Dynamic Group Testing to Control and Monitor Disease Progression in a Population

Proactive testing and interventions are crucial for disease containment during a pandemic until widespread vaccination is achieved. However, a key challenge remains: Can we accurately identify all new daily infections with only a fraction of tests needed compared to testing everyone, everyday? Group testing reduces the number of tests but overlooks infection dynamics and non i.i.d nature of infections in a community, while on the other hand traditional SIR (Susceptible-Infected-Recovered) models address these dynamics but don't integrate discrete-time testing and interventions. This paper bridges the gap. We propose a 'discrete-time SIR stochastic block model' that incorporates group testing and daily interventions, as a discrete counterpart to the well-known continuous-time SIR model that reflects community structure through a specific weighted graph. We analyze the model to determine the minimum number of daily group tests required to identify all infections with vanishing error probability. We find that one can leverage the knowledge of the community and the model to inform nonadaptive group testing algorithms that are order-optimal, and therefore achieve the same performance as complete testing using a much smaller number of tests.