Mathematical Modelling Of Causes And Control Of Malaria
Abstract
Malaria, an infectious disease caused by the Plasmodium parasite, is transmitted between humans through the bites of female Anopheles mosquitoes. To understand and manage this disease, mathematical modeling describes the dynamics of malaria transmission and the interactions between human and mosquito populations using mathematical equations. These equations detail the relationships between different variables within the compartments of the model. The study aims to identify key parameters influencing the transmission and spread of endemic malaria and to develop effective prevention and control strategies through mathematical analysis. The malaria model employs fundamental mathematical techniques, resulting in a system of ordinary differential equations (ODEs) with four variables for humans and three for mosquitoes. Qualitative analysis of the model includes dimensional analysis, scaling, perturbation techniques, and stability theory for ODE systems. The model’s equilibrium points are derived and analyzed for stability, revealing that the endemic state has a unique equilibrium where the disease persists, and re-invasion remains possible. Simulations demonstrate the temporal behavior of the populations and the stability of both disease-free and endemic equilibrium states. Numerical simulations suggest that combining insecticide-treated bed nets, indoor residual spraying, and chemotherapy is the most effective approach for controlling or eradicating malaria. However, reducing the biting rate of female Anopheles mosquitoes through the use of insecticide-treated bed nets and indoor residual spraying proves to be the most crucial strategy, especially as some antimalarial drugs face resistance.
Chapter One
1.0 INTRODUCTION:
This chapter introduces the Mathematical Modelling Of Causes And Control Of Malaria and its relevance, states the research problems, research questions, and objectives, provides a background of the study, and should also include the research hypothesis [INTRO48578]…
Chapter Two: Literature Review
2.0 INTRODUCTION:
This chapter provides the background and context of the research problems, reviews the existing literature on the Mathematical Modelling Of Causes And Control Of Malaria, and acknowledges the contributions of scholars who have previously conducted similar research [REV48578] …
Table of Content
Title page
Certification
Dedication
Acknowledgement
Abstract
Table of contents
CHAPTER ONE
INTRODUCTION
1.1 Background Of The Study
1.2 Aims and Objectives
CHAPTER TWO
LITERATURE RIVEW
2.0 Introduction
2.1 Introduction of Exposed Class In Mosquito Population
2.2 Age And Exposed Class In Human Population
2.3 Migration And Visitation
2.4 Social And Economic Factors
2.5 Varying Popolation Size
2.6 Other Immunity Models
2.7 Host-Pathogen Variability And Resistant Strain Models
2.8 Environmental Factors
2.9 The Effect Of Sickle- Cell Gene On Malaria
2.10 Malaria Control
2.11 Vector Control and Protection Against Mosquito Bites
2.12 Case Management
2.13 Prophylatic Drugs
2.14 Vaccination
2.15 Stochastic Models
2.16 Conclusion
CHAPTER THREE
3.1 Formulation Of The Model
3.2 Analysis Of The Model
3.3 Equations Of The Model
3.4 Existence Of Equilibrium Points Without Disease
3.5 The Endemic Equilibrium Point
CHAPTER FOUR
4.0 Analysis
4.1 Estimation Of Parameters
4.2 Population Data For Mosquitoes
4.3 Equations Of The Model
4.4 Disease-Free Equilibrium Points
4.5 The Endemic Equilibrium Point
CHAPTER FIVE
5.1 Summary And Conclusion
REFERENCES