Information Theoretic Optimal Surveillance for Epidemic Prevalence in Networks

TL;DR

This work reframes epidemic surveillance on networks as an information-theoretic subset selection problem, introducing TestPrev to maximize the mutual information between observed nodes and the outbreak prevalence $Z$, thereby revealing the full outbreak size distribution. It proves that TestPrev is NP-hard and generally hard to approximate, distinguishes it from prior CZK-based objectives, and develops a suite of algorithms including exact methods for trees and 1-hop models, a closed-form solution for simple paths, and a scalable sampling-based GreedyMI for general networks. Empirical results across synthetic and real networks show that GreedyMI achieves substantial variance reduction in prevalence and outperforms degree- and vulnerability-based baselines, especially with moderate budgets. The paper lays groundwork for distribution-level insights into outbreaks and points to extensions such as incorporating time-to-peak and spatial spread.

Abstract

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.

Figures (26)

• Figure 1: 1-hop example on a bipartite network
• Figure 2: Performance of GreedyMI vs baselines under Known-source seeding (averaged over 10 runs).
• Figure 3: Performance of GreedyMI vs baselines under Random-source seeding.
• Figure 4: Comparison of the degree distributions of GreedyMI and Vulnerable in Random-source seeding (Y-axis in log-scale).
• Figure 5: Vulnerability vs Influence of GreedyMI and Vulnerable in Random-source seeding. The "Network" corresponds to a sample of nodes that do not feature in any of the solution sets.

Theorems & Definitions (17)

• Lemma 1
• Theorem 1
• Lemma 2
• proof
• Lemma 3
• Theorem 6
• proof
• proof
• proof
• proof