniques

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 outbreaks in the presence of immunized nodes as well as to find (nearly) optimal immunization sets for a given choice of parameters and costs. The algorithm scales linearly with the size of the graph and it can be made efficient even on large networks. We compare its performance with topologically based heuristics, greedy methods, and simulated annealing.