Surveillance of the recurrence time of the effectiveness of national and region-level quarantines of COVID-19 pandemic in Chile

The World Health Organization has recommended a range of social and health measures to mitigate the spread of coronavirus disease 2019 (COVID-19), including strategies such as quarantines, border closures, social distancing, and mask usage, among others. Specifically, the Chilean authorities implemented the "step-by-step" plan, built on the concept of dynamic quarantine. Numerous studies have examined the effectiveness of these quarantines in Chile during the pandemic, utilizing data published by the Chilean Ministry of Health. This study's primary aim was to enhance our understanding of quarantine effectiveness in Chile during the pandemic. We accomplished this by analyzing the distributional behavior of the time until the COVID-19 pandemic was deemed under control or not. In our study, we defined an event with two potential outcomes related to the instantaneous reproductive number (Rt), which signifies the time until a change in the event outcome occurs. Importantly, we did not predefine a specific temporal observation unit. These findings allowed us to complement the concept of effective quarantine by considering the dynamics generated by the protocols, such as phase 1 of the quarantine, in achieving natural herd immunity in response to the number of COVID-19 cases and Rt. We assessed the behavior of the mean and median residual lifetime until the initiation of controlled/uncontrolled episodes of the COVID-19 pandemic based on Rt in all regions of Chile. Despite variations in the distribution of residual times for controlled/uncontrolled episodes in different regions, there was a similar observation during the period considered (between March 2020 and March 2021): the mitigation measures did not produce a clear positive effect for controlling the epidemic. The residual times of episodes with Rr,t > 1 were not different from those episodes with Rr,t ≤ 1.