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
