A MATHEMATICAL MODEL FOR CHOLERA TRANSMISSION DYNAMICS IN RUBAGA UGANDA

ABSTRACT

 In this research work, Mathematical Model for Cholera Transmission Dynamics in Rubaga Kampala District of Uganda, SBIR model was developed and analyzed. The model consists of five non liner ordinary differential equations. The effective reproductive number, (the number of secondary infections when a single infective individual is introduced into a population where a proportion is protected) was obtained. Further the disease free and endemic equilibrium where obtained and analyzed for stability. Numerical simulation of the various state variables where obtained using mattab software. And it shows that the vaccination is capable of reducing the number of susceptible when the coverage is high.

TABLE OF CONTENTS

Contents

DECLARATION .1

.TUUKO HENRY

1163-07184-06345

APPROVAL ii

DEDICATION iii

ACKNOWLEDGEMENTS iv

ABSTRACT vii

CHAPTERONE 1

INTRODUCTION 1

1.1 background of the study 1

1.2 problem statement 2

1.3 objectives of the study 2

1.4 Purpose of the study 2

1.5 Significance 2

1.6 Research questions 3

1.7 Scope of the study 3

CHAPTER TWO~ 4

LITERATURE REVIEW 4

2.l virology and medical background 4

2.2 Transmission, signs and symptoms 4

2.2.1 Transmission 4

2.2.2 Symptoms 4

2.3 Diagnosis, treatment and prevention 4

2.3.1 Diagnosis 4

2.3.2 Treatment 4

2.3.3 Prevention of Cholera 5

2.4 Pathogenesis and life cycle s

2.4.1 Pathogenesis 5

2.4.2 Life cycIe’ . 6

2.5 literature review 6

CHAPTERTHREE 8

RESEARCH METHODOLOGY 8

3.0 Introduction 8

3.1.1 Research Design 8

3.2 Model Formulation And Analysis 8

3.3 Deterministic Mathematical Model For Cholera Transmission Dynamics 8

CHAPTER FOUR 10

MODEL ANALYSIS 10

4.0 Data analysis 10

4.1 EquiIibrium state of the mod~I 10

4,1.2 Disease Free Equilibrium (DFE) 11

4.2 Endemic equilibrium state 11

4.3 The basic effective reproductive number (Re) 12

4.4 Stability of the disease free equilibrium 14

CHAPTER FIVE 20

DISCUSSIONS, SUMMARY AND RECOMMENDATIONS OF THE STUDY 20

5.0 Introduction 20

5.1 Discussion of the study 20

5.2 Summary of the findings 20

5.3 Recommendations for further research 20

REFERENCES 21