A Mathematical Model For Measles Transmission Dynamics In Luweero District Of Uganda

ABSTRACT

In this research work, Mathematical Model for Measles Transmission Dynamics in Luweero

District of Uganda, SVEIR 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 effective 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 mat lab software. And it shows that the vaccination is capable of reducing the

number of susceptible when the coverage is high.

TABLE OF CONTENTS

DECLARATION~.

APPROVAL

DEDICATION

ACKNOWLEDGEMENTS iv

ABSTRACT

TABLE OF CONTENTS

CHAPTER ONE 1

1 .0 The Introduction

.1 Background of the study

1 .2 Problem statement 2

1 .3 The purpose of the study 2

1 .4 Objectives of the study 2

1 .5 Research questions 3

1 .6 Sign ifi icance of the study 3

1 .7 Scope of the study 4

I.7.lContextual scope 4

I .7.2 Geographical scope 4

I .7.3Time scope 4

CHAPTER TWO

2.0 Virology and medical background 5

2.1.1 Virology 5

2.1 .2 Medical back ground 6

2.2 Transmission, signs and symptoms 7

2.2.1 Transmission 7

2.2.2Signs of measles 8

2.2.3 Symptoms 9

2.3 Diagnosis, treatment and prevention 9

2.3.1 Diagnosis 9

2.3.2 Treatment of measles 10

vi

2.3.3 Prevention.Error! Bookmark not defined.

2.4 Management of Outbreaks 13

2.5.0 Life cycle and pathogenosis 14

2.5.1 Measles virus infection cycle 14

2.5.2 Pathogenesis 17

2.6 Review of literature 19

CHAPTER THREE 25

RESEARCH METHODOLOGY 25

3.0 Introduction 25

3.1 Research Design 25

3.2 mathematical model of infectious diseases 25

3.2 Model formulation and analysis 26

CHAPTER FOUR 29

DATA PRESENTATION ANALYSIS AND INTEPRETATION OF FINDINGS 29

4.0 Data analysis 29

4.1 causes and effects of measles infection 29

4.2 symptoms of measles infection 30

4.3 cure and preventive measures for measles infection 30

4.4 Equilibrium state of the model 32

4.4.2 Disease Free Equilibrium (DFE) 33

4.5 Endemic equilibrium state 34

4.6 Stability of the disease free equilibrium 36

Table 1: Parameters of the models, their interpretations and numerical values 38

4.7 The basic effective reproductive number (Re) 38

4.7.1 Numerical simulation 40

Figure 1. Simulation of susceptible population with, parameter values are as given in table I 41

Figure 2: Simulation Vaccinated population with time, parameter values are as given in table I 41

Figure 3.Simulation of exposed population with time, parameter values are as given in table I 42

Figure 4: Simulation of Infected population with time, parameter values are as given in table 1 43

FigureS: Simulation of recovered population with time, parameter values are as given in table 1 43

VII

CHAPTER FIVE ~

SUMMARY OF FINDINGS DISCUSSION ,CONCLUSION AND RECOMMENDATION 45

5.0 Introduction 45

5.1 SUMMARY OF FINDINGS AND DISCUSSION 45

5,2 Recommendations 49

5.3 AREAS FOR FURTHER RESEARCH 50

5.4 CONCLUSION 50

APPENDICES 52

APPENDIX: A 52

QUESTIONNAIRE FOR THE RESPONDENTS 52

SECTIONA~ 52

BIO DATA OF THE RESPONDENTS 53

SECTIONfr 54

SIGNSOF MEASLES DISEASE 54

SECTION C

TREATMENT AND CONTROL OF MEASELS INFECTION 55

SECTIOND 56

MEASURES OF CONTROLLING MEASELS 56

REPORTED CASES ON MEASLES IN ZIROBWE HEALTH CENTRE IV IN LUWEERO DISTRICT

SINCE 2000-2017 57

APPENDIX B 58

INTERVIEW GUIDE 58

APPENDIX C: PROPOSED BUDGET 2018 59

APPENDIX D’ 60

ACTION PLAN 60