TABLE OF CONTENTS
Title page
Certification
Acknowledgement
Dedication
Abstract
Table of Contents
CHAPTER ONE
1.1 Background to the study
1.2 Aim of the study
1.3 The scope of the study
1.4 Limitation of the study
CHAPTER TWO
2.1 Malaria models
2.2 Sickle cell – malaria models
CHAPTER THREE
3.1 Sickle cell disease
3.2 Sickle cell crises
3.3 Genetics
3.4 Pathophysiology
3.5 Management of SCA
3.6 Malaria disease
3.7 The plasmodium life cycle
3.8 Malaria treatment and control
3.9 Malaria and AS genotype
3.10 Malaria and SS genotype
CHAPTER FOUR
4.1 Introduction
4.2 Model formulation
4.2.1 Model equations
4.3 Model analysis
4.3.1 Disease free equilibrium points
4.3.2 The basic reproduction number
4.3.3 Local stability of the DFE
4.3.4 Endemic equilibrium points
4.4 Numerical analysis
CHAPTER FIVE
5.1 Conclusion
5.2 Recommendation
5.3 Recommendation for future study
REFERENCES
ABSTRACT
In this thesis, we study the interaction between the dynamics of malaria and sickle cell. The main aim is to investigate the dynamics of malaria transmission in sickle cell populace and how to modulate or regulate the amount of malaria parasite in sickle cell gene carriers. For this, we developed a mathematical model that describes the interactions between malaria and sickle cell gene. The model includes both homozygous (SS) and heterozygous for sickle cell gene carriers (AS) and we assumed that AS individuals are not treated since they do not show clinical symptoms. We split our infected SS class into treated and non-treated groups. We then analyzed the model by computing the endemic and the disease free equilibria. Using the Jacobian matrix method, we observed that DFE is stable. We also calculated the reproductive number R0, and found that R0 < 1, both our analytical and numerical results indicated that, when R0 < 1, then malaria is wiped out in both populations. We also carried out numerical analysis and from our figures we observe that for R0 < 1, the infected populations converged to zero as the susceptible populations increased for both SS and AS humans and mosquitoes. We thus concluded that Administering of drugs to both SS and AS individuals irrespective of whether symptoms show or not will help to reduce the infected classes to zero and increase the susceptible classes of both SS and AS genotypes.
CHAPTER 1
INTRODUCTION
1.1 BACKGROUND: ABOUT SICKLE CELL DISEASE
Sickle-cell disease (SCD), also known as sickle-cell anaemia (SCA) and drepanocytosis, is a hereditary blood disorder that is characterized by the blood cell assuming an abnormal, rigid and sickle shape.
Sickled red blood cells have reduced oxygen carrying capacity and usually get stuck in small blood vessels causing organ damage. They are continuously destroyed by the spleen in about 10 – 20 days as compared to 120 days for normal red blood cells. The bone marrow fails to produce new cells fast enough to replace the destroyed sickled cells which causes more complications among people having it.
Every individual has two copies of haemoglobin inherited one from the father and the other from the mother. If both copies are normal, then he/she is said to be homozygous for HbAA (AA genotype). If a child inherits the two copies of mutated gene, he/she is said to be homozygous for HbSS (SS genotype). Such individuals have sickle cell anaemia and usually die before reaching adulthood. When a single mutated gene is inherited, the individual is heterozygous for HbAS (AS genotype). Heterozygous for HbAS individuals are characterized by the sickle cell trait and are referred to as sickle cell carriers. Sickle cell carriers are less affected by sickle cell anaemia complications as the normal haemoglobin can still supply oxygen to vital body organs.
There is a 50% chance that parents with the sickle cell trait will pass on the same trait ( AS ) to their child, a 25% chance that their child will have both copies of normal haemoglobin (AA) and a 25% chance that the child will have the two mutated genes ( SS ). And if one parent has sickle-cell anaemia and the other has sickle-cell...
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