Variable pool testing for infection spread estimation

We present a method for efficient estimation of the prevalence of infection in a population with high accuracy using only a small number of tests. The presented approach uses pool testing with a mix of pool sizes of various sizes. The test results are then combined to generate an accurate estimation over a wide range of infection probabilities. This method does not require an initial guess on the infection probability. We show that, using the suggested method, even a set of only $50$ tests with a total of only $1000$ samples can produce reasonable estimation over a wide range of probabilities. A measurement set with only $100$ tests is shown to achieve $25\%$ accuracy over infection probabilities from $0.001$ to $0.5$. The presented method is applicable to COVID-19 testing.