Identifying outbreaks in sewer networks: An adaptive sampling scheme under network's uncertainty.

Motivated by the implementation of a SARS-Cov-2 sewer surveillance system in Chile during the COVID-19 pandemic, we propose a set of mathematical and algorithmic tools that aim to identify the location of an outbreak under uncertainty in the network structure. Given an upper bound on the number of samples we can take on any given day, our framework allows us to detect an unknown infected node by adaptively sampling different network nodes on different days. Crucially, despite the uncertainty of the network, the method allows univocal detection of the infected node, albeit at an extra cost in time. This framework relies on a specific and well-chosen strategy that defines new nodes to test sequentially, with a heuristic that balances the granularity of the information obtained from the samples. We extensively tested our model in real and synthetic networks, showing that the uncertainty of the underlying graph only incurs a limited increase in the number of iterations, indicating that the methodology is applicable in practice.