Optimal Testing Strategy for Containing COVID-19: A Case-Study on Indian Migrant Worker Population

We study the problem of targeted, district-level COVID testing of local residents and incoming migrants in order to contain the growth of infection rates in the district. We present a generic optimization problem to solve the optimal testing strategy that set differentiated testing rates on local and migrant populations based on their travel history, relative severity of the epidemic in their origin regions, and whether or not they have COVID-related symptoms. Our optimization problem minimizes the total number of tests that are needed to contain the virus spread assuming a Susceptible-Infected-Quarantined-Recovered (SIQR) transmission dynamics. We provide a complete characterization of the set of optimal testing strategies, and propose a simple greedy algorithm for computing an optimal strategy. We also study the comparative statics of the optimal strategy with respect to several key parameters related to the social distancing policy and epidemic transmission. Finally, we calibrate our model and compute the optimal testing strategies at district level for an Eastern India state Odisha based on the acquired data on migrants' travel logs and active COVID cases.