MATHEMATICAL MODEL OF CEREBROSPINAL MENINGITIS IN OBUASI MUNICIPALITY OF ASHANTI REGION, GHANA

MATHEMATICAL MODEL OF CEREBROSPINAL MENINGITIS IN OBUASI MUNICIPALITY OF ASHANTI REGION, GHANA

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ABSTRACT

Meningococcal disease is a serious health threat in the human body which begins rapidly with a relative high case fatality rate particularly in the absence of treatment and thus is a priority when it comes to prevention. Delayed treatment can lead to death or invasive meningococcal disease which causes complications such as neurologic disorder, loss of limbs, hearing loss and paralysis even in survivors. In this work, therefore the main objective is to investigate the epidemiology of meningococcal meningitis in Obuasi municipality to develop a model for predict the spreading and combating of cerebrospinal meningitis within the municipality. Using SEIR model we employed the simple Susceptible-Exposed-Infectious and Recovered model to compute those affected ones. The model equations are solved numerically with MatLab that employ Runge-Kutta method. Simulation and sensitivity analysis are then performed on the model equations to determine the effect of the parameter values on the spread of the disease. The simple vi

TABLE OF CONTENTS

DECLARATION............................................................................................................ii

ACKNOWLEDGEMENTS...........................................................................................iii

DEDICATION...............................................................................................................iv

ABSTRACT....................................................................................................................v

TABLE OF CONTENTS...............................................................................................vi

LIST OF TABLE ...........................................................................................................ix

LIST OF FIGURES ........................................................................................................x

CHAPTER 1 ..................................................................................................................1

INTRODUCTION.........................................................................................................1

1.1 BACKGROUND INFORMATION .........................................................................1

1.1.1 SYMPTOMS OF CSM..........................................................................................5

1.1.2 RISK FACTORS FOR CEREBROSPINAL MENINGITIS EPIDEMIC.............8

1.1.3 TREATMENT OF CEREBROSPINAL MENINGITS.........................................9

1.2 STATEMENT OF THE PROBLEM......................................................................11

1.3 OBJECTIVE OF THE STUDY..............................................................................12

1.4 METHODOLOGY..................................................................................................12

1.5 JUSTIFICATION....................................................................................................13

1.6 ORGANIZATION OF THE STUDY.....................................................................13

CHAPTER 2 ................................................................................................................14

LITERATURE REVIEW...........................................................................................14

2.1 INTRODUCTION ..................................................................................................14

2.2 THE SEIR MODEL WITH VECTOR / VACCINATION.....................................21

CHAPTER 3 ................................................................................................................24

METHODOLOGY......................................................................................................24

3.1 INTRODUCTION ..................................................................................................24

3.2 DESCRIPTION FOR vii

3.5 DESCRIPTION FOR viii

4.17 SENSITIVITY ANALYSIS OF AN ENDEMIC EQULIBRIUM STATE WITH DECREASE PARAMETERS.......................................................................................60

CHAPTER 5 ................................................................................................................61

CONCLUSION AND RECOMMENDATIONS......................................................61

5.1. INTRODUCTION .................................................................................................61

5.2. CONCLUSIONS....................................................................................................61

5.3. RECOMENDATIONS...........................................................................................62

REFERENCES............................................................................................................63

APPENDIX..................................................................................................................71

MATHLAB CODES.....................................................................................................71

M-FILE FOR CSM WITHOUT VACCINATION.......................................................71

SCRIPTS FOR CALLING M-FILE WITHOUT VACCINATION.............................71

M-FILE FOR CSM WITH VACCINATION...............................................................72

SCRIPTS FOR CALLING M-FILE WITH VACCINATION.....................................72ix

LIST OF TABLE

Table 3.1 Model parameters and its interpretations without vaccination……………26

Table 3.1 Model parameters and its interpretations………………………………….31

Table 4.1 Figures depicting the effect of change in initial proportion of SEIR……..48

Table 4.2 for each period x

LIST OF FIGURES

Figure 1.1 Portals of entry resulting in meningitis, meningoencephalitis, and intracranial

mass lesions. From Mahon and Manuselis, 2000…………………………….2

Figure 1.2: The African Meningitis Belt (Source: Moore 1992)…………………………3

Figure 1.3: Four month old female with gangrene of knee due to meningococcemia.

Courtesy of CDC/Mr. Gust…………………………………………………...7

Figure 3.1. Flowchart of the SEIR Cerebrospinal meningitis without Vaccination…….26

Figure 3.1 Flow chart for model of Cerebrospinal meningitis

with vaccination…………...………………………………………………….30

Figure 4. 1 Evolution of Susceptible population per year in Obuasi……………………48

Figure 4. 2 Evolution of Exposed population per year in Obuasi……………………….48

Figure 4. 3 Evolution of Infectious population per year in Obuasi……………………...48

Figure 4. 4 Evolution of Recovered population per year in Obuasi……………………..48

Figure 4. 5 Evolution of Susceptible population per year in Obuasi……………………49

Figure 4. 6 Evolution of Exposed population per year in Obuasi……………………….49

Figure 4. 7 Evolution of Infected population per year in Obuasi………………………..49

Figure 4. 8 Evolution of Recovered population per year in Obuasi……………………..49

Figure 4. 9 Evolution of Susceptible population per year in Obuasi…………………....50

Figure 4. 10 Evolution of Exposed population per year in Obuasi……………………...50

Figure 4. 11 Evolution of Infectious population per year in Obuasi…………………….50

Figure 4. 12 Evolution of Recovered population per year in Obuasi…………………....50

Figure 4.13 Phase portrait of disease free saddle equilibrium point…………………….561


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