Adaptive Test Allocation for Outbreak Detection and Tracking in Social Contact Networks

Abstract

We present a general framework for adaptive allocation of viral tests in social contact networks and arbitrary epidemic models. We pose and solve several complementary problems. First, we consider the design of a social sensing system whose objective is the early detection of a novel epidemic outbreak. In particular, we propose an algorithm to select a subset of individuals to be tested in order to detect the onset of an epidemic outbreak as fast as possible. We pose this problem as a hitting time probability maximization problem and use submodularity optimization and Monte Carlo techniques to obtain solutions with explicit quality guarantees. Second, once an epidemic outbreak has been detected, we consider the problem of using the data from the sensing system to obtain estimates of the initial patient and the current status of the epidemic. Finally, we consider the problem of adaptively distributing viral tests over time in order to maximize the information gained about the current state of the epidemic. We formalize this problem in terms of mutual information and propose an adaptive allocation strategy with quality guarantees. For these problems, we derive analytical solutions for any stochastic compartmental epidemic model with Markovian dynamics, as well as efficient Monte Carlo--based algorithms for non-Markovian dynamics or large networks. We illustrate the performance of the proposed framework in numerical experiments involving a model of COVID-19 applied to a real human contact network.