A Mathematical Model for Malaria A Cases Study Some Selected Health Centers in Jinja District of Uganda

ABSTRACT

 In this research work, a deterministic mathematical mode for malaria transmission was developed and analysed. The model consists of seven ordinary differential equations with two sub-populations. The human subpopulation consists of the susceptible, exposed, infected human compartments while the mosquito sub-population consists of the susceptible, exposed and infected mosquito compartments. The disease free and endemic equilibrium were obtained and analysed for stability. Further, the basic reproductive number of the model was obtained.

TABLE OF CONTENTS

DECLARATION .

APPROVAL

DEDICATION

ACKNOWLEDGEMENTS iv

CHAPTER ONE 1

1.0 The Introduction 1

1.1 Background of the study 1

1.4 Objectives of the study 2

1.5 Significance of the study 3

1.6 Research questions 3

1.7 Scope of the study 3

1.7.1Contextual scope 3

1.7.2 Geographical scope 4

1.7.3Time scope 4

CHAPTER TWO 5

2.0 Virology and medical background

2.1.1 Virology

2.1.2 Medical back ground 6

2.2 Transmission, signs and symptoms 7

2.2.1 Transmission 7

2.2.2Signs and symptoms of Malaria 7

2.3 Diagnosis, treatment and prevention 8

2.3.1 Diagnosis 8

2.3.3 Prevention 11

2.4.0 Life cycle and pathogenosis 12

2.4.1 Malaria infection cycle 12

2.4.2 Pathogenesis 13

vi

2.5 Review of literature .14

CHAPTER THREE 15

RESEARCH METHODOLOGY 15

3.0 Introduction 15

3.1.1 Research Design 15

3.2 Mathematical model of infectious diseases 15

3.2 Model formulation and analysis 16

CHAPTER FOUR 19

MODEL ANALYSIS 19

4.ODataanalysis 19

4.1 Equilibrium state of the model 19

4.1.2 Disease Free Equilibrium (DFE) 20

4.2 Endemic equilibrium state 20

4.3 The basic effective reproductive number (Re) 23

4.4 Stability ofthe disease free equilibrium 26

CHAPTER FIVE 27

DISCUSSIONS, SUMMARY AND RECOMMENDATIONS 27

5.0 Introduction 27

5.1 Discussion oft he study 27

5.2 Summary of the Study 28