A Theoretical Analysis of Mass Testing Strategies to Control Epidemics

One of the strategies used in some countries to contain the COVID-19 epidemic has been the test-and-isolate policy, generally coupled with contact tracing. Such strategies have been examined in several simulation models, but a theoretical analysis of their effectiveness in simple epidemic model is, to our knowledge, missing. In this paper, we present four epidemic models of either SIR or SEIR type, in which it is assumed that at fixed times the whole population (or a part of the population) is tested and, if positive, isolated. We find the conditions for an epidemic to go extinct under such a strategy; for these types of models we provide an appropriate definition of R0, that can be computed either analytically or numerically. Finally, we show numerically that the final-size relation of SIR models approximately holds for the four models, over a large parameter range.