Global stability for linear system and controllability for nonlinear system in the dynamics model of diabetics population

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

doi:10.1088/1742-6596/1025/1/012086

Cited by 5 publications

(4 citation statements)

References 6 publications

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“…For the stability analysis of the mathematical model, the method of quadratic Lyapunov for linear system by Permatasari et al [11] was adopted to analyzed the stability of linear system of equations ( 1) to (5).…”

Section: Stability Analysis Of the Disease Prevalence Equilibrum Stat...mentioning

confidence: 99%

“…then the system is globally asymptotically stable [11]. = − so that the system is globally asymptotically stable [11].…”

Section: Lyapunov Stability Of Linear Systemmentioning

confidence: 99%

“…An analytical solution was obtained and graphical profile of the solution was shown using Mapple software. The results showed that model parameters have an effect in determining the number of people living with diabetes, Permatasari et al [11] proposed method of quadratic Lyapunov function for determining stability of linear system. The method was applied to linear system of dynamics of diabetics population.…”

Section: Introductionmentioning

confidence: 99%

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Eigenvalue Elasticity Analysis of Mathematical Model of Dynamics of Diabetes and its Complications in a Population

Aye Patrick Olabanji

2024

AMCI

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In this paper, a mathematical model of dynamics of diabetes and its complications was presented to explore the parameters with the greatest impact on the model. The model allows for the individuals to move from the susceptible class to the treated class. The model exhibit one equilibrum state, namely, the disease prevalent equilibrium state. The local and global asymptotic stability of the equilibrium state was determined using quadratic Lyapunov method. Eigenvalue elasticity analysis of the model parameters was carried out and parameter d (mortality rate due to complications) has the highest positive eigenvalue elasticity value. Also, using the eigenvalue sensitivity analysis, the parameter d has the highest positive value. The analysis revealed that parameter d has the greatest impact on the formulated mathematical model of disease dynamics which must be put into consideration by the health care policy makers in order to reduce the rate of mortality due to the disease.

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Section: Stability Analysis Of the Disease Prevalence Equilibrum Stat...mentioning

confidence: 99%

“…then the system is globally asymptotically stable [11]. = − so that the system is globally asymptotically stable [11].…”

Section: Lyapunov Stability Of Linear Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Eigenvalue Elasticity Analysis of Mathematical Model of Dynamics of Diabetes and its Complications in a Population

Aye Patrick Olabanji

2024

AMCI

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“…Optimal control theory is used. Permatasari et al [10] considered the model developed by [9]. Global stability and controllability for linear and nonlinear systems are presented, respectively.…”

Section: Introductionmentioning

confidence: 99%

An Application of Nonstandard Finite Difference Method to a Model Describing Diabetes Mellitus and Its Complications

TURHAN ÇETİNKAYA

2023

Journal of New Theory

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In this study, a mathematical model describing diabetes mellitus and its complications in a population is considered. Since standard numerical methods can lead to numerical instabilities, it aims to solve the problem using a nonstandard method. Among the nonstandard methods, nonstandard finite difference (NSFD) schemes that satisfy dynamical consistency are preferred to make the model discrete. Both continuous and discrete models are analyzed to show the stability of the model at the equilibrium points. The Schur-Cohn criterion is used to perform stability analysis at the equilibrium point of the discretized model. Thus, asymptotically stability of the model is presented. Moreover, the advantages of the NSFD method are emphasized by comparing the stability for different step sizes with classical methods, such as Euler and Runge-Kutta. It has been observed that the NSFD method is convergence for larger step sizes. In addition, the numerical results obtained by NSFD schemes are compared with the Runge–Kutta–Fehlberg (RKF45) method in graphical forms. The accuracy of the NSFD method is observed.

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Population models of diabetes mellitus by ordinary differential equations: a review

Nasir

Daud

2021

Mathematical Population Studies

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Global stability for linear system and controllability for nonlinear system in the dynamics model of diabetics population

Cited by 5 publications

References 6 publications

Eigenvalue Elasticity Analysis of Mathematical Model of Dynamics of Diabetes and its Complications in a Population

Eigenvalue Elasticity Analysis of Mathematical Model of Dynamics of Diabetes and its Complications in a Population

An Application of Nonstandard Finite Difference Method to a Model Describing Diabetes Mellitus and Its Complications

Population models of diabetes mellitus by ordinary differential equations: a review

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