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

In spite of sigmoidal curves following the four above described stages sequentially, we anticipated that the growth of COVID-19 cases may not necessarily obey this sequence in practice, since the dynamics of the disease is likely complex and highly responsive to the implementation or relaxation of public health measures. This implies that a country that has already reached a stationary stage could resume exponential growth, for example by seeding a new outbreak via importation. Likewise, decelerating countries could as well regain acceleration by relaxing prevention measures. Furthermore, some countries may face multiple cycles of acceleration and deceleration prior to reaching a stationary growth. These scenarios could produce more complex growth curves that deviate from the sigmoidal shape by mounting different arrangements of exponential, deceleration and stationary stages. Of note, MR has sufficient flexibility to model these complex scenarios and can easily accommodate curves exhibiting arbitrary permutations of these four stages. In addition, the near-zero acceleration that is intimately related to the stationary stage in sigmoidal curves could also arise from a non-zero constant growth rate in practice. In such cases, the growth curve would exhibit a linear pattern, which can be interpreted as a fifth growth stage that is not observed in classic sigmoidal functions. Such linear pattern may appear if the deceleration stage does not form an enough deep valley prior to acceleration rising up again towards zero. Again, MR is capable of modeling these anomalous behaviors. In this study we sought to ascertain whether these five stages of growth curves could have direct implications in understanding the dynamics of COVID-19 prevalence both globally and locally. We further developed a Hidden Markov Model (HMM) to automate the detection of transitions between stages in the growth curve using acceleration and growth rate data obtained with MR as input (see Material and Methods).