Fractal kinetics of COVID-19 pandemic

Anna L. Ziff; Robert M. Ziff

In Fig. 6 , the confidence intervals are calculated as follows. First, robust standard errors are calculated to account for heteroskedasticity. These standard errors are more conservative, which is advantageous considering our small sample size. Next, we calculate the critical value (the 95th quantile) from a t-distribution with n − 2 degrees of freedom. The value n changes with each point along the x-axis. As fewer periods are considered, the critical value increases. The degrees of freedom is a function of this n, but subtracting two to account for the fact that two parameters are estimated (β 0 , β 1 ). The standard errors are quite small for these calculations. Considering periods 2-27 produces a bootstrapped standard error of 0.033, using 5,000 bootstrap replications. Fig. 7 shows the estimated power-law exponents starting at period 8 and adding more periods forward. This mirrors our process of testing this model as more data were published on the number of deaths. The coefficient is stable. The confidence intervals are calculated analogously to those in Fig. 6 . Note that data at period 24 are omitted due to probable inaccuracy, as we discuss above. Power−law Exponent 1 − 3 9 2 − 3 9 3 − 3 7 4 − 3 9 5 − 3 9 6 − 3 9 7 − 3 9 8 − 3 7 9 − 3 9 1 0 − 3 9 1 1 − 3 9 1 2 − 3 9 1 3 − 3 9 1 4 − 3 9 1 5 − 3 9 1 6 − 3 9 1 7 − 3 9 1 8 − 3 9 1 9 − 3 9 2 0 − 3 9 2 1 − 3 9 2 2 − 3 9 2 3 − 3 9 2 4 − 3 9 2 5 − 3 9 2 6 − 3 9 2 7 − 3 9 2 8 − 3 9 2 9 − 3 9 3 0 − 3 9 3 1 − 3 9 3 2 − 3 9