Runs Test for the Residuals of The Morgan-Mercer-Flodin (MMF) Model Used for Modelling the Total Number of Covid-19 Cases for Brazil

Abstract

Numerous papers fail to conduct statistical diagnostics of the nonlinear model that was used, and the data may be nonrandom, which is a need for all parametric statistical evaluation procedures that rely on random data. Whenever the diagnostic tests find that the residuals reflect a pattern, there are a range of treatments available, such as nonparametric analysis or transferring to a different model, which should resolve the issue. Organisms’ growth including viral infection cases over time usually exhibit a sigmoidal growth profile that exhibits lag time, acceleration to a maximal value and a final phase where the rate decreases and eventually reaches zero or an asymptote (A) is observed. For the analysis of the COVID-19 pandemic, the total infection case of SARS-CoV-2 in Brazil as of 15th of July 2020 to the 20th of December 2020 was modelled using several primary growth models with the Morgan-Mercer-Flodin (MMF) model found to be the best. We were the first to note on the high suitability of the MMF model to fit total death and infection cases for COVID-19. The least-squares technique used in normal nonlinear regression including in the MMF model must be subjected to the notion that the residual values must be random. In order to satisfy this requirement, we conduct the Wald–Wolfowitz runs test statistical diagnosis tests. The maximum number of runs counting was 5, and the predicted number of runs under the premise of randomness was 25.96. The z-value indicates how many normal errors the number of runs discovered exceeds the anticipated number of runs, and the p-value indicates how severe this z-value is. The significance is the same as with the other data on p-values. The null hypothesis that the residuals are really random can be rejected if the p-value is less than 0.05. Because the p-value was smaller than 0.05, the null hypothesis was dismissed, implying that there is strong evidence of non-randomness of the residues and further remedy is needed.