MATHEMATICAL MODELING OF THE EFFECT OF IRRESPONSIBLE IMMIGRANT ON THE TRANSMISSION DYNAMICS OF HIV

Emmanuel Ayoola 39 PAGES (5554 WORDS) Project
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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


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APA

Emmanuel, A (2018). MATHEMATICAL MODELING OF THE EFFECT OF IRRESPONSIBLE IMMIGRANT ON THE TRANSMISSION DYNAMICS OF HIV. Afribary.com: Retrieved August 05, 2020, from https://afribary.com/works/mathematical-modeling-of-the-effect-of-irresponsible-immigrant-on-the-transmission-dynamics-of-hiv-4417

MLA 8th

Ayoola, Emmanuel. "MATHEMATICAL MODELING OF THE EFFECT OF IRRESPONSIBLE IMMIGRANT ON THE TRANSMISSION DYNAMICS OF HIV" Afribary.com. Afribary.com, 29 Jan. 2018, https://afribary.com/works/mathematical-modeling-of-the-effect-of-irresponsible-immigrant-on-the-transmission-dynamics-of-hiv-4417 . Accessed 05 Aug. 2020.

MLA7

Ayoola, Emmanuel. "MATHEMATICAL MODELING OF THE EFFECT OF IRRESPONSIBLE IMMIGRANT ON THE TRANSMISSION DYNAMICS OF HIV". Afribary.com, Afribary.com, 29 Jan. 2018. Web. 05 Aug. 2020. < https://afribary.com/works/mathematical-modeling-of-the-effect-of-irresponsible-immigrant-on-the-transmission-dynamics-of-hiv-4417 >.

Chicago

Ayoola, Emmanuel. "MATHEMATICAL MODELING OF THE EFFECT OF IRRESPONSIBLE IMMIGRANT ON THE TRANSMISSION DYNAMICS OF HIV" Afribary.com (2018). Accessed August 05, 2020. https://afribary.com/works/mathematical-modeling-of-the-effect-of-irresponsible-immigrant-on-the-transmission-dynamics-of-hiv-4417