Fitting a Nonlinear Curve to the Ratio (Positive/Tested) of COVID-19 in Japan

We examine the number of people infected with COVID-19 in Japan from March 1st, 2020 to November 19th, 2022. To estimate the trends of infected people, we introduce a ratio defined by the number of "Positive" people to "Tested" people. The bar graphs of the ratios increase rapidly from November, 2021. We divide the ratios into 3 intervals (increasing, decreasing, and oscillating) along the time series and evaluate the fitting curve for each interval. Mathematica built-in function named FindFit is applied to calculate the coefficients of the curve. When FindFit does not converge within the given iteration times, we slightly change the initial value, reverse the sign of the coefficients of the curve, or increase the number of parameters for the curve. As the results, the number of iteration times and the residual errors are reduced. Keywords : COVID-19, PCR tested, Tested positive, Ratio, Week sum, Sinc(x), Nonlinear curve