Measles Hotspot Detection Using Bipartite Network Modelling Approach

Tang Jie Jie

Bachelor of Computer Science with Honours

(Computational Science)

2020

UNIVERSITI MALAYSIA SARAWAK

THESIS STATUS ENDORSEMENT FORM

TITLE: MEASLES HOTSPOT DETECTION USING BIPARTITE NETWORK

MODELLING APPROACH

ACADEMIC SESSION: 2019/2020, SEMESTER 2

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MEASLES HOTSPOT DETECTION USING BIPARTITE NETWORK MODELLING

APPROACH

Tang Jie Jie

This project is submitted in partial fulfilment of the requirements

for the degree of

Bachelor of Computer Science with Honours

(Computational Science)

Faculty of Computer Science and Information Technology

UNIVERSITY MALAYSIA SARAWAK

PENGESAHAN HOTSPOT MEASLES MENGGUNAKAN PENDEKATAN MODEL

RANGKAIAN BIPARTITE

Tang Jie Jie

Projek ini dikemukakan bagi memenuhi keperluan untuk

Ijazah Sarjana Muda Sains Komputer dengan Kepujian

(Sains Pengkomputeran)

Fakulti Sains Komputer dan Teknologi Maklumat

UNIVERSITY MALAYSIA SARAWAK

Declaration

I hereby declare that this thesis is based on my original work except for quotations and citations,

which have been duly acknowledged. This thesis has not been accepted for any degree and is not

concurrently submitted in the candidature of any other degree.

Name of the student: Tang Jie Jie

Date: 13/08/2020

i

ACKNOWLEDGEMENTS

First and foremost, I am grateful to the God for the good health and wellbeing that were

necessary to complete my final year project. Secondly, I would like to take this opportunity to

thank my supervisor, Associate Professor Dr Jane Labadin for sharing expertise, continuos

encouragement and valuable guidance throughout the period of completing my final year project.

Her willingness to give her time so generously has been very much appreciated. I am thankful for

the invaluable experience I gained from her through conducting a research for disease modelling.

Besides, I would like to extend my gratitude to Hong Bong Hao. He is a senior student of UNIMAS

whom has undergone his degree of master study. He also gives a lot of good advices to me

throughout my whole final year project. Finally, I would like to express my very great appreciation

to my examiner Mr. Terrin Lim. I would like to thank him for believing in my ability to complete

my final year project. He has also given some ideas for my project's improvement. Last but not

least, I am deeply grateful to my dearest family members. Thanks to my parents for raising me

with a love of knowledge and always encouraged me when I am faces the difficulties. I also thanks

to my sibling who are always give me endless support and motivation. My family contributed

significantly to the accomplishment of my final year project. Thank you.

ii

TABLE OF CONTENTS

Contents

ACKNOWLEDGEMENTS.................................................................................................................... i

TABLE OF CONTENTS ...................................................................................................................... ii

LIST OF FIGURES ............................................................................................................................... v

LIST OF TABLES................................................................................................................................ vi

ABSTRACT ......................................................................................................................................... vii

ABSTRAK ...........................................................................................................................................viii

CHAPTER 1 INTRODUCTION .......................................................................................................... 1

1.1 Introduction ................................................................................................................................. 1

1.2 Problem Statement ...................................................................................................................... 3

1.3 Aims and Objectives .................................................................................................................... 3

1.4 Scopes ........................................................................................................................................... 3

1.5 Brief Methodology ....................................................................................................................... 4

1.6 Significant of Project ................................................................................................................... 6

1.7 Project Schedule........................................................................................................................... 6

1.8 Expected Output .......................................................................................................................... 7

1.9 Thesis Outline .............................................................................................................................. 7

1.10 Summary .................................................................................................................................... 8

CHAPTER 2: LITERATURE REVIEW .............................................................................................. 9

2.1 Introduction ................................................................................................................................. 9

2.2 Understanding of Measles Disease............................................................................................... 9

2.3 Understanding of Disease Modelling ......................................................................................... 11

2.4 Understanding the Disease Hotspot Studies .............................................................................. 20

2.5 Disease Modelling Related to Bipartite Network Model ........................................................... 21

2.6 Summary .................................................................................................................................... 24

CHAPTER 3 METHODOLOGY ....................................................................................................... 25

3.1 Introduction ............................................................................................................................... 25

3.2 Current Research Scenario ....................................................................................................... 25

3.2.1 Assumptions ............................................................................................................................ 26

3.3.1 Basic Building Block of the Bipartite Measles Contact Network Model ........................... 28

3.4 Bipartite Graph Formulation .................................................................................................... 29

3.5 Research Data and Potential Parameters .................................................................................. 32

iii

3.5.1 Raw Data ............................................................................................................................. 32

3.5.2 Potential Parameters Used .................................................................................................. 33

3.6 Model Formulation .................................................................................................................... 34

3.6.1 Formulation of Human Node Quantification ..................................................................... 35

3.6.2 Formulation of Location Node Quantification ................................................................... 35

3.6.3 Formulation of Link Weight Quantification ...................................................................... 35

3.7 Summary .................................................................................................................................... 36

CHAPTER 4 TESTING AND IMPLEMENTATION ....................................................................... 37

4.1 Introduction ............................................................................................................................... 37

4.2 Research Data ............................................................................................................................ 37

4.3 Data Pre-processing ................................................................................................................... 37

4.4 Quantification of Location Node Parameters ........................................................................... 40

4.4.1 Quantification of Frequency of Location is Visited by a Patient Parameter, Fl................ 40

4.4.2 Quantification of Total Duration of Patient Stayed in a Location Parameter, Dp (s) ....... 42

4.4.3 Quantification of Number of Susceptible Humans Parameter, Sl ..................................... 43

4.5 Quantification of Human Node Parameters.............................................................................. 44

4.5.1 Quantification of Frequency of Human Visited a Location, Fh ........................................ 45

4.5.2 Quantification of Total Duration of Human Stayed in a Location, Du ............................. 49

4.5.4 Quantification of Vaccination Parameter, V ...................................................................... 50

4.5.5 Quantification of Age of Susceptible Human Parameter, As ............................................. 52

4.5.6 Quantification of Pregnancy Parameter, P ........................................................................ 53

4.6 Quantification of Link Weight .................................................................................................. 55

4.7 HITS Search Algorithm ............................................................................................................. 60

4.7.1 Generation of Hub and Authority Matrix .......................................................................... 61

4.7.2 Generation of Hub and Authority Principal Eigenvector .................................................. 64

4.7.3 Assignment of Nodes’ Label and Measles Hotspot Ranking Values .................................. 65

4.7.4 Ranking of Bipartite Nodes in BMC Network ................................................................... 67

4.8 Summary .................................................................................................................................... 68

CHAPTER 5 MODEL ANALYSIS AND EVALUATION ................................................................ 70

5.1 Introduction ............................................................................................................................... 70

5.2 Benchmark Verification ............................................................................................................ 70

5.3 Analytical Verification ............................................................................................................... 76

5.4 Parameter Significance Analysis ............................................................................................... 79

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5.5 Summary .................................................................................................................................... 82

CHAPTER 6 CONCLUSION ............................................................................................................. 83

6.1 Introduction ............................................................................................................................... 83

6.2 Conclusion of Research.............................................................................................................. 83

6.3 Limitation................................................................................................................................... 84

6.4 Future Works ............................................................................................................................. 85

REFERENCES .................................................................................................................................... 86

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LIST OF FIGURES

Figure 1.1 Bipartite-Network Based Methodology Framework (BNB-MF) (Liew,2016) .......5

Figure 1.2 Gantt chart of workflow throughout Final Year Project 1 and 2 ..........................6

Figure 2.1 Symptom of measles (Thompson, 2015) ................................................................ 10

Figure 2.2: Description of Parameters and values for the model (Peter, Afolabi, Victor,

Akpan & Oguntolu (2018) ...................................................................................................... 12

Figure 2.3: The simulation of infected population (Peter, Afolabi, Victor, Akpan &

Oguntolu (2018) ....................................................................................................................... 12

Figure 2.4: The simulation of exposed population (Peter, Afolabi, Victor, Akpan &

Oguntolu (2018) ....................................................................................................................... 13

Figure 2.5: The simulation of recovered population (Peter, Afolabi, Victor, Akpan &

Oguntolu (2018) ....................................................................................................................... 13

Figure 2.6 SEIPR compartmental model (Chan, Labadin and Podin, 2018) ........................ 15

Figure 2.7: Comparison of the projected infected population with the actual cases identified

using the standard SEIPR (Left) and SIR (Right) model. (Chan, Labadin and Podin, 2018)

................................................................................................................................................. 16

Figure 2.8: Movement rates between classes of the SIR model (Keeling, 2001) ................... 17

Figure 2.9: Bipartite network (Pavlopoulos, Kontou, Bouyioukos, Markou & Bagos, 2018)

................................................................................................................................................. 19

Figure 2.10: Epidemiological network. An example of a patient-location network

(Pavlopoulos, Kontou, Bouyioukos, Markou & Bagos, 2018) ................................................ 20

Figure 3.1: Epidemiological Triangle (CDC, n.d.) ................................................................. 28

Figure 3.2: Modified Epidemiological Triangle ..................................................................... 29

Figure 3.3: Basic Building of BMC Network ......................................................................... 30

Figure 3.4 An example of BMC network................................................................................ 31

Figure 4.1 Pre-process of location nodes (Kok, 2017) ............................................................ 38

Figure 4.2: Declare GPS Coordinates .................................................................................... 39

Figure 4.3 Code of the Location Declaration Generator ....................................................... 39

Figure 4.4 Bipartite Measles Contact (BMC) Network ......................................................... 60

Figure 5.1 Benchmark Ranking and BMC Network Model Ranking for Location Node .. 672

vi

LIST OF TABLES

Table 2.1 Summary of Disease Modelling Related to Bipartite Network Model .................. 23

Table 3.1.1 Datasets of Research Data ................................................................................... 32

Table 3.2 Potential Parameters Used...................................................................................... 33

Table 4.1 Link matrix of BMC network ................................................................................. 41

Table 4.2: Total Duration of Patient Stayed in a Location, Dp ............................................. 43

Table 4.3 Number of Susceptible Humans ............................................................................. 44

Table 4.4 Parameter values of Fh ........................................................................................... 45

Table 4.5 Frequency of Human Visit a Location ................................................................... 48

Table 4.6: Total Duration of Human Stayed in a Location, Du ............................................ 49

Table 4.7 Vaccination parameter, V ....................................................................................... 51

Table 4.8 Age of susceptible human parameter, As ............................................................... 52

Table 4.9 Pregnancy parameter, P ......................................................................................... 54

Table 4.10 Complete normalized parameters for location nodes .......................................... 56

Table 4.11 Complete normalized parameters for human nodes ............................................ 57

Table 4.12 MCS matrix ........................................................................................................... 58

Table 4.13 Hub Matrix ............................................................................................................ 62

Table 4.14 Authority Matrix ................................................................................................... 63

Table 4.14: Principal Eigenvector of the (a) location node and (b) human node .................. 66

Table 4.18 Ranking of (a) location nodes and (b) human nodes ............................................ 67

Table 5.1 RMSE Analysis of Location Nodes ......................................................................... 73

Table 5.2 RMSE Analysis of Human Nodes ........................................................................... 75

Table 5.3 SRCC indicators ..................................................................................................... 77

Table 5.4 Calculation of sum of [𝐝𝑴𝑯𝑹_𝑯𝒖𝒃𝑴𝒂𝒕𝒓𝒊𝒙 ]𝟐 .................................................... 78

Table 5.5 SRCC of “Leave-one-out” parameter analysis ...................................................... 80

Table 5.6 SRCC of “Leave-multiple-out” parameter analysis .............................................. 81

vii

ABSTRACT

The Health Ministry confirmed that there is an outbreak of measles among the Orang Asli

in Gua Musang, Kelatan (Abas, 2019). The outbreak of measles surprises the government of

Malaysia. Our government were facing the difficulties to control the measles outbreak due to lack

of information regarding possible stating source of the outbreak. Besides, our government also

lack of information to know the possible hotspot of measles in order for government to take action

efficiently. This will cause the measles disease increases if government didn’t take any action.

Thus, in order to prevent similar incident happens in future, this research was done to find the

hotspot of measles in Malaysia. This in turn can help in the reduction of the spread of measles

disease.

viii

ABSTRAK

Kementerian Kesihatan mengesahkan bahawa terdapat pecahnya campak di kalangan

Orang Asli di Gua Musang, Kelatan (Abas, 2019). Wabak campak telah mengejutkan kerajaan

Malaysia. Kerajaan kita menghadapi kesukaran untuk mengawal wabak campak kerana

kekurangan maklumat mengenai kemungkinan menyatakan sumber wabak tersebut. Di samping

itu, kerajaan kita juga kekurangan maklumat untuk mengenal pasti hotspot campak yang mungkin

bagi kerajaan mengambil tindakan dengan cekap. Ini akan menyebabkan penyakit campak

meningkat jika kerajaan tidak mengambil tindakan. Oleh itu, kajian ini dilakukan untuk mencari

hotspot campak di Malaysia untuk mengelakkan insiden serupa berlaku pada masa akan datang.

Ini seterusnya dapat membantu dalam pengurangan penyebaran penyakit campak.

1

CHAPTER 1 INTRODUCTION

1.1 Introduction

Measles has always been an endemic disease in many countries of the world, yet it is epidemic in

some countries. The recent surge in measles is due to a combination of travelers returning from

countries with measles outbreaks, and low vaccination rates in certain regions of the United States

fueled by the anti-vaccination movement, the researchers said (Preidt, 2019). In Geneva, measles

cases have continued increases in 2019 (WHO, 2019). Even the data is provisional and not yet

complete, it indicates a clear trend that measles is increases from year to year. Many countries are

in the midst of sizeable measles outbreaks. Current outbreaks include the Democratic Republic of

the Congo, Ethiopia, Georgia, Kazakhstan, Kyrgyzstan, Madagascar, Myanmar, Philippines,

Sudan, Thailand and Ukraine, causing many deaths - mostly among young children (WHO, 2019).

Cases of measles have spiked in Malaysia in recent years. Being a member state of the

Western Pacific Region (WPR), in order to meet the global goal of measles elimination by 2012,

Malaysia needed to achieve zero incidence of measles by 2011, and remain so by 2012.

Nevertheless, this initiative has not been successful, as demonstrated by the national measles

outbreak that occurred in year 2011. This outbreak was unanticipated as Malaysia had reached a

95% coverage for measles vaccination as early as 2009, the population immunity threshold needed

to prevent more outbreaks. (Anderson,1992; Fine,1993).

Measles is a highly contagious illness caused by a virus that replicates in the nose and

throat of an infected child or adult. This occurs when someone with measles cough, talking or

sneezing, releasing infectious droplets into water, where they can be inhaled by others. Before

infected people get sick, they carry the virus in their respiratory tract so that they can spread disease

without realizing it. This is due to there is an incubation period of 8 to 12 days. The period of

2

incubation is the internal between measles virus exposure and the onset of first symptoms

(Perlstein, Mersch, & Melissa (n.d)). Generally, the initial symptoms include high fever, koplik

spots (mouth spots typically 2-3 days before rash and last 3-5 days), loss of appetite, red eyes,

malaise, and sometimes cough.

Approximately 500,000 people in United States were reported to have had measles every

year before the National Measles Vaccination Program was initiated in 1963, of who 500 died,

48,000 were hospitalized and 1,000 had permanent brain damage (Seward, 2014). The Ministry of

Health reported that the number of measles cases in Malaysia increased exponentially from 195

cases in 2013 to 1934 cases in 2018, an increase of almost 900% over a period of 5 years with six

deaths related to measles, of which none were immunized (WHO, 2019).

Measles is preventable. Measles can be prevented with measles-mumps-rubella (M.M.R.)

vaccine which was first licensed in 1963 (Belluck & Hassan, 2019). The vaccine provides

protection against three diseases: measles, mumps, and rubella. MMR vaccine is given later than

some other childhood vaccines because antibodies transmitted from mother to baby can provide

some infectious defense and make MMR vaccine less active up to around 1 year of age. Children

can also receive MMRV vaccine that protects against measles, mumps, rubella, and varicella. This

vaccine is only licensed for use in children between the ages of 12 months and 12 years old.

Because of vaccination, over 21 million lives have been saved and measles deaths have fallen by

80% since 2000. (Belluck & Hassan, 2019).

In this situation, the government should be able to identify possible measles hotspot and

develop a strategy to effectively control the spread of disease early on. Mathematical and

simulation disease models are helpful utilities to understand and analyse the behaviour of specific

3

disease spread. Furthermore, a disease model can be used to determine the hotspots of specific

diseases, which is measles in this research.

1.2 Problem Statement

There is no one model can be used to identify the hotspot for measles in Malaysia. In this case,

this research may provide a hotspots analysis for measles outbreak in Malaysia. Insufficient

research about the hotspot detection of measles in Malaysia may cause the precaution step cannot

be taken due to lack of awareness and knowledge in this case. It is important to have model that

can help predicting the hotspot of measles and authorities can take action more effectively.

Mathematical and simulation disease models are useful utilities to access the situation while also

offering perceptions to most efficient control strategies. Action that can been taken by authorities

is give post-exposure prophylaxis (vaccine, immunoglobulin) to susceptible individuals,

implement isolation and quarantine if needed in order to prevent the measles disease (Hum, 2018).

1.3 Aims and Objectives

This research aims:

1) To formulate contact network model of measles using bipartite network approach.

2) To identify the critical parameters that affect the measles hotspot detection.

3) To identify the measle hotspots in Malaysia to assist local authorities in containing the

disease effectively.

1.4 Scopes

This research is conducted to formulate contact network model of measles using bipartite network

model. Measles hotspot will be identified based on the two-node types network which consists of

4

human node and location node. Human is the target victim in the disease transmission; whereas

location is the carrier of the measles virus.

Besides, this research is also done to detect hotspots of measles in Malaysia. This research

will help us better understand the relationship between the human nodes and location nodes. Not

only that, this research focuses on how measles spread in a location and become the hotspot of

measles. Public health and medical agencies are the main users for this research outcome. The

project outcome would help them in planning prevention measures to control measles in Malaysia.

However, assume data will be made available as the project scope is on model formulation.

1.5 Brief Methodology

A methodology framework is needed to achieve our research goals, prove the hypothesis, and thus

answer the research question. This research will focus on formulating contact network model of

measles transmission and identifying the hotspots of measles. This research will first need to

identify the crucial parameters involved, such as the nodes and their relationships, areas populated

by humans and human population number.

The methodology framework used is the Network model, more specifically Bipartite-

Network Based Methodology Framework (BNB-MF). With a web-based graph search algorithm,

the BNM method was used successfully to evaluate malaria hotspot (Eze, 2013). It inspired us to

analyze the approach used. BNB-MF can be generally separated into three stages, the problem

characterization stage, model construction, and model analysis and evaluation stage (Liew, 2016).

Principle processes are detailed in every stage of framework to guide the modelling activities.

Hence, the framework is a process-oriented methodology framework (Liew, 2016).

5

Figure 1.1 Bipartite-Network Based Methodology Framework (BNB-MF) (Liew,2016)

6

1.6 Significant of Project

The significance of this research is that using the bipartite network model in identifying the

hotspots of the measles disease. The inputs of the model are the location and the human nodes, and

the link related to these bipartite nodes. Identifying the measles hotspot could help public health

officials and decision-makers prioritize surveillance and direct measures to high-risk areas to

eliminate the measles disease probable source. Besides, with this research, another network-based

model can be constructed to test its usefulness in analyzing the transmission of measles disease.

1.7 Project Schedule

This research is done in two phases, which is throughout Final Year Project 1 (FYP 1) and Final

Year Project 2 (FYP 2). This research is estimated to complete within two semesters. Figure 1.2

show the Gantt chart of workflow throughout Final Year Project 1 and 2.

Figure 1.2 Gantt chart of workflow throughout Final Year Project 1 and 2

7

1.8 Expected Output

Overall, this research should produce a prototype of the measles model, which can analyze the

quantitative parameters associated with the transmission of measles. This research should also be

able to confirm which two nodes can be used accurately and the relationship between two nodes.

Thus, the expected output of this research is to identify the measles hotspot in Malaysia using

bipartite network model.

1.9 Thesis Outline

This thesis consists of five chapters. The content of the chapters is summarized as follows:

Chapter 1: Introduction

This chapter provides an overview and describes the background of this research. The

research’s main problem statement is discussed, accompanied by describing the aims and scope of

this research accordingly. The brief methodology used in this research is also discussed in this

chapter. The significance of this research is highlighted. Not only that, project schedule and

expected outcome also presented in this chapter.

Chapter 2: Literature Review

This chapter discusses the outcomes from the reviews of literature on research related to

measles disease, disease modelling, disease hotspot studies and disease modelling related to

bipartite network model, particularly on the aspects of approaches employed, limitations of these

approaches and opportunities offered to solve this research problem.

Chapter 3: Methodology

8

This chapter focuses on research methodology. For further review, the requirement will be

gathered. This chapter presents the three processes in the stage 1 of the BNM-RMF shown in

Figure 1.1.

Chapter 4: Model Analysis

This chapter discusses the processes to construct a complete network model, being Stage

2 of the BNM-RMF shown in Figure 1.1. For further analysis, the requirements will be collected.

The modelling framework will be constructed on the basis of the analysed criterion.

Chapter 5: Conclusion and Future Work

This chapter concludes the overall research and findings. The achievement and results of

this research will be presented. This chapter ends with some suggestions that could strengthen the

solution for future work.

1.10 Summary

Specific disease modelling can aid government efforts to treat potential outbreaks of disease. In

this case, this research focuses only on the disease of measles. The results obtained from the

measles disease model can be used by government or public health organizations to improve the

health of our nation. In conclusion, a well-done simulation of the disease can provide guidance to

control a high-efficiency disease outbreak.

9

CHAPTER 2: LITERATURE REVIEW

2.1 Introduction

This chapter is intended to present the literature review associated with this research. Although

the literature covers a wide variety of such theories, this literature review will include previously

research conducted by others to discuss and understand theories, strengths and technological

advancement in regards to the current research problem.

Titles included in this chapter are Understanding of the Measles Disease, Understanding

of Disease Modelling, Understanding the Disease Hotspot Studies, Disease Modelling Related

Studies and a summary of the chapter.

2.2 Understanding of Measles Disease

Since this research focuses on measles as a disease, it is important to comprehend the

characteristics of measles. The characteristics of the measles are also called as potential data

attributes and can be used to solve the problem of this study.

Measles also known as rubeola, is an acute febrile viral disease that is preventable, highly

contagious. The time of incubation is 10 to 14 days, although there have been records of longer

periods. Pregnant women and unvaccinated young children are at high risk of contracting measles,

and measles affect young children more frequently (Kondamudi, 2019).

In the case of this study, we focus more on measles hotspot in Malaysia as the number of

measles cases in Pahang, Malaysia increased exponentially by 200 percent (21 cases) in March of

this year compared to only seven cases reported during the same period between January and

March in year 2018 (Tajuddin, 2019). The Ministry of Health announced that Malaysia's number

of measles cases increased exponentially from 195 cases in 2013 to 1,934 cases in 2018, a rise of

10

nearly 900 percent over a 5-year period with six measles-related deaths, none of which were

immunized. The number of unimmunized cases of measles rose from 125 cases (69%) in 2013 to

1,467 cases (76%) in 2018(WHO, 2019). In 2019, the number of measles cases in Pahang has

risen alarmingly by 200 percent (21 cases) compared to only seven cases reported between 1st of

January and 6th of March 2018 in during the same period. This happens due to the fact that public

are failure to provide immunization (Tajuddin, 2019).

The causative species is the measles virus, a member of the family of Paramyxoviridae

and the genus of Morbillivirus. It is an enveloped, single-stranded, non-segmented RNA virus

with a negative sense. Measles virus has no reservoir for animals and only exists in humans.

Respiratory droplets, small particle aerosols and close contact spread measles from person to

person (Kondamudi, 2019). Early symptoms begin 1 to 2 weeks after a person has been exposed

to the disease. Signs include nausea, cough, runny nose, and eyes that are swollen and watery. Red

spots appear on the skin 3 to 5 days later, sometimes with small bumps. The rash starts on the

head and extends to other areas of the body downwards (Thompson, 2015).

Figure 2.1 Symptom of measles (Thompson, 2015)

11

2.3 Understanding of Disease Modelling

Mathematical modelling plays a very important approach of understanding, predicting a disease’s

behavior and controlling potential outbreaks (Keeling, 2017). Mathematical models were used

since the work of Bernoulli in 1760 to research the spread of infectious diseases. But it was only

after Ross and Kermack and McKendricks pioneering work that the field of computational

epidemiology started to be seen as a serious alternative in predicting and managing infectious

diseases (Hernandez & Gusman, 2013).

Mathematical modelling approach is the focus of past research on measles disease. For

instance, the study conducted by Peter, Afolabi, Victor, Akpan & Oguntolu (2018) developed a

mathematical model for the transmission of measles disease by considering recurrent infection

and vaccination. Numerical examples show that vaccination can prevent the spread of the disease.

Depending on individuals' epidemiological status, the model divides the human population into

five (5) compartments. The compartments included Susceptible S, Vaccinated V, Expose E,

Infected I, and R recovered. Figure 2.2 shows the set of parameter values and the state variables

which were used in order to support the analytical results; Figure 2.3 shows the simulation of

infected population; Figure 2.4 shows the simulation of exposed population and figure 2.5 shows

the simulation of recovered population.