Detecting Viruses in Contact Networks with Unreliable Detectors

TL;DR

This paper presents optimization models for virus detection in contact networks considering unreliable detectors, introducing heuristics and analysis of false-negative impacts to improve detection strategies.

Contribution

It develops models for virus detection with unreliable detectors, incorporating false negatives, and proposes efficient heuristics with analysis of their effectiveness.

Findings

Heuristic methods are highly efficient and produce high-quality solutions.

False-negative detector effects can sometimes be ignored without significant solution loss.

Optimization models effectively guide detector placement in contact networks.

Abstract

This paper develops and analyzes optimization models for rapid detection of viruses in large contact networks. In the model, a virus spreads in a stochastic manner over an undirected connected graph, under various assumptions on the spread dynamics. A decision maker must place a limited number of detectors on a subset of the nodes in the graph in order to rapidly detect infection of the nodes by the virus. The objective is to determine the placement of these detectors so as to either maximize the probability of detection within a given time period or minimize the expected time to detection. Previous work in this area assumed that the detectors are perfectly reliable. In this work, it is assumed that the detectors may produce false-negative results. In computational studies, the sample average approximation method is applied to solving the problem using a mixed-integer program and a greedy heuristic. The heuristic is shown to be highly efficient and to produce high-quality solutions. In addition, it is shown that the false-negative effect can sometimes be ignored, without significant loss of solution quality, in the original optimization formulation.