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

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Open Journal of Applied Sciences 2013年第7期3卷 421-429页

作者： jean marie ntaganda Department of Applied Mathematics School of Pure and Applied Science College of Science and Technology University of Rwanda (Huye Campus) Butare Rwanda

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 ... 详细信息

关键词： Fuzzy Logic Optimal Control Membership Function Membership Degree Glucose Insulin Numerical Simulation

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

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Open Journal of Applied Sciences 2013年第1期3卷 56-61页

作者： jean marie ntaganda Benjamin Mampassi Department of Mathematics and Computer Science Dakar University Dakar Senegal National University of Rwanda Butare Rwanda

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.

关键词： Arterial Oxygen Pressure Arterial Dioxide Pressure Cardiovascular/Respiratory System Optimal Control Problem Numerical Simulation

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

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Applied Mathematics 2012年第12期3卷 2000-2006页

作者： jean marie ntaganda Benjamin Mampassi Applied Mathematical Department National University of Rwanda Butare Rwanda Department of Mathematics and Computer Science Cheikh Anta Diop University of Dakar Dakar Senegal

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.

关键词： Graphical User Interface Arterial Oxygen Pressure Arterial Dioxide Pressure Cardiovascular/Respiratory System Optimal Control Problem Numerical Simulation Physical Activity

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

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Applied Mathematics 2015年第9期6卷 1524-1537页

作者： jean marie ntaganda Marcel Gahamanyi Department of Mathematics School of Sciences College of Science and Technology University of Rwanda Kigali Rwanda

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.

关键词： Fuzzy Logic Optimal Control Membership Function Membership Degree Hepatitis B Virus Numerical Simulation

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

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Open Journal of Applied Sciences 2016年第12期6卷 826-838页

作者： Marcel Gahamanyi jean marie ntaganda Mahamat Saleh Daoussa Haggar Department of Mathematics College of Science and Technology School of Science University of Rwanda Kigali Rwanda Department of Applied Mathematics N’djamena University N’djamena Chad

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.

关键词： Perturbation-Iteration Method Glucose Insulin Heart Rate Alveolar Ventilation Physical Activity Numerical Simulation

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

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Open Journal of Applied Sciences 2014年第11期4卷 501-514页

作者： jean marie ntaganda Mahamat Saleh Daoussa Haggar Benjamin Mampassi Department of Applied Mathematics School of Pure and Applied Sciences College of Science and Technology University of Rwanda Kigali Rwanda N’Djamena University N’Djamena Chad Cheikh Anta Diop University Dakar Senegal

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.

关键词： Fuzzy Logic Optimal Control Membership Function Membership Degree Hypoxemic-Hypoxia Pressure Carbon Dioxide Oxygen Numerical Simulation

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

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Open Journal of Applied Sciences 2015年第9期5卷 527-541页

作者： jean marie ntaganda Mahamat Saleh Daoussa Haggar Benjamin Mampassi College of Science and Technology School of Sciences Department of Mathematics University of Rwanda Butare Rwanda Department of Mathematics Faculty of Exact and Applied Sciences N’Djamena University N’Djamena Chad Department of Mathematics Faculty of Sciences and Technology Dakar University Dakar Senegal

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.

关键词： Fuzzy Logic Optimal Control Membership Function Membership Degree Hepatitis C Virus Uninfected Hepatocytes Infected Hepatocytes Numerical Simulation

Simplified Mathematical Model of Glucose-Insulin System

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American Journal of Computational Mathematics 2018年第3期8卷 233-244页

作者： jean marie ntaganda Froduald Minani Wellars Banzi Lydie Mpinganzima Japhet Niyobuhungiro jean Bosco Gahutu Eric Rutaganda Immaculate Kambutse Vincent Dusabejambo Department of Mathematics School of Science College of Science and Technology University of Rwanda Kigali Rwanda School of Medicine College of Medicine and Health Sciences University of Rwanda Kigali Rwanda

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.

关键词： Glucose Insulin Mathematical Model Parameter Identification

Density Results in Sobolev Spaces Whose Elements Vanish on a Part of the Boundary

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Chinese Annals of Mathematics,Series B 2011年第6期32卷 823-846页

作者： jean-marie Emmanuel BERNARD Laboratoire Analyse et Probabitilités Université d'Evry val d'Essonne23 Boulevard de France91037 EVRYFrance

This paper is devoted to the study of the subspace of Wm＇＂ of functions that vanish on a part γ0 of the boundary. The author gives a crucial estimate of the Poincare constant in balls centered on the boundary of γ0. Then, the convolution-translation method, a variant of the standard mollifier technique, can be used to prove the density of smooth functions that vanish in a neighborhood of γ0, in this subspace. The result is first proved for m = 1, then generalized to the case where m 〉 1, in any dimension, in the framework of Lipschitz-continuous domain. However, as may be expected, it is needed to make additional assumptions on the boundary of γ0, namely that it is locally the graph of some Lipschitz-continuous function.

关键词： Density results Boundary value problems Sobolev spaces