  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.
