Optimal timing for social distancing during an epidemic

Oscar Patterson-Lomba

Figure (2) show simulations of the model in (2)-(3) with different temporal social distancing scenarios. In particular, we explore the impact of different times at which the social distancing measures are implemented (t 0 ) in the disease dynamics and the final epidemic size. From Figure ( 2) (left) we see that if the social distancing is implemented too soon (t 0 = 50 days), then at the end of the social distancing measure (after 30 days) there are still some infected in the population, and the pool of susceptible is large enough (low population-level immunity) for the disease to take off again and still infect a large portion of the population. Conversely, if social distancing is introduced too late (t 0 = 100 days) by the time the epidemic has already largely spread in the population, then social distancing measures less effective in reducing the final epidemic size. In both these cases, social distancing measures were not applied in an optimal manner, time wise. However, if social distancing is initiated at t 0 = 80 then the resulting epidemic is more effectively flattened. These observations are crystalized in Figure ( 2) (right), which suggests that there is in fact an optimal time, t * 0 , to introduce the social distancing so that the final epidemic size is minimized. Moreover, this figure suggests that the t 0 that minimizes the final epidemic size decreases as R 0 increases. That is, the more transmissible the disease is, the sooner 4 . CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.