Mathematical Model on Glucose, Insulin and Β-Cells Mass Dynamics in Type 2 Diabetes

ABSTRACT A mathematical model, describing glucose, insulin and β-cells mass dynamics of a type 2 diabetic patient was developed in the form of a system of ordinary differential equation, considering insulin resistance, the body inability to overcome the resistance and the fact that glucose production from food intake is not constant. Numerical solution of the model using RungeKutta code in MATLAB, graphically shows rise in blood glucose concentration and further decline over time in glucose concentration below fasting glucose level as a result of low storage of glucose by the liver from food intake; rise in insulin level and fall in β-cells mass. Results from the equilibrium and stability analysis are interesting and compare favourably with available medical literature. Simulation of insulin resistance parameters showed that glucose concentration in the body is proportional to insulin resistance rate.Also, insulin resistance in glucose conversion to glycogen has a significant impact on glucose concentration in the blood.

TABLE OF CONTENT

Certification i

Declaration ii

Dedication iii

Acknowledgement iv

Abstract v

1. INTRODUCTION 1

1.1.1 Diabetes 1

1.1.2 Insulin 2

1.1.3 Mechanism of Insulin Action on Glucose Level in Blood 5

1.1.4 Blood Glucose Concentration 6

1.2 Objectives of the Study 7

1.3 Scope of the Study 7

1.4 Limitations of the Study 7

1.5 Significance of the Study 8

2. LITERATURE REVIEW 9

3. TYPE 2 DIABETES DISEASE (T2D)

3.1 Type 2 Diabetes (T2D)/Non-Insulin Dependent Diabetes Mellitus (NIDDM) 18

3.2 The Aetiology of Type 2 Diabetes 18

3.2.1 Causes of T2D 18

3.2.2 Risk Factors for the Development of T2D 19

3.3 Prevention 20

3.4 Management 20

3.5 Medication 20

3.6 Epidemiology of Diabetes (T2D) 21

3.7 Signs and Symptoms of T2D 22

3.8 Diagnoses of Diabetes 23

3.9 Insulin Resistance and Development of T2D 26

4. MODEL PRESENTATION AND ANALYSIS

4.1 Model Presentation 28

4.2 Definition of Model Parameters 30

4.3 Model Solution 31

4.4 Equilibrium Analysis of the Model 33

4.5 Stability Analysis of the Model 34

4.6 Model Simulation with Varying Degrees of Insulin Resistance 35

5. DISCUSSION AND RECOMMENDATIONS

5.1 Discussion of Results 40

5.2 Conclusion 41

vi

5.3 Recommendations 41

5.4 Suggestions for Further Studies 42

REFERENCES 43

APPENDIX A 47

APPENDIX B 49

APPENDIX C 50

APPENDIX D 53