Dynamical Dorfman Testing with Quarantine

We consider dynamical group testing problem with a community structure. With a discrete-time SIR (susceptible, infectious, recovered) model, we use Dorfman's two-step group testing approach to identify infections, and step in whenever necessary to inhibit infection spread via quarantines. We analyze the trade-off between quarantine and test costs as well as disease spread. For the special dynamical i.i.d. model, we show that the optimal first stage Dorfman group size differs in dynamic and static cases. We compare the performance of the proposed dynamic two-stage Dorfman testing with state-of-the-art non-adaptive group testing method in dynamic settings.

Group Testing with Non-identical Infection Probabilities

We consider a zero-error probabilistic group testing problem where individuals are defective independently but not with identical probabilities. We propose a greedy set formation method to build sets of individuals to be tested together. We develop an adaptive group testing algorithm that uses the proposed set formation method recursively. We prove novel upper bounds on the number of tests for the proposed algorithm. Via numerical results, we show that our algorithm outperforms the state of the art, and performs close to the entropy lower bound.