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This paper develops and analyzes optimization models for rapid detection ofviruses in large contact networks. In the model, a virus spreads in astochastic manner over an undirected connected graph, under various assumptionson the spread dynamics. A decision maker must place a limited number ofdetectors on a subset of the nodes in the graph in order to rapidly detectinfection of the nodes by the virus. The objective is to determine theplacement of these detectors so as to either maximize the probability ofdetection within a given time period or minimize the expected time todetection. Previous work in this area assumed that the detectors are perfectlyreliable. In this work, it is assumed that the detectors may producefalse-negative results. In computational studies, the sample averageapproximation method is applied to solving the problem using a mixed-integerprogram and a greedy heuristic. The heuristic is shown to be highly efficientand to produce high-quality solutions. In addition, it is shown that thefalse-negative effect can sometimes be ignored, without significant loss ofsolution quality, in the original optimization formulation.

Detecting Viruses in Contact Networks with Unreliable Detectors