Network Group Testing
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We consider the problem of identifying infected individuals in a population of size N. Group testing provides an approach to test the entire population using significantly fewer than N tests when infection prevalence is low. The original and most commonly utilized form of group testing, called Dorfman testing, treats each individual's infection probability as independent and homogenous. However, as communicable diseases spread from individual to individual through underlying social networks, an individual's network location affects their infection probability. In this work, we utilize network information to improve group testing. Specifically, we group individuals by community and demonstrate the performance gain over Dorfman testing. After introducing a network and epidemic model, we derive the number of tests used under network grouping. We prove the expected number of tests is upper bounded by Dorfman testing. In addition, we demonstrate network grouping successfully achieves the theoretical lower bound for two-stage testing procedures when networks have strong community structure. On the other hand, network grouping is equivalent to Dorfman testing when networks have no structure. We end by demonstrating network grouping outperforms Dorfman testing in the scenario of a university testing its population for COVID-19 cases.
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