Optimal timing for social distancing during an epidemic

Oscar Patterson-Lomba

Conventional wisdom suggests that the sooner social distancing measures are imple-mented, the higher the chances of curtailing the spread of the virus. Prompt and strict social distancing measures can help "flatten the epidemic" (another fashionable meme at the moment), which in turn will help prevent overwhelming the health system, while also buying us time until effective antivirals and vaccines can be deployed on a mass scale [19] . Implementing swift social distancing measures is one of the most effective ways to stop the spread of the virus, and when the facing a novel and very transmissible virus like COVID-19, social distancing is our first and most effective line of defense. However, is it true that the sooner a temporal social distancing measured is introduced the better health outcomes we will get? The answer to this question would be a resounding "yes" if such measures were to last for extended periods of time (i.e., until the epidemic is over or almost over). However, social distancing interventions are seldom extended long enough to drive the epidemic to extinction on its own. In fact, it is known that new epidemic waves can arise after the social distancing measures are lifted if the pool of susceptibles is large enough, as current models suggest [4, 15, 11] , and as it has historically happened in several occasions, including during the 1918 Spanish influenza pandemic [6] , the 2003 SARS epidemic in Canada [8] , and the 2009 H1N1 influenza epidemic in Mexico [10] . We argue that how soon temporal social distancing should start depends on what are the health outcomes we are optimizing for, and on when other effective interventions (such as antivirals or vaccines) will be available following the social distancing period. If the goal is to reduce the final number of infected cases, or reduce or delay the peak of the epidemic (i.e., flatten the epidemic curve), we show the existence of an optimal timing to initiate the social distancing period.