A Mathematical Model for the Control of Ebola Virus Disease in Nigeria

Ebola Virus Disease is one of the deadliest infectious diseases that has increased both mortality and morbidity rates primarily on the African continent. The aim of this report is to use mathematical modeling and analysis in controlling the spread of this disease. In this study, a mathematical model which represents the transmission and control processes of Ebola Virus Disease among human and vector hosts is developed. The Well-Posedness, Equilibrium States (i.e Disease Free Equilibrium and Endemic Equilibrium) is analyzed. Furthermore, the Stability and Sensitivity Analysis is performed and the basic Reproduction Number (R0) of the model is obtained. The model equations are solved numerically using the MATLAB ODE45 algorithm and simulations are performed to visualize the effects of each control parameter on the spread and control of the disease. Also, it is concluded that for the control of the disease, the treatment factor is important to the real-life situation being modeled. Hence, it is recommended that the model results be implemented in an endemic area by governmental bodies and health organizations

Table of Contents

Certification i

Dedication ii

Acknowledgement iii

Abstract iv

Table of Contents vi

List of Tables vii

List of Figures viii

1 INTRODUCTION 1

1.1 Background Information 1

1.2 Motivation 3

1.3 Aim and Objectives of Research 3

1.4 Definition of Terms 4

2 LITERATURE REVIEW 7

2.1 Historical Development 7

2.2 Justification of the Study 10

2.3 Research Questions 11

3 STATEMENT OF PROBLEM 12

3.1 Model Formulation 12

3.1.1 Biological Assumptions 14

4 METHODOLOGY 16

4.1 Qualitative Analysis of Model 16

4.1.1 Well-Posedness of the Model 16

4.1.2 Equilibrium State 18

4.1.3 Stability Analysis 19

4.2 Basic Reproduction Number (RO) 22

4.3 Sensitivity Analysis 24

4.4 Method of Solution 25

5 RESULTS AND DISCUSSION 26

5.1 Numerical Simulations 26

6 CONCLUSION AND RECOMMENDATION 31

6.1 Conclusion 31

6.2 Recommendation 31

References 33