ABSTRACT
This project proposes a non – linear mathematical model to study the effect of irresponsible infected immigrants on the spread of HIV/AIDS in a heterogeneous population with a constant recruitment of susceptible. The equilibrium points, stability analysis and numerical simulation on the model are presented. It is realised that at the disease – free equilibrium, the model is stable when the basic reproduction number R0<1 and unstable otherwise. The Routh – Hurwitz stability condition was employed to examine the stability of the disease – free equilibrium. Also, the endemic equilibrium is stable as it satisfies the Bellman and Cooke’s condition for stability. The analysis further shows that strict immigration policies such as screening and reduction in the number of immigrants into a given population, and behavioural change of all classes of individuals should be considered in efforts aimed at controlling the spread of the disease.
TABLE OF CONTENTS
COVER PAGE
TITLE PAGE i
DECLARATION ii
DEDICATION iii
APPROVAL PAGE iv
ACKNOWLEDGEMENT v
TABLE OF CONTENT vi
ABSTRACT viii CHAPTER ONE: INTRODUCTION
1.1 Background of Study 1
1.2 Statement of the Problem 5
1.3 Aim and Objectives of the Study
1.4 Significance of Study 6
1.5 Scope of the Study 7
1.6 Operational Definition of Terms 8
CHAPTER TWO: LITERATURE REVIEW
2.0 Introduction 10
2.1 Modeling Infectious Disease 10
CHAPTER THREE: METHODOLOGY
3.0 Introduction 15
3.1 Existing Model Formation and Equilibrium States 15
3.2 Modified Model 17
3.3 Equilibrium State of the Model 20
CHAPTER FOUR: STABILITY ANALYSIS OF THE EQUILIBRIUM STATES
4.1 Stability of Disease – free Equilibrium State 23
4.2 Stability of the Endemic Equilibrium State 29
CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATIONS
5.1 Summary 35
5.2 Conclusion 35
5.3 Recommendation 36
REFERENCE
