Optimal timing for social distancing during an epidemic

Oscar Patterson-Lomba

Simulations for the optimal t 0 when an effective intervention is available in the future So far, the model has assumed that the only available intervention to curtail the spread of the disease is social distancing, and that other pharmacological interventions are not available at any point; or put differently, t I = ∞. This assumption is most often wrong, as treatment options (e.g., vaccines, antivirals) typically become available at some point during the course of the epidemic. Here we explore a model with finite values of t I , and see how the optimal social distancing time varies with t I and R 0 . Figure (7) (left) shows that as t I decreases so does the optimal social distancing time if the goal is to reduce the final size (similar results are obtained if the goal is to flatten the epidemic curve, see Appendix 4) . If the epidemic is only moderately transmissible (e.g., 1 < R 0 < 2) and pharmacological interventions are available relatively quickly (e.g., t I < 200 days), the optimal social distancing should be initiated almost immediately after the start of the epidemic. Intuitively, this result makes sense; if effective interventions become available soon after the start of the epidemic, a large second wave post social distancing is less likely because the intervention would prevent it. Figure (7) (right) shows that the optimal timing for social distancing decreases sharply (particulalrly if the goal is to reduce the final size) as t I decreases, regardless of the epidemic containing strategy being employed. Note that if t I is large enough (i.e., the intervention comes long after the peak of the epidemic with no containing measures [∼ 90 days, see Figure ( 2) (left)]), then the optimal time stops depending on the value of t I . In the previous section we noted that if the objective is to minimize final size, then 9 . 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.