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

The MR technique adopted here aimed at fitting a smooth growth curve to the COVID-19 prevalence data, such that the resulting curve could describe the cumulative number of cases as a function of time. For n recorded days in a given country or territory, let x be a n-dimensional column vector of days since the first case report and y the reciprocal column vector with elements corresponding to the cumulative number of cases. Relative to day d, we define y d and x d as k-sized subset vectors of y and x, respectively, where k = 1 + 2s and s is a free parameter representing the number of offset days before and after day d. Hereafter, we refer to s as the "smooth factor", since it controls the compromise between over-smoothing (large s) and over-fitting (small s) the curve to the data. Finally, we define X d = [1 k x d ], where 1 k is a k-dimensional column vector with all elements equal to one. The local growth rate was estimated by ordinary least squares regression: