How long does a lockdown need to be?

Social distancing, often in the form of lockdown, has been adopted by many countries as a way to contrast the spreading of COVID-19. We discuss the temporal aspects of social distancing in contrasting an epidemic diffusion. We argue that a strategy based uniquely on social distancing requires to maintain the relative measures for a very long time, while a more articulate strategy, which also uses early detection and prompt isolation, can be both more efficient on reducing the epidemic peak and allow to relax the social distancing measures after a much shorter time. We consider in more detail the situation in Italy, simulating the effect of different strategies through a recently introduced SIR-type epidemiological model. The short answer to the question in the title is: "it depends on what else you do".

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