Growth rate and acceleration analysis of the COVID-19 pandemic reveals the effect of public health measures in real time

Yuri Tani Utsunomiya; Adam Taiti Harth Utsunomiya; Rafaela Beatriz Pintor Torrecilha; Silvana Cassia Paulan; Marco Milanesi; Jose Fernando Garcia

To exemplify the ability of our framework in detecting complex arrangements of growth stages that substantially deviate from the sigmoidal model, we selected Denmark, Estonia and Qatar ( Figure 4) . All three countries experienced deceleration phases that did not culminate in stationary growth. Instead, a brief linear growth was formed after deceleration, which was followed by a new exponential growth stage. Estonia has further entered a new deceleration phase on March 27 th . These observations indicate that the growth dynamics of COVID-19 cases is more complex than previously appreciated. Therefore, analyzing the raw growth curve alone, dissociated from its derivatives, is very limiting for inference and may hamper the understanding of the pandemic evolution. In part, the lack of combined analysis of growth rate and acceleration in this pandemic is to be blamed on scarce availability of tailor made, user-friendly software. To aid to the analysis of growth rate and acceleration of COVID-19 cases, we built a web application using R (9) and Shiny (8) . This application automatically loads the latest ECDC case reports and applies MR to extract growth rate and acceleration from real-time data. The app also performs automated classification of growth stages with HMM (albeit free parameters should be manually tuned for improved results). Users are not limited to case reports from ECDC, since the app allows for the upload of custom data (e.g., city, region, province or state), which can be used to monitor the growth behavior of COVID-19 locally. Upon closing of the COVID-19 pandemic, this tool could be further used in the analysis of future outbreaks and epidemics, or even of historical disease data. A limiting factor however is that the proposed framework relies on updated case reports, such that sub-notification, delayed communication and the elapsed time between sample collection, diagnostic results and reporting may impact the real-time inference of growth dynamics in disease transmission and consequently jeopardize the timely detection of transitions in the growth curve. In spite of that limitation, the presented tool remains highly useful to monitor the growth behavior of epidemics.