The CDC Problem: Distributed Spatial Sampling and Detection of Poisson Processes

In this paper, we study epidemic detection in a geographical region where a center for disease control (CDC) relies on two distinct testing agencies to assess an outbreak. Each agency operates within a defined area, and the quality of their testing performance can vary, leading to missed detections or false negatives. The CDC observes the test results from each agency and must detect whether an outbreak is occurring (or not). The CDC’s role is to perform distributed spatial sampling, i.e., define specific regions tested by each agency to optimize the collective detection error and enhance the reliability of epidemic detection. We refer to this decision-making challenge as the CDC problem. In this work, we focus on the CDC problem under the assumptions that (i) the epidemic is modeled as a spatially homogeneous Poisson counting process, and (ii) testing results are only affected by missed detections (without considering false positives). For this setting, we analyze how the distributed spatial sampling strategies (which may comprise disjointed or partially overlapping regions) of the testing agencies influence the overall detection accuracy. We derive optimal coverage strategies for each agency (and hence, for the CDC), with the objective of minimizing detection error. Notably, we demonstrate that the optimal error exponent can be expressed as a simple optimization problem, which we solve completely for the case of two testing agencies.