Adaptive Surveillance Testing for Efficient Infection Rate Estimation

In this paper, we study a surveillance testing problem where the learner aims to monitor the infection rate in a community with large population. At each time t, the learner is able to collect samples from a randomly selected group of individuals in the community and perform group testing. The test result is equal to one if at least one individual in the selected group is infected and zero otherwise. Assume each individual is infected according to an independent and identically distributed Bernoulli random variable with parameter p. Our objective is to design an efficient testing procedure to decide the number of samples included in each step for group testing and obtain an accurate estimate of the infection rate p with high probability. We present a two-phase adaptive testing algorithm and show that it reduces the number of tests required to achieve the desired accuracy level compared with the single-sample testing approach. When p is sufficiently small, which is the regime of interest in practice, it leads to an order-of-magnitude improvement. Simulation corroborates theoretical results.