Expanding Covid-19 Testing: Mathematical Guidelines for the Optimal Sample Pool Size Given Positive Test Rate

Widespread testing is essential to the mitigation of the spread of any virus, and is particularly central to the discussion on transitioning out of national quarantine. Sample pooling is a method that aims to multiply testing capability by using one testing kit for multiple samples, but will only be successful under certain conditions. This paper gives precise guidelines on those conditions for success: for any proposed sample pool size, explicit bounds on the positive infection rate are given that are informed by both discrete and statistical modeling.