Existence and characterization of optimal control in mathematics model of diabetics population

Permatasari, A. H.; Tjahjana, R. Heru; Udjiani, Titi

doi:10.1088/1742-6596/983/1/012069

Cited by 16 publications

(8 citation statements)

References 9 publications

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“…To control the second and the third compartiment, they introduce a single control in thier system. T. T. Yusuf proposed an optimal control strategy on a mathematical model of the diabetic population divided into two compartments, the first is the diabetic people without complication, and the second is the diabetic people with complication [22].In 2018 Permatasari et al [23] also proposed an optimal control approach to reduce the burden of pre-diabetes, they also took into account people who became disabled due to diabetes. They built a mathematical model on the healthy population, pre-diabetics and diabetics without complications, diabetics with complications and diabetics who became disabled.…”

Section: Introductionmentioning

confidence: 99%

Multi-objectives optimization and convolution fuzzy C-means: control of diabetic population dynamic

Moutaouakil¹,

Ouissari²,

Chellak³

et al. 2022

RAIRO-Oper. Res.

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The optimal control models proposed in the literature to control a population of diabetics are all single-objective which limits the identification of alternatives and potential opportunities for different reasons: the minimization of the total does not necessarily imply the minimization of different terms and two patients from two different compartments may not support the same intensity of exercise or the same severity of regime. In this work, we propose a multi-objectives optimal control model to control a population of diabetics taking into account the specificity of each compartment such that each objective function involves a single compartment and a single control. In addition, the Pontryagin's maximum principle results in expansive control that devours all resources because of max-min operators and the control formula is very complex and difficult to assimilate by the diabetologists. In our case, we use a multi-objectives heuristic method, NSGA-II, to estimate the optimal control based on our model. Since the objective functions are conflicting, we obtain the Pareto optimal front formed by the non-dominated solutions and we use fuzzy C-means to determine the important main strategies based on a typical characterization. To limit human intervention, during the control period, we use the convolution operator to reduce hyper-fluctuations using kernels with different size. Several experiments were conducted and the proposed system highlights four feasible control strategies capable of mitigating socio-economic damages for a reasonable budget.

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Section: Introductionmentioning

confidence: 99%

Multi-objectives optimization and convolution fuzzy C-means: control of diabetic population dynamic

Moutaouakil¹,

Ouissari²,

Chellak³

et al. 2022

RAIRO-Oper. Res.

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“…In 2021, Avendaño-Valencia et al [13] developed a video-based eye-tracking method with the help of a Heteroscedastic Auto-Regressive with eXogeneous input model for detection of diabetes complications associated with the nervous system. Some of the previous diabetic population models were governed by ordinary differential equations [14][15][16][17][18][19][20][21]. These ordinary differential equations models considered the progression of diabetes instantaneously.…”

Section: Introductionmentioning

confidence: 99%

A time-delay model of diabetic population: Dynamics analysis, sensitivity, and optimal control

Nasir¹

2021

Phys. Scr.

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Diabetes, also known as diabetes mellitus, is a chronic degenerative disease with a variety of adverse complications. Due to its slow progression, a mathematical model of the diabetic population with time lag is developed. This novel study aims to analyze the stability of the diabetic equilibrium and also formulate an optimal control problem with lags. We show that under some values of parameters, a limit cycle arises through Hopf bifurcation. Sensitivity analysis, which used the direct differential method, reveals which parameters have a major impact on the model dynamics. An optimal control strategy is developed with two control variables for the description of the control strategy. A suitable objective function is formulated to minimize the total number of diabetics and the relative cost of implementing the controls. The resulting optimality system is solved numerically by using the Forward-Backward Sweep Method. Graphical results are examined with different parameter values and are compared with and without controls. The total number of diabetics continued to increase without controls, but the number of these individuals decreased after control. The optimal controls prevent the progression of diabetes complications by awareness, education, and medical care at the least cost.

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“…Their model shows that, using optimal control, the number of diabetics with and without complications can be significantly reduced in a period of 10 years. In 2018 Permatasar et al [8] proposed Mathematical model to elaborate the prevalence of diabetics has been determined by diabetes complication (DC) model. In the DC model, people with diabetes were classified into two compartments, uncomplicated diabetics (D) and complicated diabetics (C).…”

Section: Introductionmentioning

confidence: 99%

“…The equilibrium point of the model indicates the influential parameters that can be controlled to address the issue. Also, many researches have focused on this topic and other related topics [7][8][9]16,[20][21][22].…”

Section: Introductionmentioning

confidence: 99%

A multi-age mathematical modeling of the dynamics of population diabetics with effect of lifestyle using optimal control

Kouidere

Khajji

Balatif

et al. 2021

J. Appl. Math. Comput.

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Existence and characterization of optimal control in mathematics model of diabetics population

Cited by 16 publications

References 9 publications

Multi-objectives optimization and convolution fuzzy C-means: control of diabetic population dynamic

Multi-objectives optimization and convolution fuzzy C-means: control of diabetic population dynamic

A time-delay model of diabetic population: Dynamics analysis, sensitivity, and optimal control

A multi-age mathematical modeling of the dynamics of population diabetics with effect of lifestyle using optimal control

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