Ultimate Bounds for a Diabetes Mathematical Model Considering Glucose Homeostasis

Gamboa, Diana; Coria, Luis N.; Valle, Paul A.

doi:10.3390/axioms11070320

Cited by 5 publications

(3 citation statements)

References 23 publications

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“…Each chromosome may include a set of genes. It is used for glucose normalization in diabetic patients (Jasim and Al Mashhadany, 2021;Gamboa et al, 2022;Medhi et al, 2023).…”

Section: Methodsmentioning

confidence: 99%

Application of Genetic Algorithms for Medical Diagnosis of Diabetes Mellitus

Tyagi,

Kumar,

Gupta

2024

IJERR

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The system of glucose-insulin control and associated problems in diabetes mellitus were studied by mathematical modeling. It is a helpful theoretical tool for understanding the basic concepts of numerous distinct medical and biological functions. It delves into the various risk factors contributing to the onset of diabetes, such as sedentary lifestyle, obesity, family history, viruses, and increasing age. The study emphasizes the importance of mathematical models in understanding the dynamic characteristics of biological systems. The study emphasizes the increasing prevalence of diabetes, especially in India, where urbanization and lifestyle changes contribute to the rising incidence. The present investigation describes the use of John Holland's evolutionary computing approach and the Genetic Algorithm (GA) in diabetes mellitus. The Genetic Algorithm is applied to address issues related to diabetes, offering a generic solution and utilizing MATLAB's Genetic Algorithm tool. The Mathematical Model provides differential equations representing glucose and insulin concentrations in the blood. The results represent testing outcomes for normal, prediabetic, and diabetic individuals, optimized with Genetic Algorithm showcased through fitness value plots. The conclusion highlights the effectiveness of Genetic Algorithm as an optimization tool in predicting optimal samples for diabetes diagnosis. The paper encourages the use of heuristic algorithms, such as Genetic Algorithms, to address complex challenges in the field of diabetes research. Future scope includes further exploration of biomathematics and Genetic Algorithm applications for enhanced understanding and management of diabetes mellitus. It is critical for people with diabetes to consistently check their blood glucose levels and follow their treatment plan.

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“…Each chromosome may include a set of genes. It is used for glucose normalization in diabetic patients (Jasim and Al Mashhadany, 2021;Gamboa et al, 2022;Medhi et al, 2023).…”

Section: Methodsmentioning

confidence: 99%

Application of Genetic Algorithms for Medical Diagnosis of Diabetes Mellitus

Tyagi,

Kumar,

Gupta

2024

IJERR

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“…En este modelo se utilizan los mismos parámetros que los del modelo anterior, añadiendo el aumento de glucosa provocado por la secreción de epinefrina (Ge) y la eficiencia de la epinefrina en suprimir la secreción de Ordinarias (EDOs) de primer orden [13] . En años recientes, ha sido aplicado en el estudio de diferentes sistemas dinámicos tales como sistemas biológicos que describen el desarrollo y evolución de enfermedades como el cáncer o la diabetes [14][15] [16] . El método es estrictamente analítico, lo que implica que es posible encontrar la solución del problema sin la necesidad de resolver el sistema de EDOs por algún método numérico.…”

Section: Masa De Células β En El Momento Tunclassified

Nonlinear Mathematical Analysis based on an Insulin-Pancreatic Cells Model in the Presence of Epinephrine

Gamboa,

Campos

2024

Rev. Mex. Ing. Biomed.

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In this work, a nonlinear model is studied based on ordinary differential equations that describe the relationship between the mass of cells and the secretion of epinephrine. It analyzes the impact of stress associated with the cause of increased blood pressure and glucose levels in the body. The mathematical analysis is based on the appliance of the nonlinear control theory to define the maximum load capacity for each state variable, establishing a bounded positive invariant domain through the Localization of Compact Invariants Sets (LCIS) method. The objective is to determine the effects of epinephrine secretion on the increase of blood glucose levels; therefore, this analysis's results define the necessary and sufficient conditions in which epinephrine raises insulin and glucose levels in the presence of cells. The interest in studying this type of disease focuses on searching for a treatment or an analysis that guarantees complete control of glucose levels. This work's development and mathematical analysis strengthen current research on insulin-dependent diabetes mellitus around critical epinephrine factors that imply an increase in glucose in the body.

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“…Srivastava et al [ 50 ] have focused on a fractional-order model of diabetes and they considered model with its complications. For more knowledge about diabetes and related studies, see in [ 16 , 17 , 20 , 54 , 58 ]…”

Section: The Diabetes Mellitus Modelmentioning

confidence: 99%

A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors

Karaağaç

Owolabi

Pindza

2023

Int. J. Dynam. Control

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The concept of a Caputo fractal-fractional derivative is a new class of non-integer order derivative with a power-law kernel that has many applications in real-life scenarios. This new derivative is applied newly to model the dynamics of diabetes mellitus disease because the operator can be applied to formulate some models which describe the dynamics with memory effects. Diabetes mellitus as one of the leading diseases of our century is a type of disease that is widely observed worldwide and takes the first place in the evolution of many fatal diseases. Diabetes is tagged as a chronic, metabolic disease signalized by elevated levels of blood glucose (or blood sugar), which results over time in serious damage to the heart, blood vessels, eyes, kidneys, and nerves in the body. The present study is devoted to mathematical modeling and analysis of the diabetes mellitus model without genetic factors in the sense of fractional-fractal derivative. At first, the critical points of the diabetes mellitus model are investigated; then Picard’s theorem idea is applied to investigate the existence and uniqueness of the solutions of the model under the fractional-fractal operator. The resulting discretized system of fractal-fractional differential equations is integrated in time with the MATLAB inbuilt Ode45 and Ode15s packages. A step-by-step and easy-to-adapt MATLAB algorithm is also provided for scholars to reproduce. Simulation experiments that revealed the dynamic behavior of the model for different instances of fractal-fractional parameters in the sense of the Caputo operator are displayed in the table and figures. It was observed in the numerical experiments that a decrease in both fractal dimensions and leads to an increase in the number of people living with diabetes mellitus.

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Ultimate Bounds for a Diabetes Mathematical Model Considering Glucose Homeostasis

Cited by 5 publications

References 23 publications

Application of Genetic Algorithms for Medical Diagnosis of Diabetes Mellitus

Application of Genetic Algorithms for Medical Diagnosis of Diabetes Mellitus

Nonlinear Mathematical Analysis based on an Insulin-Pancreatic Cells Model in the Presence of Epinephrine

A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors

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