Development and Analysis of a Mathematical Model for the Population Dynamics of Diabetes Mellitus During Pregnancy

Daud, Auni Aslah Mat; Toh, Cher Qing; Saidun, Salilah

doi:10.1134/s2070048220040067

Cited by 20 publications

(10 citation statements)

References 13 publications

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“…i.e., the solutions of Model (2.1) are always non-negative. Alternatively, the general solution of initial value problems for the non-homogeneous constant coefficient linear system is given by variation of constants formula [14] x i = e At x i (0) + e At t 0 e −As c i ds.…”

Section: Positivity and Boundedness Of The Solutionsmentioning

confidence: 99%

“…Unlike infectious diseases, mathematical modelling is seldom applied to NCDs. It has been shown recently that the population dynamics of NCDs can be described and are better modelled by linear systems [2,[11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…This study will attempt to address these issues. Three NCDs have been studied recently, in which the mathematical models of thyroid disorder [11], hypertension [13] and diabetes mellitus during pregnancy are proposed and studied using stability and sensitivity analysis [14]. However, to date, no mathematical model of VTE has been studied in the literature.…”

Section: Introductionmentioning

confidence: 99%

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A general model of non-communicable diseases and its qualitative analysis without finding the eigenvalues

Daud¹,

Qing²

2021

J. Math. Computer Sci.

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Obtaining the analytical solutions of a linear ordinary differential equations is impossible without finding the eigenvalues. In this study, a general linear model of non-communicable disease (NCD) is formulated using the compartmental analysis and its qualitative properties are analyzed without finding the eigenvalues. NCDs are diseases which are not passed from person to person. The proof of the qualitative properties of the general model including the existence and uniqueness of its solution and equilibrium, and the positivity and boundedness of its solutions are provided. The global stability of the general model is analyzed using the theorem of compartmental matrix and Lyapunov function. It is found that the model has one unique non-negative equilibrium which is globally exponentially stable. As a real-world example, the general model and its qualitative analysis are implemented to a NCD, namely venous thromboembolism (VTE) among pregnant and postpartum women. VTE is selected in this study as it is a major global health burden due to its association with disability and lower quality of life and death.

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Section: Positivity and Boundedness Of The Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A general model of non-communicable diseases and its qualitative analysis without finding the eigenvalues

Daud¹,

Qing²

2021

J. Math. Computer Sci.

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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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“…They proposed to study an optimal control approach with delay in state and control variables in a discrete mathematical model of kouidere et al [5], that time with delay represent the measuring the extent of interaction with the means of treatment or awareness campaigns. Also, many researches have focused on this topic and other related topics, and Sweatman et al [14] introduce a mathematical model of diabetes and dietrelated lipid metabolism, leptin sensitivity, insulin sensitivity and VLDLTG clearance predict pathways to health and type II diabetes, and also Auni Aslah Mat Daud et al [46] proposed a mathematical model of the population dynamics of DM during pregnancy is developed and analyzed. Four independent variables have been considered, namely the numbers of nonpregnancy nondiabetic women, diabetic nonpregnant women, diabetic pregnant women and diabetic pregnant women with complication.…”

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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Development and Analysis of a Mathematical Model for the Population Dynamics of Diabetes Mellitus During Pregnancy

Cited by 20 publications

References 13 publications

A general model of non-communicable diseases and its qualitative analysis without finding the eigenvalues

A general model of non-communicable diseases and its qualitative analysis without finding the eigenvalues

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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