A population model of diabetes and pre-diabetes

Boutayeb, Abdesslam; Chetouani, Abdelaziz

doi:10.1080/00207160601167037

Cited by 20 publications

(26 citation statements)

References 20 publications

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“…Different simulations can be carried out using various values of parameters. In the present numerical approach, we use the following parameters values taken from [4] 0.5 Table 1: Parameter vales used in numerical simulation E(0) = 6660000; D(0) = 10200000; C(0) = 5500000; n = 1000; h = 0.01; T = nh = 10 years λ 1 (n) = 0; λ 2 (n) = 0; λ 3 (n) = 0; Since control and state functions are on different scales, the weight constant value is chosen as follows: A = 3550000;…”

Section: Numerical Simulationmentioning

confidence: 99%

“…Consequently, the burden of diabetes can be reduced by controlling the number of people evolving from the stage of pre-diabetes to the stages of diabetes with and without complications. Following previous mathematical models on diabetes and prediabetes ( [4], [5], [6]) the present paper proposes an optimal control approach modeling the dynamics of a population with diabetes.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal control approach to the dynamics of a population of diabetics

Derouich¹,

Boutayeb²,

Boutayeb³

et al. 2014

ams

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Diabetes is a chronic disease with a huge and growing socioeconomic burden affecting individuals, families and the whole society. In this paper, we propose an optimal control approach modeling the evolution from pre-diabetes to diabetes with and without complications. We show the existence of an optimal control and then use a numerical implicit finite-difference method to monitor the size of population in each compartment. Our model shows that, using optimal control, the number of diabetics with and without complications can be significantly reduced in a period of 10 years.

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Section: Numerical Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal control approach to the dynamics of a population of diabetics

Derouich¹,

Boutayeb²,

Boutayeb³

et al. 2014

ams

Self Cite

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show abstract

“…Di erent simulations can be carried out using various values of parameters. In the present numerical approach, we use the following parameter values taken from [2]:…”

Section: Numerical Simulationmentioning

confidence: 99%

“…During the last decade, a large number of mathematical models have been developed to simulate, analyse, and understand the dynamics of a population of diabetics; in a related research work, Boutayeb and Chetouani [2] and Derouich et al [3] proposed a mathematical model for the dynamics of the population of diabetes patients with or without complications using a system of ordinary di erential equations. Also, many researches have focused on this topic and other related topics [4,5,[12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Strategy for a Discrete Time to the Dynamics of a Population of Diabetics with Highlighting the Impact of Living Environment

Kouidere

Balatif

Ferjouchia

et al. 2019

Discrete Dynamics in Nature and Society

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Nowadays, Diabetes is one of the most common diseases, which has a huge and growing socio-economic burden affecting individuals, families, and the whole society. In this paper, we propose an optimal control approach modeling the evolution from pre-diabetes to diabetes with and without complications and the effect of living environment. We show the existence of an optimal control and then use a numerical implicit finite-difference method to monitor the size of population in each compartment.

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“…These mathematical models aim at understanding and analyzing the dynamics of diabetics. In a related research work, in 2004 Boutayeb et al [ 3 ] introduced introduced the diabetes complication (DC) model to find out how many changes of diabetics without complications (D) and diabetics with complications (C). In the DC model the number of new patients (incidence) of diabetes is assumed to be constant.…”

Section: Introductionmentioning

confidence: 99%