A new modified logistic growth model for empirical use

Windarto Windarto, Eridani Eridani, Utami Dyah Purwati

Abstract


Richards model, Gompertz model, and logistic model are widely used to describe growth model of a population. The Richards growth model is a modification of the logistic growth model. In this paper, we present a new modified logistic growth model. The proposed model was derived from a modification of the classical logistic differential equation. From the solution of the differential equation, we present a new mathematical growth model so called a WEP-modified logistic growth model for describing growth function of a living organism. We also extend the proposed model into couple WEP-modified logistic growth model. We further simulated and verified the proposed model by using chicken weight data cited from the literature. It was found that the proposed model gave more accurate predicted results compared to Richard, Gompertz, and logistic model. Therefore the proposed model could be used as an alternative model to describe individual growth.

Keywords


mathematical model; growth function; modified logistic growth.

Full Text:

PDF

References


M. Selvaggi, V. Laudadio, C. Dario and V. Tufarelli. Modelling Growth Curves in a Nondescript Italian Chicken Breed: an Opportunity to Improve Genetic and Feeding Strategies. J. Poult. Sci., 52: 288–294, 2015.

I. Inounu, D. Mauluddin, R.R. Noor and Subandriyo. Analisis Kurva Pertumbuhan Domba Garut dan Persilangannya. Jurnal Ilmu Ternak dan Veteriner, 12(4): 286–299 (Text in Indonesian), 2007.

S.E. Aggrey. Comparison of Three Nonlinear and Spline Regression Models for Describing Chicken Growth Curves. Poultry Science, 81:1782–1788, 2002.

H. Neˇsetˇrilov´a. Multiphasic growth models for cattle. Czech J. Anim. Sci., 50 (8): 347–354, 2005.

A.O. Raji, S.T. Mbap, and J. Aliyu. Comparison of different models to describe growth of the japanese quail (coturnix japonica). Trakia Journal of Sciences, 2:182–188, 2014.

N.B. Anthony, D.A. Emmerson, K.E. Nestor, W.L. Bacon, P.B. Siegel and E.A. Dunnington. Comparison of growth curves of weight selected populations of turkeys, quail and chickens. Poultry Science, 70:13–19, 1991.

R.E. Ricklefs. Modification of growth and development of muscles of poultry. Poultry Science, 64:1563–1576, 1985.

S. Mignon-Grasteau, C. Beaumont, E. Le Bihan-Duval, J.P. Poivey, H. de Rochambeau and F.H. Richard. Genetic parameters of growth curve parameters in male and female chickens. British Poultry Science, 40:44–51, 1999.

J. Stewart. Calculus Early Transcendental Seventh Edition. Brooks/Cole Cengage Learning, 2012.

M.A.J.S. van Boekel. Kinetic Modeling of Reactions in Foods, CRC Press, 2009.

P.J. Moatea, L. Dougherty, M.D. Schnall, R.J. Landis, R.C. Boston. A modified logistic model to describe gadolinium kinetics in breast tumors. Magnetic Resonance Imaging, 22:467–473, 2004.

L. von Bertalanffy. A quantitative theory of organic growth. Human Biology, 10(2): 181–213, 1938.

A. Tsoularis. Analysis of logistic growth models. Res. Lett. Inf. Math. Sci., 2: 23–46, 2001.

F.J. Richards. A flexible growth function for empirical use. Journal of Experimental Botany, 10(29): 290–300, 1959.

A.A. Blumberg. Logistic growth rate functions. Journal of Theoretical Biology, 21: 42–44, 1968.

M.E. Turner, E. Bradley, K. Kirk and K. Pruitt. A Theory of Growth. Mathematical Biosciences, 29: 367–373, 1976.

J. France, J. Dijkstra, Ms. Dhanoa. Growth functions and their application in animal science. Annales de zootechnie, 45 (Suppl1): 165–174, 1996.

J.P. LaSalle. The stability of dynamical systems. SIAM, Philadelphia, 1976.

J.E. Beyer. On length-weight relationship computing the mean weight of the fish of a given length class. Fish Bytes, 5(10):11-13, 1987.

O.S. Ogunola, O.A. Onada, A.E. Falaye. Preliminary evaluation of some aspects of the ecology (growth pattern, condition factor and reproductive biology) of African pike, Hepsetus odoe (Bloch 1794), in Lake Eleiyele, Ibadan, Nigeria. Fisheries and Aquatic Sciences, 21:12, 2018.

D. Pauly. Some simple methods for the assessment of tropical fish stocks. FAO Fisheries Technical Paper, 234: 52, 1983.

Windarto, S.W. Indratno, N. Nuraini, and E. Soewono. A comparison of binary and continuous genetic algorithm in parameter estimation of a logistic growth model. AIP Conference Proceedings, 1587, 2014.




DOI: http://dx.doi.org/10.5614%2Fcbms.2018.1.2.5

Refbacks

  • There are currently no refbacks.


This journal published by: Indonesian Bio-Mathematical Society, Pusat Pemodelan Matematika dan Simulasi, Jalan Ganesa No. 10 Bandung 40116