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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

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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

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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

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