Perturbation-Iteration Method for Solving Mathematical Model of Glucose and Insulin in Diabetic Human during Physical Activity

In this paper, we aim to solve a two compartmental mathematical model of ordinary differential equations for cardiovascular-respiratory system using a new recent method: Perturbation Iteration method. The description of this method for different order derivatives in the Taylor Series expansion is discussed. This method provides the solution in the form of an infinite series for ordinary differential equation. The efficiency of the method used is investigated by a comparison of Euler method and Runge Kutta. Numerical simulations of all these three methods are implemented in Matlab. The validation has been carried out by taking the values of determinant parameters of cardiovascular-respiratory system for a 30 years old woman who is supposed to make practice of three regular physical activities: Walking, Jogging and Running fast. The results are in good agreement with experimental data.

Fuzzy Logic for Solving an Optimal Control Problem of Hypoxemic Hypoxia Tissue Blood Carbon Dioxide Exchange during Physical Activity

This paper aims at using of an approach integrating the fuzzy logic strategy for hypoxemic hypoxia tissue blood carbon dioxide human optimal control problem. To test the efficiency of this strategy, the authors propose a numerical comparison with the direct method by taking the values of determinant parameters of cardiovascular-respiratory system for a 30 years old woman in jogging as her regular physical activity. The results are in good agreement with experimental data.

CARDIOGUI: An Interface Guide to Simulate Cardiovascular Respiratory System during Physical Activity

This paper aims at the presentation of an interface to simulate cardiovascular respiratory system. The authors are interested in the resolution of optimal control problem related to the performance of a 30 years old woman. The results show in the most case the determinant parameters of cardiovascular respiratory system reach the equilibrium value due to its controls that is heart rate and alveolar ventilation.

Fuzzy Logic Approach for Solving an Optimal Control Problem of an Uninfected Hepatitis B Virus Dynamics

We aimed in this paper to use fuzzy logic approach to solve a hepatitis B virus optimal control problem. The approach efficiency is tested through a numerical comparison with the direct method by taking the values of determinant parameters of this disease for people administrating the drugs. Final results of both numerical methods are in good agreement with experimental data.

Fuzzy Logic Strategy for Solving an Optimal Control Problem of Therapeutic Hepatitis C Virus Dynamics

This paper aims at the development of an approach integrating the fuzzy logic strategy for a therapeutic hepatitis C virus dynamics optimal control problem. To test the efficiency of this strategy, the authors propose a numerical comparison with the direct method by taking the values of determinant parameters of this disease for people administrating the drugs. The results are in good agreement with experimental data.

Hopf Bifurcation of a Two Delay Mathematical Model of Glucose and Insulin during Physical Activity

In this paper, we are interested in looking for Hopf bifurcation solutions for mathematical model of plasma glucose and insulin during physical activity. The mathematical model is governed by a system of delay differential equations. The algorithm for determining the critical delays that are appropriate for Hopf bifurcation is used. The illustrative example is taken for a 30 years old woman who practices regular three types of physical activity: walking, jogging and running fast.

An Optimal Control Problem for Hypoxemic Hypoxia Tissue-Blood Carbon Dioxide Exchange during Physical Activity

This paper aims at solving an optimal control problem for determining the response of hypoxia to heart rate and alveolar ventilation that are cardiovascular and respiratory control respectively during a physical activity. A two nonlinear coupled ordinary differential equations is presented. The cost function of optimal control problem is discretized using the linear B-splines functions defined on a regular grid. The results show the determinant parameters stabilized at normal value.

Fuzzy Logic Strategy for Solving an Optimal Control Problem of Glucose and Insulin in Diabetic Human

This paper aims at the development of an approach integrating the fuzzy logic strategy for a glucose and insulin in diabetic human optimal control problem. To test the efficiency of this strategy, the author proposes a numerical comparison with the indirect method. The results are in good agreement with experimental data.

Simplified Mathematical Model of Glucose-Insulin System

Mathematical modelling of glucose-insulin system is very important in medicine as a necessary tool to understand the homeostatic control of human body. It can also be used to design clinical trials and in the evaluation of the diabetes prevention. In the last three decades so much work has been done in this direction. One of the most notable models is the global six compartment-mathematical model with 22 ordinary differential equations due to John Thomas Sorensen. This paper proposes a more simplified three compartment-mathematical model with only 6 ordinary differential equations by introducing a tissue compartment comprising kidney, gut, brain and periphery. For model parameter identification, we use inverse problems technique to solve a specific optimal control problem where data are obtained by solving the global model of John Thomas Sorensen. Numerical results show that the proposed model is adaptable to data and can be used to adjust diabetes mellitus type I or type II for diabetic patients.