Estimating the true prevalence of an epidemic outbreak is a key public health problem. This is challenging because surveillance is usually resource intensive and biased. In the network setting, prior work on cost sensitive disease surveillance has focused on choosing a subset of individuals (or nodes) to minimize objectives such as probability of outbreak detection. Such methods do not give insights into the outbreak size distribution which, despite being complex and multi-modal, is very useful in public health planning. We introduce TESTPREV, a problem of choosing a subset of nodes which maximizes the mutual information with disease prevalence, which directly provides information about the outbreak size distribution. We show that, under the independent cascade (IC) model, solutions computed by all prior disease surveillance approaches are highly sub-optimal for TESTPREV in general. We also show that TESTPREV is hard to even approximate. While this mutual information objective is computationally challenging for general networks, we show that it can be computed efficiently for various network classes. We present a greedy strategy, called GREEDYMI, that uses estimates of mutual information from cascade simulations and thus can be applied on any network and disease model. We find that GREEDYMI does better than natural baselines in terms of maximizing the mutual information as well as reducing the expected variance in outbreak size, under the IC model.

翻译：准确估计流行病爆发的真实流行率是公共卫生领域的一个关键问题。这一任务具有挑战性，因为监测工作通常资源密集且存在偏差。在网络环境下，先前关于成本敏感疾病监测的研究主要集中在选择个体（或节点）子集以最小化诸如疫情检测概率等目标。此类方法未能深入揭示疫情规模分布，而该分布尽管复杂且呈多模态，却对公共卫生规划极为有用。我们提出了TESTPREV问题，即选择一个节点子集，使其与疾病流行率的互信息最大化，这直接提供了关于疫情规模分布的信息。我们证明，在独立级联（IC）模型下，所有先前疾病监测方法计算的解对于TESTPREV问题通常是高度次优的。我们还证明TESTPREV问题甚至难以近似求解。尽管这一互信息目标对于一般网络在计算上具有挑战性，但我们证明对于多种网络类型，它可以被高效计算。我们提出了一种称为GREEDYMI的贪心策略，该策略利用级联模拟估计互信息，因此可应用于任何网络和疾病模型。我们发现，在IC模型下，GREEDYMI在最大化互信息以及降低疫情规模期望方差方面均优于自然基线方法。