Assessment of Asymptotic and Logistics Growth Models on A Chemist Data


  •   Onyinebifun Emmanuel Biu

  •   Maureen Tobechukwu Nwakuya

  •   Gamage Tubona


This research considers two growth models; asymptotic growth model and logistic growth model. Both models were compared to establish a better model for modelling and prediction based on a Chemist data on the percentage concentration of isomers versus time for each Isomerization of α-Pinene at 189.50C. Results from the growth curve shows a non-linear relationship between the response (time of isomerization) and the independent variables (percentage of concentration) for all the four isomers considered. Based on the four isomers four different quadratic regressions of second-order were fitted. The problem of the initial parameters was addressed by second-order regression techniques since the models considered have three parameters to be estimated before the iterative approach was used. Estimation of parameters was done using modified version of the Levenberg-Marquardt Algorithm in Gretl statistical software. The results from both models were compared based on Aikaike Information Criteri (AIC), Bayesian Information Criteria (BIC), Mean Squared Error (MSE) and R-square. The Asymptotic Growth Model was identified to be a more adequate model for modelling and predicting growth patterns for three isomers (Dipentene, Pyronene and Dimer) while logistic growth model was seen to be a better model for predicting growth patterns of one isomer (Allo-Ocimene). This study will go a long way in directing Chemists and researchers in that field in choosing the appropriate model for their research.

Keywords: Asymptotic Growth Model; Levenberg-Marquardt Algorithm; Logistic Growth Model and Non-linear Model


Kutner MH, Nachtshien CJ, Neters Li W. Applied Linear Statistical Methods. 5th ed. McGraw-Hill Irwin; 2005.

Biu EO, Wonu N. Estimation of Parameters of Two Non-linear Regression Models Using Assumed Values: Reciprocal Power Regression Models. Asian Research Journal of Mathematic.2019;15(4): 1-19.

Mahaboob B, Venkateswarlu B, Mokeshrayalu G, Balasiddamuni P. A different approach to estimate nonlinear regression model using numerical methods. Conf. Series: Materials Science and Engineering. 2017; 263.

Hossain MdJ, Hossain MR, Datta D, Islam MdS. Mathematical Modelling of Bangladesh Population Growth. Journal of Statistics and Management System. 2015; 18(3): 289-300.

Wei H, Jiang Y, Zhang Y. A Review of Two Population Growth Models and an Analysis of Factors Affecting the Chinese Population Growth. Asian Journal of Economic Modelling. 2015; 3(1): 8-20.

Tkachenko N, Weissmann J.D, Petersen WP, Lake G, Zollikofer CPE, Callegari S. Individual-based modelling of population growth and diffusion in discrete time. PLoS ONE. 2017; 12(4): 0176101.

Suherman MM, Rakhmawati RM, Andriani H, Suyitno S, Junaidi I. The Application of Differential Equation of Verhulst Population Model on Estimation of Bandar Lampung Population. IOP Conf. Series: Journal of Physics. 2019; 1155: 0120.

Birch CPD. A new generalized logistic sigmoid growth equation compared with the Richards growth equation. Ann. Bot. 1999; 83: 713–723.

Yin X, Lantinga EA, Schapendonk AHCM, Zhong X. Some quantitative relationships between leaf area index and canopy nitrogen content and distribution. Ann. Bot. 2003; 91: 893–903.

Valent F, Schiava F, Savonnito C, Gallo T, Brusaferro S, Barbone F. Risk factors for fatal road accidents in Udine, Italy. Accident Analysis & Prevention. 2002; 34: 71–84.

Christopher YS. Logistic growth modelling of COVID-19 proliferation in China and its international implications. International Journal of Infectious Disease. 2020; 96: 582-589.

Ahmed SRA. Using logistic regression models to determine factors affecting diabetes in red sea state. International Journal of Statistics and Applied Mathematics. 2019; 4(4): 12-17.

Francois D, Youness M. Growth Models with Oblique Asymptote. Mathematical Modelling and Analysis. 2013; 18(2): 204-218

Pommerening A, Muszta A. Methods of modelling relative growth rate. Forest Ecosystems. 2015; 2.


How to Cite
Biu, O. E., Nwakuya, M. T., & Tubona, G. (2022). Assessment of Asymptotic and Logistics Growth Models on A Chemist Data. European Journal of Mathematics and Statistics, 3(5), 7–15.