COMPLEX NETWORK MODELLING AND ANALYSIS BY HAFIZ …
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COMPLEX NETWORK MODELLING AND ANALYSIS OF DENGUE EPIDEMIC IN SELANGOR, MALAYSIA BY HAFIZ ABID MAHMOOD MALIK A thesis submitted in fulfilment of the requirement for the degree of Doctor of Philosophy in Computer Science Kuliyyah of Information and Communication Technology International Islamic University Malaysia OCTOBER 2016
Transcript of COMPLEX NETWORK MODELLING AND ANALYSIS BY HAFIZ …
COMPLEX NETWORK MODELLING AND ANALYSIS
OF DENGUE EPIDEMIC IN SELANGOR, MALAYSIA
BY
HAFIZ ABID MAHMOOD MALIK
A thesis submitted in fulfilment of the requirement for the
degree of Doctor of Philosophy in Computer Science
Kuliyyah of Information and Communication Technology
International Islamic University Malaysia
OCTOBER 2016
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ABSTRACT
There are many examples of complex systems in the world from different domains of
life. For instance, the World Wide Web, electric power grids, scientific collaboration
networks, social network of friendships, and network of diseases such as HIV/AIDS.
These systems can be better analyzed by converting them into complex networks.
Mostly, complex networks are dynamic in natures which grow by adding new links
and nodes. Nodes can represent elements of the systems and links depicts the
interacting patterns between these elements. The dengue epidemic is a dynamic and
complex phenomenon which has gained much attention due to its harmful effects that
sometimes become a cause of death of a person. This problem is difficult to
understand by just observing separate components which constitute this network. For
this, modelling the way these units are interconnected with each other can enhance the
understanding towards this epidemic as a whole. In this study, the dengue spreading
phenomenon is addressed from the perspective of complex network and modelled
using the dataset of weekly dengue affected cases in Selangor, Malaysia using scale-
free network theory. Further, the dengue epidemic network is formalized and analyzed
by projecting it from two-mode to one-mode network using three projection methods.
Various network analysis metrics have been utilized in this study (such as: Closeness
centrality, Betweenness centrality, Degree measures, Short path-length, and
Eigenvector centrality). It is believed that this modelling and analysis will
considerably help to comprehend the complex nature of the dengue epidemic network.
This research reveals the focal nodes of the dengue virus, and the most crucial time is
also highlighted when dengue virus is on its peak. Furthermore, we mathematically
modelled the influence of the external and internal factors which become the cause of
the dengue virus diffusion, and some exogenous factors have been shown that
supressed the Aedes aegypti (dengue vector) network. Moreover, results showed that
the dengue epidemic network comprises a scale-free network features which negates
the theory of randomness. So, proper precautionary measures can be taken to prevent
or reduce this disease. All the outcomes are valuable for the health officials and
decision makers who deal with the epidemics.
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خلاصة البحث
هناك أمثلة كثيرة من الأنظمة المعقدة في العالم من مختلف مجالات الحياة. على سبيل المثال: الشبكة العالمية للانترنت، وشبكات الطاقة الكهربائية، وشبكات التعاون العلمي، والشبكة الاجتماعية من
م يمكن تحليلها بشكل الصداقات، وشبكة الأمراض مثل فيروس نقص المناعة البشرية / الإيدز. هذه النظأفضل عن طريق تحويلها إلى شبكات معقدة. في الغالب فإن الشبكات المعقدة هي حيوية في الطبيعة التي تنمو فيها وذلك عن طريق إضافة وصلات وعقد جديدة. يمكن للعقد ان تمثل عناصر النظم، بينما
الضنك ظاهرة ديناميكية ومعقدة حيث تصور الروابط أنماط التفاعل بين هذه العناصر. يعتبر وباء حمىاكتسب الكثير من الاهتمام نظرا لآثاره الضارة التي تصبح أحيانا سببا في الوفاة. انهاء مثل هذه المشكلة لا يمكن أن تتم عبر مراقبة طريقة انتشارها. لهذا، فإن معرفة نموذج شبكة انتشار الوباء وترابط وحدات
أن تعزز الفهم تجاه هذا الوباء ككل. في هذه الدراسة، تم التعامل مع الشبكة مع بعضها البعض يمكن ظاهرة انتشار حمى الضنك ونمذجتها من وجهة نظر شبكة معقدة باستخدام قاعدة بيانات باستخدام
النطاق. وتم أخذ العينات من حالات حمى الضنك الأسبوعية المتكررة في ولاية -نظرية الشبكة خاليةزيا. علاوة على ذلك، تم تكوين شبكة وباء حمى الضنك وتحليلها من خلال اسقاطه من سيلانجورفي مالي
اثنين باستخدام ثلاث طرق إسقاط. تم استخدام مختلف مقاييس تحليل -واحد الى وضع-شبكة وضع، مركزية البين (Closeness centrality)الشبكة في هذه الدراسة )مثل: مركزية التقارب
(Betweenness centrality) ودرجة المقاييس ،(Degree measures) قصر طول المسار ،(Short path-length) والمتجه الذاتي المركزي ،(Eigenvector centrality) يعتقد أن هذه .
النمذجة والتحليل سوف تساعد بشكل كبير في فهم الطبيعة المعقدة لشبكة وباء حمى الضنك. يكشف لفيروس حمى الضنك، وسلط الضوء على الوقت الأكثر أهمية أيضا عندما هذا البحث العقد المحورية
يكون فيروس حمى الضنك في ذروته. علاوة على ذلك، قمنا بصياغة طريقة رياضية لتأثير العوامل الخارجية والداخلية التي أصبحت سببا في انتشار فيروس حمى الضنك، كما أظهرت بعض العوامل
اضافة الى ذلك، أظهرت النتائج أن شبكة وباء حمى الضنك تضم ميزات الخارجية لحمى الضنك. المجاني وهذا ينفي نظرية العشوائية. لذلك، يمكن اتخاذ تدابير وقائية مناسبة لمنع أو الحد -شبكة النطاق
من هذا المرض. أخيراً تعتبر هذه النتائج مفيدة وقيمة للعاملين في مجال الصحة وصناع القرار الذين املون مع الأوبئة.يتع
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APROVAL PAGE
The thesis of Hafiz Abid Mahmood Malik has been approved by the following:
_____________________________
Mohamed Ridza Wahiddin
Supervisor
_____________________________
Asadullah Shah
Internal Examiner
_____________________________
Stanislaw Chwirot
External Examiner
_____________________________
Tahir Ahmad
External Examiner
_____________________________
Noor Mohammad Osmani
Chairman
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DECLARATION
I hereby declare that this thesis is the result of my own investigations, except
where otherwise stated. I also declare that it has not been previously or concurrently
submitted as a whole for any other degrees at IIUM or other institutions.
Hafiz Abid Mahmood Malik
Signature ........................................................... Date .........................................
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COPYRIGHT
INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA
DECLARATION OF COPYRIGHT AND AFFIRMATION OF
FAIR USE OF UNPUBLISHED RESEARCH
COMPLEX NETWORK MODELLING AND ANALYSIS OF
DENGUE EPIDEMIC IN SELANGOR, MALAYSIA
I declare that the copyright holder of this thesis is Hafiz Abid Mahmood Malik
Copyright © 2016 Hafiz Abid Mahmood Malik. All rights reserved.
No part of this unpublished research may be reproduced, stored in a retrieval system,
or transmitted, in any form or by any means, electronic, mechanical, photocopying,
recording or otherwise without prior written permission of the copyright holder
except as provided below
1. Any material contained in or derived from this unpublished research may
be used by others in their writing with due acknowledgement.
2. IIUM or its library will have the right to make and transmit copies (print
or electronic) for institutional and academic purposes.
3. The IIUM library will have the right to make, store in a retrieved system
and supply copies of this unpublished research if requested by other
universities and research libraries.
By signing this form, I acknowledged that I have read and understand the IIUM
Intellectual Property Right and Commercialization policy.
Affirmed by Hafiz Abid Mahmood Malik
……..…………………….. ………………………..
Signature Date
DEDICATION
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I dedicate this thesis to my loving parents, my beloved wife and my lovely daughter
Arisha Abid for their prayers, love, support and patience.
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ACKNOWLEDGEMENTS
All praises for ALLAH, Who bestowed me the courage and power of brain to
accomplish this goal.
I would like to thank my brothers and elder sister who always prayed for my
success to achieve this goal.
A very special thanks to my supervisor Professor Dr. Mohamed Ridza
Wahiddin for his untiring efforts, support, encouragement and leadership, and for that,
I will be forever grateful.
I wish to express my appreciation and thanks to my friends Dr. Abdul Waheed,
Dr. Ahmad Waqas, Dr. Zeeshan Bhatti, Dr. Nadeem Mahmood and Abdul Rehman
Gilal who were always ready to help me. Many thanks to the members of my thesis
evaluation committee. May ALLAH shower His blessings on all of my well-wishers.
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TABLE OF CONTENTS
Abstract .................................................................................................................... ii Abstract in Arabic .................................................................................................... iii Aproval Page ............................................................................................................ iv
Declaration ............................................................................................................... v Copyright ................................................................................................................. vi Dedication ................................................................................................................ vi Acknowledgement ................................................................................................... viii Table of Contents ..................................................................................................... ix
List of Tables ........................................................................................................... xii List of Figures .......................................................................................................... xiii
List of Symbols ........................................................................................................ xvii
List of Abbreviations ............................................................................................... xviii
CHAPTER ONE: INTRODUCTION .................................................................. 1 1.1 Background Of The Study ...................................................................... 1
1.2 Dengue Epidemic.................................................................................... 2 1.3 Dengue Virus Transmission ................................................................... 4
1.4 Problem Background (Dengue Issue In Malaysia) ................................. 5 1.5 Motivation To This Work ....................................................................... 8 1.6 Problem Statement .................................................................................. 10
1.7 Research Scope ....................................................................................... 10 1.8 Research Hypothesis ............................................................................... 11
1.9 Research Aims and Objectives ............................................................... 11
1.10 Research Questions ............................................................................... 11
1.11 Significance Of The Study.................................................................... 12 1.12 Research Methodology and Process ..................................................... 12
1.13 Thesis Contribution .............................................................................. 13 1.14 Simulation Tool Used In The Research ................................................ 14
1.15 Organization Of Thesis ......................................................................... 16 1.16 Chapter Summary ................................................................................. 18
CHAPTER TWO: LITERATURE REVIEW ..................................................... 19 2.1 Theoretical Background.......................................................................... 19
2.1.1 Introduction ................................................................................... 19 2.1.2 Graph Theory ................................................................................ 19 2.1.3 Complex Network Models ............................................................ 20
2.1.4 The Small-World Effect ................................................................ 20 2.1.5 The Random Graph Theory: Paul Erdös and Alfred Renyi .......... 21 2.1.6 WS small-world Model (1998) ..................................................... 22 2.1.7 Scale-Free Network (SFN) - Barabasi and Albert Model
(1999)............................................................................................ 23 2.2 Network Analysis Metrics ...................................................................... 26
2.2.1 Adjacency Matrix .......................................................................... 26 2.2.2 Degree Of Node ............................................................................ 28 2.2.3 Node Centrality ............................................................................. 28
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2.2.4 Degree Centrality Of Node ........................................................... 29
2.2.5 Distance / Short Path-Length ........................................................ 31 2.2.6 Closeness Centrality ...................................................................... 33
2.2.7 Betweenness Centrality ................................................................. 34 2.2.8 Eigenvector Centrality .................................................................. 35 2.2.9 Density Of Network ...................................................................... 37 2.2.10 Clustering Coefficient ................................................................. 37
2.3 Related Work .......................................................................................... 39
2.3.1 Introduction ................................................................................... 39 2.3.2 The SIR (Susceptible Infected Removed) model .......................... 40 2.3.3 The SIS (Susceptible Infected Susceptible) model ....................... 41
2.4 Chapter Summary ................................................................................... 43
CHAPTER THREE: MODELLING THE DENGUE EPIDEMIC
NETWORK ............................................................................................................ 45 3.1 Introduction............................................................................................. 45 3.2 Network And Its Types ........................................................................... 45
3.2.1 Static And Dynamic Networks ..................................................... 46 3.2.2 Directed And Undirected Networks .............................................. 46
3.2.3 Weighted And Un-Weighted Networks ........................................ 46 3.2.4 Bipartite And Uni-Partite Networks ............................................. 47
3.3 Attribute Analysis Of The Dataset ......................................................... 48 3.4 Two-Mode Network ............................................................................... 50 3.5 Modelling The Dengue Epidemic As Two-Mode Network ................... 51
3.6 Types Of Projection For Two-Mode Weighted Network ....................... 54 3.7 Chapter Summary ................................................................................... 57
CHAPTER FOUR: NETWORK ANALYSIS OF THE DENGUE
EPIDEMIC ............................................................................................................. 58 4.1 Introduction............................................................................................. 58 4.2 One-Mode Degree, Two-Mode Degree And Strength Of Nodes ........... 58
4.3 Closeness Centrality In the Dengue Network ......................................... 65
4.4 Betweenness Centrality .......................................................................... 69 4.5 Eigenvector Centrality ............................................................................ 72 4.6 Distance / Short path-length ................................................................... 74 4.7 Clustering Coefficient ............................................................................. 76 4.8 Network Projection From Node Perspective .......................................... 78
4.9 Density Of The Network ........................................................................ 80 4.10 Scale-Free Features Of The Dengue Epidemic Network ..................... 83 4.11 Chapter Summary ................................................................................. 92
CHAPTER FIVE: ROBUSTNESS OF THE DENGUE COMPLEX
NETWORK UNDER TARGETED VERSUS RANDOM ATTACK ............... 94 5.1 Introduction............................................................................................. 94
5.2 Node Removal ........................................................................................ 95 5.3 Random Versus Targeted Attacks .......................................................... 96 5.4 Robustness Of Network Under Links Removal ..................................... 97 5.5 Result Analysis On Targeted versus Random Removal ......................... 98 5.6 Central Node Identification And Its Removal Impact ............................ 104
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5.7 Representation Of Nodes On Real Map ................................................. 107
5.8 Chapter Summary ................................................................................... 111
CHAPTER SIX: INFLUENCE OF INTERNAL AND EXTERNAL
FACTORS IN THE DENGUE EPIDEMIC NETWORK .................................. 113 6.1 Introduction............................................................................................. 113 6.2 Possible Causes Of the Dengue Virus Diffusion .................................... 113
6.2.1 Scenario 1 ...................................................................................... 113
6.2.2 Scenario 2 ...................................................................................... 116 6.3 Modelling The Infection Influence ......................................................... 117
6.3.1 Modelling The Internal Exposures ................................................ 119 6.3.2 Modelling The External Exposures............................................... 120 6.3.3 Modelling The Exposure Curve .................................................... 122
6.4 Results And Discussions ........................................................................ 123
6.5 Chapter Summary ................................................................................... 127
CHAPTER SEVEN: CONCLUSION AND FUTURE WORK ......................... 129 7.1 Introduction............................................................................................. 129
7.1.1 Innovative Aspect Of The Study ................................................... 129
7.2 Summary Of Findings ............................................................................ 130 7.2.1 Highlights And Brief Discussion On Network Analysis .............. 130
7.2.2 Highlights And Brief Discussion On Robustness Analysis .......... 134 7.2.3 Highlights And Brief Discussion On Internal and External
Influence Analysis ........................................................................ 136
7.3 Answer To The Research Questions Of The Study ................................ 137 7.3.1 Appropriate Network Analysis Metrics And Projection
Method .......................................................................................... 137 7.3.2 Scale-Free Network Topology ...................................................... 138
7.3.3 Influence Of External Factors In The Dengue Epidemic
Network ........................................................................................ 138 7.3.4 Immunization Effect On The Focal Hubs ..................................... 139
7.4 Practical Implications Of The Research ................................................. 139
7.5 Conclusion .............................................................................................. 139 7.6 Limitations Of The Study ....................................................................... 140
7.6.1 Dataset ........................................................................................... 140 7.6.2 R-Project Tool ............................................................................... 141 7.6.3 Mathematical Model ..................................................................... 141
7.6.4 Clustering Coefficient ................................................................... 141 7.7 Future Work ............................................................................................ 141
REFERENCES ...................................................................................................... 143
APPENDIX A ......................................................................................................... 150 APPENDIX B ......................................................................................................... 167
APPENDIX C ......................................................................................................... 171
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LIST OF TABLES
Table 2.1 Different methods of defining triplet values 38
Table 3.1 Dengue cases in Selangor (2013-2014) 48
Table 4.1 The distance between nodes using weighted Newman method 75
Table 4.2 The distance between nodes using Sum method 75
Table 4.3 Clustering coefficient of dengue cases in Selangor 77
Table 4.4 Power-law exponent of few real-world networks 83
Table 5.1 Centrality scores when different values of ∝ are used. 98
Table 5.2 Fifteen percent random removal effect of links 99
Table 5.3 Targeted link removal effect 100
Table 5.4 Targeted 5% versus random removal of links up to 65% 103
Table 5.5 Score of four centrality measures 106
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LIST OF FIGURES
Figure 1.1 Dengue affected areas in the world 3
Figure 1.2 Aedes aegypti 3
Figure 1.3 Transmission of Dengue virus 5
Figure 1.4 Number of cases and incidence rate of dengue fever in Malaysia
(2008-2012). Source: Ministry of Health, Malaysia (2014) 6
Figure 1.5 Number of infected cases in different weeks during 2012-2014. 6
Figure 1.6 Dengue comparison from 1995-2015 7
Figure 1.7 Dengue incidence rate state-wise in Malaysia 8
Figure 1.8 Research Process 13
Figure 1.9 Screen shot of R-Project IDE 15
Figure 1.10 Screen shot of IGOR Pro 16
Figure 2.1 Bridge problem 20
Figure 2.2 Evolution of a Random Graph 21
Figure 2.3 Rewiring of links 22
Figure 2.4 Random Distribution vs Power-law Distribution 24
Figure 2.5 Birth of Scale-free Network 25
Figure 2.6 Scale-free Network 26
Figure 2.7 An example of undirected network 27
Figure 2.8 Node centrality 28
Figure 2.9 Degree centrality 29
Figure 2.10 Weighted degree centrality 30
Figure 2.11 Closeness centrality 33
Figure 2.12 Betweenness centrality 34
Figure 2.13 Eigenvector centrality (EvC) 36
Figure 3.1 A simple network 45
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Figure 3.2 Examples of various types of networks 47
Figure 3.3 State-wise map of Malaysia 49
Figure 3.4 An example of Two-mode network 51
Figure 3.5 Projection of Two-mode network into One-mode network 52
Figure 3.6 Two-mode network of dengue cases and weeks 53
Figure 3.7 The projected one-mode network of the two-mode dengue network
from localities perspective shown in Figure 3.6 53
Figure 3.8 The two-mode network of dengue with weighted links 56
Figure 3.9 The projected network of dengue where localities are primary nodes
after applying the Sum method 56
Figure 4.1 Result of two-mode degree 59
Figure 4.2 Results of one-mode degree by using three projection methods 60
Figure 4.3 Degree of nodes using weighted Newman method 61
Figure 4.4 Strength of nodes of Gombak network using weighted Newman
method 62
Figure 4.5 Strength of nodes of Selangor network using weighted Newman
method 63
Figure 4.6 Strength of nodes of Gombak network using Sum method 65
Figure 4.7 Closeness centrality of Gombak network using weighted Newman
method 66
Figure 4.8 Closeness centrality of Selangor network using weighted Newman
method 67
Figure 4.9 Closeness centrality using Sum method 68
Figure 4.10 Betweenness centrality of Gombak network using weighted
Newman method 70
Figure 4.11 Betweenness centrality of Gombak network using Sum method 71
Figure 4.12 Betweenness centrality of Selangor network using weighted
Newman method 72
Figure 4.13 Eigenvector centrality 73
Figure 4.14 Power-law form of EVC 74
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Figure 4.15 Comparison among different methods of clustering coefficients 78
Figure 4.16 Graphical representation of the dengue network in Gombak 79
Figure 4.17 Graphical representation of the dengue network in Selangor 80
Figure 4.18 Density of the network 81
Figure 4.19 Density of nodes 82
Figure 4.20 Density of clusters 82
Figure 4.21 The distribution of dengue cases on log-log scale with power-law
exponentγ=-1.9 84
Figure 4.22 Node strength of Newman projection 85
Figure 4.23 Node strength of Sum projection 86
Figure 4.24 Weight of links 87
Figure 4.25 Dengue cases in Gombak, Selangor. 88
Figure 4.26 Dengue cases in Hulu Langat, Selangor. 90
Figure 4.27 Dengue cases in Petaling, Selangor 91
Figure 4.28 Week-wise comparison among six districts 92
Figure 5.1 (a) A toy network. (b) Few nodes are removed from the network.
(c) The remaining clusters in the network. 96
Figure 5.2 Targeted vs random removal of links (Betweenness centrality) 101
Figure 5.3 Targeted vs random removal of links (Closeness centrality measure) 102
Figure 5.4 A network with five nodes and four links 105
Figure 5.5 Real map of Gombak with 58 dengue affected localities. 108
Figure 5.6 Targeted 8% nodes (localities). 109
Figure 5.7 Targeted 8% nodes are recovered/removed/treated. 110
Figure 5.8 Remaining 66% network 111
Figure 6.1 Influence of Internal diffusion (Scenario 1: Case 1) 114
Figure 6.2 Influence of External diffusion (Scenario 1: Case 2) 115
Figure 6.3 Influence of External suppression (Scenario 2) 117
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Figure 6.4 Comparison between case 1 and case 2 (Scenario 1) 124
Figure 6.5 Destruction of network due to external factor (Scenario 2) 126
Figure 6.6 Dengue cases in Selangor 127
Figure 8.1 Incidence and Case Fatality Rate of reported dengue cases Malaysia
(2000 – 2012) 171
Figure 8.2 Distribution of Dengue Cases by Types, Area and Gender
(Malaysia,2012) 171
Figure 8.3 Top 10 Communicable Diseases (Malaysia, 2010 & 2011) 172
Figure 8.4 Circulating dengue serotypes 1990-2012 172
Figure 8.5 Distribution of Dengue Cases by Age Group (2012) 173
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LIST OF SYMBOLS
𝛼 Tuning Parameter
𝛾 Power-law Scaling exponent
𝜔 Triplet value
𝑑 Distance
𝑑𝑊 Weighted distance
𝜏𝑖 Number of two-paths centered on node i
𝜏𝑖, ∆ Number of 2-paths that are closed by a triangle
𝜏∗ Number of four paths
𝜏∗∆ Number of 4-paths that are closed by being part of at least one 6-cycle
Np Primary nodes
Ns Secondary nodes
𝐶𝐵(𝑖) Betweenness centrality of node i
𝐶𝐵𝑊𝛼 Weighted betweenness centrality of node i
𝐶𝐷(𝑖) Degree centrality of node i
𝐶𝐷𝑊𝛼 Weighted degree centrality of node i
𝐶𝐶(𝑖) Closeness centrality of node i
𝐶𝐶𝑊𝛼 Weighted closeness centrality of node i
𝐺𝐶 Global clustering coefficient
𝐶(𝑖) Local clustering coefficient of node i
𝜏∗ 𝜔 Value of four paths
𝜏∗∆𝜔 The value of 4-paths that are closed by being part of at least one 6-
cycle
Ci Local cluster in the dengue epidemic network
Cj Global cluster in the dengue epidemic network
𝜆𝑖𝑛𝑡 Internal hazard function
Λ𝑖𝑛𝑡(𝑖) (𝑡) Internal exposure
𝜆𝑒𝑥𝑡(𝑡) Event profile
η(x) Exposure curve
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LIST OF ABBREVIATIONS
HIV Human Immunodeficiency Virus
AIDS Acquired Immunodeficiency Syndrome / Acquired Immune Deficiency
Syndrome
DF Dengue Fever
DHF Dengue Hemorrhagic Fever
DENV Dengue Virus
DENV-1 Dengue virus serotype-1
DENV-2 Dengue virus serotype-2
DENV-3 Dengue virus serotype-3
DENV-4 Dengue virus serotype-4
MOH Ministry Of Health
ER Erdos and Renyi
WS Watts and Strogtz
BA Albert-László Barabási and Réka Albert
SFN Scale-free network
EVC Eigenvector centrality
GL Gombak Locality
HLL Hulu Langat Locality
HSL Hulu Selangor Locality
PL Petaling Locality
AM Arithmetic Mean
GM Geometric Mean
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CHAPTER ONE
INTRODUCTION
1.1 BACKGROUND OF THE STUDY
Complex networks play a significant role in the research of epidemic diseases and in
their modelling (Moheeput, Goorah, & Ramchurn, 2013). There are many examples of
complex systems in the world, either natural or artificial. These systems can be
represented through complex networks. The network can be represented through
nodes/vertices and links/edges, where nodes show elementary units in the systems and
links express connectivity or interaction patterns between these nodes (Nicosia,
Criado, Romance, Russo, & Latora, 2012). During the last decade, many complex
systems have been modelled and analyzed by using graph theory and complex
networks (Nicosia et al., 2012). For example, the social contacts includes, the social
networks of friendship, a covert network of terrorists, sexual contact network, and
scientific collaboration network are all complex networks (Barthélemy, Barrat, Pastor-
Satorras, & Vespignani, 2004; Boguna, Pastor-Satorras, & Vespignani, 2003; M. E.
Newman, 2001; Padrón, Nogales, & Traveset, 2011). In the category of technological
networks; the Internet, the World Wide Web, router network and electric power grid
have been analyzed as complex networks (Avdeeva & Herczeg, 2008; A W Mahesar,
Shah, & Wahiddin, 2014; Pastor-Satorras, Vázquez, & Vespignani, 2001). Similarly,
in biology and medicine, the network of diseases such as HIV/AIDS, smallpox,
malaria, and dengue can also be represented as complex network to analyse the
spreading phenomenon (Allen & Ackleh, 2005; Kim, Lee, & Levy, 2013; Malik,
Mahesar, Abid, & Wahiddin, 2014). Also, researchers have agreed that many of the
real-world systems, when modelled and analyzed as complex networks, have similar
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structural properties (Barabasi & Bonabeau, 2003). Therefore, currently many
research trends in these networks continue to model and analyse many real-world
systems by converting them into complex networks in order to further increase their
understanding. Further, research and study of these networks have played important
role for immunization in the networks against epidemic and network tolerance to
attacks (Barthélemy, Barrat, Pastor-Satorras, & Vespignani, 2005; Pastor-Satorras et
al., 2001). In this study, the dengue epidemic phenomenon has been formalized from
the perspective of complex network. The dataset of weekly dengue epidemic cases in
Selangor has been obtained from the Ministry of Health Malaysia, and modelled for
the topological analysis using a two-mode network method.
Three projection methods have been utilized to transform the two-mode
network into a one-mode network. Further, by applying different network analysis
metrics, this research reveals the main hubs which have the highest impact of dengue
virus. Moreover, the influence of internal and external factors has been observed and
analyzed.
1.2 DENGUE EPIDEMIC
The dengue epidemic has mostly been reported in the tropical and sub-tropical regions
of the world. In the last decade, however, its outbreak has been reported in many other
countries, including those in Europe. According to an estimate, around 2.5 billion of
the world population is in danger of contracting Dengue Fever (DF) and Dengue
Hemorrhagic Fever (DHF) (Padjadjaran, 2001). In 2012, World Health Organization
(WHO) reported that there might be 50 to100 million dengue infections worldwide
every year. It is estimated that approximately 3.6 billion people are living in dengue
affected parts of the world (Figure 1.1) (Eduardo & Pessanha, 2012).
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Figure 1.1 Dengue affected areas in the world
Source: World Health Organization map production (2012)
Dengue virus is a mosquito-borne disease. Aedes aegypti and Aedes albopictus
are the main super spreader vectors of this virus, that is transmitted to humans through
their bite (Eduardo & Pessanha, 2012). This is a small dark mosquito that can be
identified by the white bands on its legs and a silver-white pattern of scales on its
body (Figure 1.2) This urban mosquito normally bites during day-time in two peaks of
biting activities, two hours after sunrise and a few hours before sunset (Expert Panel
on Asylum Seekers., 2012)
Figure 1.2 Aedes aegypti
Source: http://marketmonitor.com.ph/bacterium/
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1.3 DENGUE VIRUS TRANSMISSION
As said in section 1.2, dengue virus is transmitted to human by the Aedes aegypti bite.
It has been observed that only female Aedes aegypti are the source of dengue virus,
meaning that only female mosquito of this species are able to spread this disease
(Coutinho, Burattini, Lopez, & Massad, 2006; Derouich, Boutayeb, & Twizell, 2003).
The life expectancy of the female Aedes aegypti is between 12 to 56 days, averaging
at 34 days (Amaku et al., 2014; Side & Noorani, 2013). A female Aedes aegypti mates
with a male mosquito in order to grow its generation through laying eggs (a natural
way) but its virus might be transferred by the infected people such as, if Aedes aegypti
bites any human, and that human becomes infected with the dengue virus (DENV).
Later, if any other mosquito (not the species of Aedes aegypti) bites the infected
human, they may also get the dengue infection and becomes a source of DENV
(Figure 1.3) (Eduardo & Pessanha, 2012). Further, the dengue symptoms appear
during 4 to 14 days of the mosquito bite. Four serotypes of dengue virus known as
DENV-1, DENV-2, DENV-3 and DENV-4 have been diagnosed (Eduardo &
Pessanha, 2012; Schapira et al., 2012; Ximenes & Massad, 2013). All these dengue
serotypes can be detected from the infectedperson’sbloodsamples.Anypersonwho
is infected by any one of these serotypes will never be infected again by the same
serotype (Coutinho et al., 2006; Derouich et al., 2003; Massad et al., 2008).
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Figure 1.3 Transmission of Dengue virus
1.4 PROBLEM BACKGROUND (DENGUE ISSUE IN MALAYSIA)
According to the report, on 21 November 2015 there were 107,079 dengue cases with
293 deaths reported in Malaysia (Herriman, 2015). This was a clear increase
compared to the report, where MOH recorded over 43,000 cases with 92 deaths
(WHO, 2015). In year 2014, during the 42nd
week from October 12 to October 18 a
total of 2,160 cases of dengue fever were reported. This was an increase of 338 cases
(19%) in comparison to the previous week (41st) that had 1,822 cases. An increase in
the dengue cases has also been recorded in ten states in Malaysia over the previous
week (41st) namely; Selangor, Melaka, Kuala Lumpur & Putrajaya, Terengganu,
Penang, Perak, Kelantan, Negeri Sembilan, Pahang and Johor. The cumulative cases
of the dengue fever that were reported nationwide from 05 January to 18 October
2014 were 82,738. An increase of 212% (56,211 cases) was reported compared to the
same period in 2013 (MOH, 2014). In the 41st week, four deaths from complications
due to DF were reported, two in Perak and one in Terengganu and Kuala Lumpur,
respectively. The increasing number of dengue cases indicates that this disease is an
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epidemic and there is a desperate need to address this issue in the country. Figure 1.4
shows the number of cases and incidence rate of dengue fever in Malaysia (2008-
2012).
Figure 1.4 Number of cases and incidence rate of dengue fever in Malaysia (2008-
2012). Source: Ministry of Health, Malaysia (2014)
According to the Ministry of Health Malaysia, the DF and DHF cases have
been increasing exponentially after 2012 as shown in Figure 1.5
Figure 1.5 Number of infected cases in different weeks during 2012-2014.
Source: National Centre for laboratory and Epidemiology, Ministry of Health
Malaysia, January 2012 up to 17 May 2014 (Hemisphere & Islands, 2014).
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