# Test for the Presence of Autocorrelation in the Morgan-Mercer-Flodin (MMF) Model used for Modelling the Total Number of COVID-19 Cases for Brazil

• A. Aisami Department of Biochemistry, Faculty of Science, Gombe State University, Nigeria
• Umar Abubakar Department of Biological Sciences, Faculty of Science, Gombe State University, P.M.B. 027, Gombe, Nigeria
• Motharasan Manogaran Department of Biochemistry, Faculty of Biotechnology and Biomolecular Sciences,
• M.Y. Shukor Department of Biochemistry, Faculty of Biotechnology and Biomolecular Sciences,
Keywords: COVID-19; MMF model; Nonlinear regression; Autocorrelation; Durbin-Watson test

### Abstract

Mathematical models can be used to conduct COVID-19 pandemic analyses, including theoretical, quantitative, and simulation analyses. COVID-19 pandemic models such as the modified Gompertz, von Bertalanffy, modified logistics including the recent MMF model which was the best model in fitting the total number of COVID-19 cases for Brazil. We were the first to note the high suitability of the MMF model to fit total death and infection cases for COVID-19. The least-squares approach, which is employed in conventional nonlinear regression, including the MMF model, must be subjected to the idea that data points do not rely on one another and that the value of a data point is not impacted by the value of data points that came before or after it. This is known as autocorrelation and the Durbin-Watson test can be utilized to check the conformity of this model to non-autocorrelation. The value of the Durbin-Watson statistics was d =0.648. The statistic is approximately equal to 2(1− p). We then test the hypothesis H0: ρ= 0 versus the alternative hypothesis of H1: ρ > 0. From the Durbin-Watson table [1,2] for n=50 and 4 parameters, the lower critical value for dL was 1.206, while the upper critical value dU was 1.537. According to this, the d value was lower than the lower critical value or dL, resulting in the null hypothesis being rejected or indicating that there is evidence of autocorrelation. This demonstrates that the MMF model used in the nonlinear regression model for modelling the total number of COVID-19 cases for Brazil needs remedial action, perhaps identifying potential outliers
Published
2021-07-31
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