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POPULATION DYNAMICS OF MALARIA-DENGUE CO-INFECTION

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TABLE OF CONTENTS
TITLE PAGE ii
CERTIFICATION iii
STATEMENT OF ORIGINALITY iv
DEDICATION v
ACKNOWLEDGEMENT vi
TABLE OF CONTENTS vii
ABBREVIATIONS x
LIST OF FIGURES xi
LIST OF TABLES xii
ABSTRACT xiii
CHAPTER ONE
INTRODUCTION
Background of the Study 1
Pathogenesis of Malaria-Dengue Coinfection 2
Malaria Epidemiology 3
Dengue Epidemiology 4
Diagnosis of Malaria-Dengue Coinfection 5
The Uncommon Nature of Malaria-Dengue Coinfection 7
Statement of the Problem 8
Aims and Objectives of the Study 8
Significance of the Study 9
Scope of the Study 9

CHAPTER TWO
LITERATURE REVIEW
2.1 Introduction 10
2.2 Review of Malaria Models 10
2.2.1 Malaria Model with Treatment 11
2.2.2 Malaria Model with Repeated Exposure 12
2.3 Dengue Models 16
2.3.1 Dengue Model with Imperfect Vaccine 16
2.3.2 Dengue Model in the Presence and Absence of Awareness 20
2.4 Coinfection models 22
2.5 Area of Research Interest
CHAPTER THREE
MODEL DESCRIPTION AND ANALYSIS
3.1 Basic Assumptions 25
3.2 Model Formulation 25
3.3 Transmission by Malaria and Dengue Infected Individuals 26
3.4 Transmission by Vectors 27
3.5 Derivation of Model Equations 28
3.6 Basic Properties of the Model 39
3.7 Analysis of Sub-models 50
3.7.1 Dengue only Model 50
3.7.1.1 Stability of Disease–Free Equilibrium (DFE) 51
3.7.1.2 Existence of Endemic Equilibrium Point (EEP) of the Dengue Only Model 52
3.7.1.2.1 Bifurcation Analysis 54
3.7.1.3 Analysis of the Mass Action Model 61
3.7.1.4Analysis of Endemic Equilibrium for the Mass Action Model 62
3.7.1.5Global Stability of the DFE of the Mass Action Model 63
3.7.2 Malaria Only Model 65
3.7.2.1 Stability of Disease-Free Equilibrium (DFE) 66
3.7.2.2 Backward Bifurcation Analysis 67
3.7.2.3 Effect of Prior Immunity (re-infection) on Malaria Transmission Dynamics 72
3.7.2.4 Backward Bifurcation Analysis for Malaria only Model without Prior Immunity 75
3.8 Malaria-Dengue Coinfection Model 79
3.9 Effect of Malaria on Dengue Infection 90
3.10 Effect of Dengue on Malaria Infection 92
CHAPTER FOUR
SIMULATION
4.1 Numerical Simulation 94
4.2 Discussion of Result 104
CHAPTER FIVE
SUMMARY AND CONCLUSION
5.1 Summary of Research Finding 106
5.2 Conclusion 107
5.3 Area for further study 107
5.4 Contribution to Knowledge 107
REFERENCES 108

LIST OF ABBREVIATIONS
DFE – Disease Free Equilibrium
EEP – Endemic Equilibrium Point
LAS- Locally Asymptotically Stable
GAS- Global Asymptotically Stable


LIST OF FIGURES
Fig 1: Flow Diagram of Model (3.27) 35
Fig. 2: Backward bifurcation diagram for the dengue only model (3.33), showing the force of infection against the reproduction number. 97
Figure 3: Backward bifurcation diagram for the malaria only model (3.54), showing the force of infection against the reproduction number. 97
Fig. 4 : plots of the number of malaria infected and coinfected individuals without malaria prior immunity. 99
Fig. 5: plots of the number of malaria infected and coinfected individuals with malaria prior immunity. 100
Fig. 6: plots of the number of malaria infected individuals with prior immunity, recovered individuals with and without malaria prior immunity and coinfected individuals with malaria prior immunity 103


LIST OF TABLES
Table 2.1: Description of parameters for model (2.5) Niger and Gumel (2008) 14
Table 2.2: Description of Parameters of model (2.10) and (2.13) 19
Table 2.3: Description of parameters used for model (2.14) 21
Table 3.1: Description of variables in model (3.27) 36
Table 3.2: Description of the parameters in model (3.27) 37
Table 4.1:Baseline values and ranges of the parameters of the Malaria-dengue model (3.17), with the total population () of Nigeria as of 3rd of august 2019 estimated at 199,707,545 (Worldometer, 2019). 95

ABSTRACT
Malaria and dengue are two deadly vector-borne diseases which has become a global public health issue as reports has shown that people infected annually are 100 million (for malaria) and 40-80 million (for dengue). This study investigates thesynergistic interaction between malaria and dengue using a mathematical model to assess the impact of malaria prior immunity as well as treatment on the dynamics of malaria-dengue coinfection in a human population.
In the absence of malaria, the dengue only model undergoes backward bifurcation when the reproduction number is less than unity. This phenomenon is removed when the standard incidence is replaced with mass action incidence. In the absence of dengue as well as malaria prior immunity, the malaria model without prior immunity undergoes backward bifurcation. The complete malaria-dengue coinfection model undergoes the phenomenon of backward bifurcation.
The coinfection model was numerically simulated to investigate the impact of various treatment strategies for singly infected and coinfected individuals with and without malaria prior immunity. It is observed that previous exposure to malaria infection does not affect coinfected individuals but has impact on singly infected individuals with malaria. The study also revealed that with high treatment rates the incidence of the coinfection can be reduced if not totally eliminated.

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