The Verhulst logistic function is among the most popular function to describe a growth phenomenon. Initially the theory is applied in studying the growth of living organism populations. However now it finds the applications in any growth phenomenon, including social, education, and engineering. There is a huge number of applications of the logistic function in various field. One of the strength of the model is its capability in estimating the carrying capacity or the maximum level of the growth. This upper bound is very important to obtain and has many practical implication. However, in some circumstances the function may fail to estimate this upper bound, especially when the growth is still at the beginning phase. In pedagogical context of mathematical modeling this failure is regarded as a good example in explaining the modeling process, in which when a model fails to comply with the reality, one should proceed to refine the model following the full cycle of modeling process. In this paper we present a modified growth model of the Verhulst logistic function, since when it is applied to the COVID-19 pandemic data in Indonesia, it cannot estimate the carrying capacity satisfactory. The modification has improved the estimation performance in terms of the root of the mean square error measure (RMSE).
Keywords
COVID-19 Pandemic, Empirical Model, Indonesia, Verhulst Logistic Equation, Pedagogical Aspect.
The Verhulst logistic function is among the most popular function to describe a growth phenomenon. Initially the theory is applied in studying the growth of living organism populations. However now it finds the applications in any growth phenomenon, including social, education, and engineering. There is a huge number of applications of the logistic function in various field. One of the strength of the model is its capability in estimating the carrying capacity or the maximum level of the growth. This upper bound is very important to obtain and has many practical implication. However, in some circumstances the function may fail to estimate this upper bound, especially when the growth is still at the beginning phase. In pedagogical context of mathematical modeling this failure is regarded as a good example in explaining the modeling process, in which when a model fails to comply with the reality, one should proceed to refine the model following the full cycle of modeling process. In this paper we present a modified growth model of the Verhulst logistic function, since when it is applied to the COVID-19 pandemic data in Indonesia, it cannot estimate the carrying capacity satisfactory. The modification has improved the estimation performance in terms of the root of the mean square error measure (RMSE).
Keywords
COVID-19 Pandemic, Empirical Model, Indonesia, Verhulst Logistic Equation, Pedagogical Aspect.