Approximations of hospital statistics of recoveries from COVID-19

Hospital statistics on COVID-19 recoveries in Irkutsk are presented in the form of the rate of recovery over a certain number of days from the full group of patients. The recovery time varies from 1 to 182 days. The number of cases considered reaches ~100000 cases. For the convenience of using the data, it is proposed to approximate the table for the recovery rate by various types of nonlinear functions. The following variants of approximating functions have been studied: Gaussian, Lorentz, modified Lorentz, Weibull function, Johnson functions. For comparison with statistics, methods were used to minimize the standard deviations of approximating functions from experimental data. The least squares method is used for functions with two and three parameters, the coordinate descent method, and the gradient descent method for functions with four fitting parameters. It is shown that the best fitting results are provided by a modified Lorentz function with four parameters. According to the degree of discrepancy with experimental statistics, the approximating functions are arranged in the following order: the Weibull function provides the least accurate fit (16.15%), followed by the Johnson function SU (10.65%), slightly better fit for the Johnson function SB (8.49%), for the Gaussian function (5.8%), for the Lorentz function the fit is (3.2828%), the best fit is given by the modified Lorentzian function (3.2804%) under certain approximations.

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