Dynamic group testing to control and monitor disease progression in a population

ABSTRACT

In this paper, we introduce a "discrete-time SIR stochastic block model"that also allows for group testing and interventions on a daily basis. Our model can be regarded as a discrete version of the well-known continuous-time SIR stochastic network model [1] and relies on a specific type of weighted graph to capture the underlying community spread. Given that infection model, we then formulate a dynamic group-testing problem by asking (a) what is the minimum number of tests needed everyday to identify all infections? and (b) are there nonadaptive group testing strategies that achieve this with vanishing error probability? Our results show that one can leverage the knowledge of the community infection model to compute a lower bound on the number of tests and also inform nonadaptive group testing algorithms, so that they can achieve (almost) the same performance as complete individual testing with a much smaller number of tests. Moreover, these algorithms are order-optimal, under specific conditions. © 2022 IEEE.