# A theoretical analysis of Test-and-Isolate strategy

## Abstract

The recent COVID-19 outbreak has stimulated the development of several non-pharmaceutical interventions, especially before vaccines were widely available. One of them is Test-and-Isolate where a theoretical analysis of this strategy could provide useful general insights that can then be specialized into more complex models. In this talk, we analyze three different models which mathematically consist of impulsive differential equations. The first model is a homogeneous SIR model, in which, at fixed intervals of time, the whole population is tested: individuals who test positive are isolated and do not transmit the infection any longer. The second model is as well a SIR model, but we assume that the population is divided into two groups that are tested alternately in each testing session. Finally, the third model is of SEIR type with only one testing group (as in the first case) with the assumption that Exposed individuals cannot be detected through testing. For each of these models, we calculate the effectiveness of the testing procedure needed to ensure control of the epidemic and calculate the control reproductive number R0_c.