Testing and preemptive quarantine for the control of epidemics

Testing prior symptoms onset and preemptive quarantine of closest contacts are important control actions to mitigate epidemic spreading, especially when asymptomatic and pre-symptomatic shedding is relevant. In order to understand the effects of testing and preemptive quarantine, in this work we introduce a compartmental model that includes novel detection and isolation rates to better capture the state distribution of the close contacts of infected individuals. Moreover, since preemptive quarantine might be seen as an overlay restrictive measure and might be not properly followed, we explicitly include in the model the compliance with the entry and the exit from quarantine. We study the asymptotic stability of the disease-free equilibrium. We show that increasing the number of tests allows to eradicate the epidemic, while increasing the number of quarantined individuals per detected might negatively affect the stability, though it may reduce the peak of active cases.