Mathematical Approaches in the Study of Diabetes Mellitus

Rȧjeswari, S.; Ponnusamy, Vijayakumar

doi:10.1007/978-981-19-7892-0_18

Cited by 2 publications

(1 citation statement)

References 25 publications

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“…Así mismo, en [8] se reporta un análisis global enfocado a las biomatemáticas para continuar estudiando las hipótesis con las que algunos modelos de DM se definen con base a datos experimentales o in-silico. Es por ello, la inquietud de continuar estudiando los modelos con el que se predice DMT1 se convierte en un desafío vigente y, por ende, el análisis matemático mediante el método de Localización de Conjuntos Compactos Invariantes fortalece las hipótesis en el desarrollo de cada modelo que se ha propuesto en la literatura.…”

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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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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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Chaos in Physiological Control Systems: Health or Disease?

Boubaker

2024

Chaos Theory and Applications

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During the 90s, the Rössler’s have reported in their famous book “Chaos in Physiology”, that “physiology is the mother of Chaos”. Moreover, several researchers have proved that Chaos is a generic characteristic of systems in physiology. In the context of disease, like for example growth of cancer cell populations, Chaos often refers to irregular and unpredictable patterns. In such cases, Chaos signatures can be used to prove the existence of some pathologies. However, for other physiological behaviors, Chaos is a form of order disguised as disorder and can be a signature of healthy physiological functions. This is for example the case of human brain behavior. As the boundary between health and disease is not always clear-cut in chaotic systems in physiology, some conditions may involve transitions between ordered and chaotic states. Understanding these transitions and identifying critical points can be crucial for predicting Healthy vs. pathological Chaos. Using recent advances in physiological Chaos and disease dynamics, we try in this article to answer the crucial question: when Chaos be a sign of health or disease?

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Mathematical Approaches in the Study of Diabetes Mellitus

Cited by 2 publications

References 25 publications

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

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

Chaos in Physiological Control Systems: Health or Disease?

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