A new working paper by Jakob Jonnerby (Oxford) and co-authors analyzes how to optimally prioritize testing resources under scarcity.
The paper formalizes mathematically the decision problem of how to allocate testing resources taking into account heterogeneity in the population. It allows also for pooled testing (group testing). Those tested positive are isolated. The paper analyzes the problem analytically and provides a numerical simulation showing that, even if the testing resources are severly constrained, utilizing them optimally can substantially reduce the health burden.
Link to paper here.