A non-linear population model of diabetes mellitus

Boutayeb, Abdesslam; Chetouani, Abdelaziz; Achouyab, A.; Twizell, E. H.

doi:10.1007/bf02896393

Cited by 37 publications

(24 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the obtained results were divergent at points adjacent to the boundary. Twizell and his coworkers [13,14] have also solved some other higher-order problems and encountered the same problems. Liu and Wu [15], utilizing the generalized differential quadrature rule, have solved similar problems.…”

Section: Introductionmentioning

confidence: 87%

The Variational Iteration Method for a Class of Eighth-Order Boundary-Value Differential Equations

Abbasbandy

Shirzadi

2008

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

The variational iteration method, a well-known method for solving functional equations, is employed to solve a class of eighth-order boundary-value problems, which govern scientific and engineering experimentations. Some special cases of the mentioned equations are solved as examples to illustrate the ability and reliability of the method. The results reveal that the method is very effective and convenient.

show abstract

Section: Introductionmentioning

confidence: 87%

The Variational Iteration Method for a Class of Eighth-Order Boundary-Value Differential Equations

Abbasbandy

Shirzadi

2008

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

show abstract

“…For this reason, a polynomial model is fitted for diabetic patients which are associated with age. 7 A short dialog about polynomial model is tended to in the accompanying that will be utilized in different branches of health sciences:…”

Section: Introductionmentioning

confidence: 99%

Polynomial approach modeling among diabetic patients associated with age in rural hilly population of Dehradun district, Uttarakhand

2018

View full text Add to dashboard Cite

Background: Diabetes mellitus is a form of infections that includes issues with the hormone insulin. It is described by constant rise of blood glucose level surprising ordinary esteem. In this paper, an exertion has been made to fit scientific model to diabetic patients and additionally its total dispersion for both genders related with time of rural population from Dehradun district, Uttarakhand.Methods: For this reason, the information have been taken from field overview in rural hilly population of Dehradun district. In this investigation, an endeavor has been given to demonstrate that the polynomial model is attempted to fit to the conveyance of diabetic patients related with age and also its cumulative distribution.Results: The fitted model provides statistically significant values with R2=0.9997 and ρcv2= 0.994857. This is the polynomial of degree four, i.e. bi-quadratic polynomial model. The polynomial model is assumed for the cumulative distribution of diabetic patients associated with age and the fitted model provides statistically significant values providing R2= 0.99998 and ρcv2= 0.999983 and shrink-age coefficient=0.00001414. This is the polynomial of degree three, i.e. cubic polynomial model. From this statistic we see that the fitted models are highly cross-validated, and their shrinkages are 0.004842857 and 0.00001414 for the models (1) and (2) respectively.Conclusions: It is discovered that the distribution of diabetic patients for both genders related with age takes after bi-quadratic polynomial model. In addition, it is found that cumulative distribution of diabetic patients takes as cubic polynomial model. Cross validity prediction power is utilized to the fitted model to verify the stability of the model in this study.

show abstract

“…There are in the literature many mathematical studies focused on this topic and everything related to it [1,2,3,4,5,6,9,11,12]. The different existing mathematical models are based on ordinary differential equations [4,11,12], partial differential equations [11], delay differential equations [10,11,13,14] and stochastic differential equations [11]. An overview of some mathematical models and software tools for the glucose-insulin regulatory system and diabetes has been done in [11].…”

Section: Introductionmentioning

confidence: 99%

“…In the last decades, some models focused on the intravenous glucose tolerance test, which consists to observe how a body reacts after the injection of a large amount of glucose [13], whereas other ones focused on the subcutaneous injection of insulin (see [17] and [9] for an overview). Another approach was to analyse the evolution of diabetes to the stage of complications [4] and an interesting one was given in [5] where the authors attempt to model mathematically the diabetes progression.…”

Section: Introductionmentioning

confidence: 99%

“…By controlling the external glucose food intake, they proved that the plasma glycemia level can be minimized. In our previous work [1], we considered a population of diabetics, divided into two subcategories, one of diabetics with complications and another one of diabetics without complications as in [4]. From the model examining the complications of individuals diagnosed with diabetes, we associated a nonlinear optimal control problem, for which we proved that there is no cyclical behavior between the number of diabetics with complications, the one of diabetics without complications and the rate at which complications are healed.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

La inexistencia del ciclo de límite en un optimo problema de control de una población de diabéticos

Bernard¹,

Cesar²,

Nuiro³

et al. 2018

RMTA

View full text Add to dashboard Cite

La diabetes, debido a sus complicaciones, es una de las enfermedades que más problemas plantean en la salud pública actual mundial. En este trabajo se parte de una población de diabéticos con y sin complicaciones y se asocia un problema de control optimal no lineal que describe la dinámica de la población. Para este modelo se prueba la existencia del estado de equilibrio y que es un punto de ensilladura. Además se obtuvo que no existen ciclos límite, lo que es un resultado importante, dado el problema que se describe. Se presentan ejemplos para los cuales el estado de equilibrio que se caracteriza no es necesariamente admisible.

show abstract

A non-linear population model of diabetes mellitus

Cited by 37 publications

References 2 publications

The Variational Iteration Method for a Class of Eighth-Order Boundary-Value Differential Equations

The Variational Iteration Method for a Class of Eighth-Order Boundary-Value Differential Equations

Polynomial approach modeling among diabetic patients associated with age in rural hilly population of Dehradun district, Uttarakhand

La inexistencia del ciclo de límite en un optimo problema de control de una población de diabéticos

Contact Info

Product

Resources

About