In this article, we propose an analysis and applications of sample pooling to the epidemiologic monitoring of COVID-19 with an economy of tests. We first show that group testing is a theoretically efficient and economic tool to provide a direct measure of the prevalence of the disease. We then introduce a precise model of the RT-qPCR process, used to test for the presence of virus in a sample. We construct a statistical model for the viral load in a typical infected individual based on clinical data from Jones et. al. (2020). Using these models, we then propose a method for the measure of the prevalence in a population, based on group testing, taking into account the increased number of false negatives associated to this method. Finally, we present an application of sample pooling for the prevention of epidemic outbreak in relatively closed connected communities (e.g. care homes for the elderly).