The Mathematics of Testing with Application to Prevalence of COVID-19

We formulate three basic assumptions that should ideally guide any well-designed COVID-19 prevalence study. We provide, on the basis of these assumptions alone, a full derivation of mathematical formulas required for statistical analysis of testing data. In particular, we express the disease prevalence in a population through those for its homogeneous subpopulations. Although some of these formulas are routinely employed in prevalence studies, the study design often contravenes the assumptions upon which these formulas vitally depend. We also designed a natural prevalence estimator from the testing data and studied some of its properties. The results are equally valid for diseases other than COVID-19 as well as in non-epidemiological settings.