Efficacy of stay-at-home policy and transmission of COVID-19 in Toronto, Canada: a mathematical modeling study

Yuan, P.; Li, J.; Aruffo, E.; Li, Q.; Zheng, T.; Ogden, N.; Sander, B.; Heffernan, J.; Gatov, E.; Gournis, E.; Collier, S.; Tan, Y.; Arino, J.; Belair, J.; Watmough, J.; Kong, J. D.; Moyles, I.; Zhu, H.

Background In many parts of the world, restrictive non-pharmaceutical interventions (NPI) that aim to reduce contact rates, including stay-at-home orders, limitations on gatherings, and closure of public places, are being lifted, with the possibility that the epidemic resurges if alternative measures are not strong enough. Here we aim to capture the combination of use of NPIs and reopening measures which will prevent an infection rebound. Methods We employ a SEAIR model with a household structure able to capture the stay-at-home policy (SAHP). To reflect the changes in the SAHP over the course of the epidemic, we vary the SAHP compliance rate, assuming that the time to compliance of all the people requested to stay-at-home follows a Gamma distribution. Using confirmed case data for the City of Toronto, we evaluate basic and instantaneous reproduction numbers and simulate how the average household size, the stay-at-home rate, the efficiency and duration of SAHP implementation, affect the outbreak trajectory. Findings The estimated basic reproduction number R_0 was 2.36 (95% CI: 2.28, 2.45) in Toronto. After the implementation of the SAHP, the contact rate outside the household fell by 39%. When people properly respect the SAHP, the outbreak can be quickly controlled, but extending its duration beyond two months (65 days) had little effect. Our findings also suggest that to avoid a large rebound of the epidemic, the average number of contacts per person per day should be kept below nine. This study suggests that fully reopening schools, offices, and other activities, is possible if the use of other NPIs is strictly adhered to. Interpretation Our model confirmed that the SAHP implemented in Toronto had a great impact in controlling the spread of COVID-19. Given the lifting of restrictive NPIs, we estimated the thresholds values of the maximum number of contacts, probability of transmission and testing needed to ensure that the reopening will be safe, i.e. maintaining an R_t<1.