On the effect of the number of tests and their time of application in tracing policies against COVID-19

In this paper we explore the effect of the number of daily tests on an epidemics control policy purely based on testing and selective quarantine, and the impact of these actions depending on the time their application starts. We introduce a general model incorporating a stochastic disease evolution, a particular weighted graph representing the population, and an optimal contact tracing strategy to allocate available tests. Simulations on a community of 50'000 individuals show that the evolution of the epidemic produces a clear non-linear response to the variation of the number of tests used and to the starting time of their application. These results suggest that not only a minimum number of tests is necessary to obtain a positive outcome from the tracing strategy but also that there exists a saturation on the contribution of additional tests. The results also show that the timing in the application of the measures is as important as the measures themselves and that an excessive delay can be hardly overcome.