A new family of mathematical models describing the human growth curve

We introduce a new family of iterative methods for solving mathematical models whose governing equations are nonlinear in nature. The new family gives several iterative schemes as special cases. We also give the convergence analysis of our proposed methods. In order to demonstrate the improved performance of newly developed methods, we consider some nonlinear equations along with two complex mathematical models. The graphical analysis for these models is also presented.

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HUMAN GROWTH CURVE

The Journal of General Physiology ◽

10.1085/jgp.10.2.205 ◽

1926 ◽

Vol 10 (2) ◽

pp. 205-216 ◽

Cited By ~ 14

Author(s):

Charles B. Davenport

Keyword(s):

Standard Deviation ◽

Growth Curve ◽

Maximum Velocity ◽

Human Growth ◽

Growth Cycle ◽

The Body ◽

Type I ◽

Low Velocity ◽

Growth Accelerations ◽

Special Growth

The human growth curve shows two (and only two) outstanding periods of accelerated growth—the circumnatal and the adolescent. The circumnatal growth cycle attains great velocity, which reaches a maximum at the time of birth. The curve of this cycle is best fitted by a theoretical skew curve of Pearson's Type I. It has a theoretical range of 44 months and a standard deviation of 5.17 months. The modal velocity is 10.2 kilos per year. The adolescent growth cycle has less maximum velocity and greater range in time than the circumnatal cycle. The best fitting theoretical curve is a normal frequency curve ranging over about 10 years with a standard deviation of about 21 months and a modal velocity of 4.5 kilos per year. The two great growth accelerations are superimposed on a residual curve of growth which measures a substratum of growth out of which the accelerations arise. This probably extends from conception to 55 years, on the average. It is characterized by low velocity, averaging about 2 kilos per year from 2 to 12 years. It is interpreted as due to many growth operations coincident or closely blending in time. Our curve shows no third marked period of acceleration at between the 3rd and 6th years. The total growth in weight of the body is the sum of the weight of its constituent organs. In some cases these keep pace with the growth of the body as a whole; great accelerations of body growth are due to great accelerations in growth of the constituent organs. In other cases one of the organs of the body (like the thymus gland) may undergo a change in weight that is not in harmony with that of the body as a whole. The development of the weight in man is the resultant of many more or less elementary growth processes. These result in two special episodes of growth and numerous smaller, blending, growth operations. Hypotheses are suggested as to the basis of the special growth accelerations.

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Mathematical models for Isoptera (Insecta) mound growth

Brazilian Journal of Biology ◽

10.1590/s1519-69842008000300009 ◽

2008 ◽

Vol 68 (3) ◽

pp. 529-533 ◽

Cited By ~ 3

Author(s):

MLT. Buschini ◽

MAP. Abuabara ◽

Miguel Petrere-Jr

Keyword(s):

Mathematical Models ◽

Growth Curve ◽

Von Bertalanffy ◽

Mean Diameter ◽

Mound Growth ◽

The Mean

In this research we proposed two mathematical models for Isoptera mound growth derived from the Von Bertalanffy growth curve, one appropriated for Nasutitermes coxipoensis, and a more general formulation. The mean height and the mean diameter of ten small colonies were measured each month for twelve months, from April, 1995 to April, 1996. Through these data, the monthly volumes were calculated for each of them. Then the growth in height and in volume was estimated and the models proposed.

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Evaluation of mathematical models to describe lamb growth during the pre-weaning phase

Semina Ciências Agrárias ◽

10.5433/1679-0359.2021v42n3supl1p2073 ◽

2021 ◽

Vol 42 (3Supl1) ◽

pp. 2073-2080

Author(s):

Antonio Leandro Chaves Gurgel ◽

◽

Gelson dos Santos Difante ◽

João Virgínio Emerenciano Neto ◽

Henrique Jorge Fernandes ◽

...

Keyword(s):

Mathematical Models ◽

Mean Square Error ◽

Growth Curve ◽

Growth Patterns ◽

The Body ◽

Coefficient Of Determination ◽

Genetic Constitution ◽

Mean Square ◽

Linear Quadratic ◽

Accuracy And Precision

The aim of this study was to evaluate the use of different mathematical models to describe the growth of lambs during the pre-weaning phase and the effect of sex on their growth curve. Data from 51 lambs (26 males and 25 females) with a genetic constitution of at least 50% Santa Inês breed were used. Lamb weight was monitored during the entire pre-weaning phase (91 days) by weighing the animals weekly on a scale suitable for sheep, to draw the body-weight growth curve. The adequacy of the models was evaluated by the coefficient of determination, simultaneous F-test for parameter identity, concordance correlation coefficient, root mean square error of prediction and decomposition of the mean square error of prediction. Pairwise mean square error of prediction analysis and delta Akaike information criterion were used to compare the models in terms of accuracy and precision. The evaluation of the adequacy of the tested models showed that the data predicted by the linear, quadratic and exponential models were similar (P > 0.05) to the observed data. In contrast, the monomolecular model generated predictions that could not be accepted as true. The linear and quadratic models showed better accuracy and precision. The first-degree linear model should be preferred over the other studied models to describe growth of sheep in the preweaning phase. Males and females exhibited distinct growth patterns.

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