Optimal Adaptive Testing for Epidemic Control: Combining Molecular and Serology Tests

Epidemic interventions based on surveillance testing programs are a fundamental tool to control the first stages of new epidemics, yet they are costly, invasive and rely on scarce resources, limiting their applicability. To overcome these challenges, we investigate two optimal control problems: (i) how testing needs can be minimized while maintaining the number of infected individuals below a desired threshold, and (ii) how peak infections can be minimized given a typically scarce testing budget. We find that in both cases the optimal testing policy for the well-known Susceptible-Infected-Recovered (SIR) model is adaptive, with testing rates that depend on the epidemic state, and leads to significant cost savings compared to non-adaptive policies. By using the concept of observability, we then show that a central planner can estimate the required unknown epidemic state by complementing molecular tests, which are highly sensitive but have a short detectability window, with serology tests, which are less sensitive but can detect past infections.