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Health Information Science
Jiming Liu
Shang Xia
Computational
Epidemiology
From Disease Transmission Modeling
to Vaccination Decision Making
Series editor
Yanchun Zhang, Victoria University, Melbourne, Victoria, Australia
Editorial Board
Riccardo Bellazzi, University of Pavia, Italy
Leonard Goldschmidt, Stanford University Medical School, USA
Frank Hsu, Fordham University, USA
Guangyan Huang, Victoria University, Australia
Frank Klawonn, Helmholtz Centre for Infection Research, Germany
Jiming Liu , Hong Kong Baptist University, Hong Kong
Zhijun Liu, Hebei University of Engineering, China
Gang Luo, University of Utah, USA
Jianhua Ma, Hosei University, Japan
Vincent Tseng, National Cheng Kung University, Taiwan
Dana Zhang, Google, USA
Fengfeng Zhou, Shenzhen Institutes of Advanced Technology, Chinese Academy
of Sciences, China
With the development of database systems and networking technologies, Hospital
Information Management Systems (HIMS) and web-based clinical or medical
systems (such as the Medical Director, a generic GP clinical system) are widely
used in health and clinical practices. Healthcare and medical service are more data-
intensive and evidence-based since electronic health records are now used to track
individuals’ and communities’ health information. These highlights substantially
motivate and advance the emergence and the progress of health informatics research
and practice. Health Informatics continues to gain interest from both academia and
health industries. The significant initiatives of using information, knowledge and
communication technologies in health industries ensures patient safety, improve
population health and facilitate the delivery of government healthcare services.
Books in the series will reflect technology’s cross-disciplinary research in IT and
health/medical science to assist in disease diagnoses, treatment, prediction and mon-
itoring through the modeling, design, development, visualization, integration and
management of health related information. These technologies include information
systems, web technologies, data mining, image processing, user interaction and
interfaces, sensors and wireless networking, and are applicable to a wide range of
health-related information such as medical data, biomedical data, bioinformatics
data, and public health data.
Series Editor: Yanchun Zhang, Victoria University, Australia;
Editorial Board: Riccardo Bellazzi, University of Pavia, Italy; Leonard Gold-
schmidt, Stanford University Medical School, USA; Frank Hsu, Fordham Uni-
versity, USA; Guangyan Huang, Victoria University, Australia; Frank Klawonn,
Helmholtz Centre for Infection Research, Germany; Jiming Liu, Hong Kong Baptist
University, Hong Kong, China; Zhijun Liu, Hebei University of Engineering, China;
Gang Luo, University of Utah, USA; Jianhua Ma, Hosei University, Japan; Vincent
Tseng, National Cheng Kung University, Taiwan; Dana Zhang, Google, USA;
Fengfeng Zhou, Shenzhen Institutes of Advanced Technology, Chinese Academy
of Sciences, China.
More information about this series at http://www.springer.com/series/11944

Jiming Liu • Shang Xia
Computational Epidemiology
From Disease Transmission Modeling
to Vaccination Decision Making
Jiming Liu Shang Xia
Department of Computer Science Department of Computer Science
Hong Kong Baptist University Hong Kong Baptist University
Kowloon, Hong Kong Kowloon, Hong Kong
ISSN 2366-0988 ISSN 2366-0996 (electronic)

ISBN 978-3-030-52108-0 ISBN 978-3-030-52109-7 (eBook)
https://doi.org/10.1007/978-3-030-52109-7
© Springer Nature Switzerland AG 2020

This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,
broadcasting, reproduction on microfilms or in any other physical way, and transmission or information
storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology
now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication
does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this book
are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or
the editors give a warranty, expressed or implied, with respect to the material contained herein or for any
errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional
claims in published maps and institutional affiliations.
This Springer imprint is published by the registered company Springer Nature Switzerland AG
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
This book is dedicated to all the people
around the world, who came together to fight
against the novel coronavirus (COVID-19)
pandemic.
Jiming Liu and Shang Xia
Preface
What Can We Learn from COVID-19?
To see a World in a Grain of Sand

And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour
William Blake (1757–1827) Auguries of Innocence
The title of this preface may look a bit unusual for a research monograph.
Nevertheless, this was indeed the kind of questions that came to our mind when
we were writing it.
This book was born in a special time. As it was being written and published, the
world was enduring one of its greatest challenges in decades, if not in centuries. The
novel coronavirus, known as COVID-19, had rapidly spread to around 200 countries
and territories in 6 continents (with only Antarctica untouched) within a few months,
resulting in more than 5 million people infected and over 300,000 deaths (as of
May 2020). All the people, no matter where they were and who they were, found
themselves caught right amid this most unprecedented global crisis, with devastating
casualties, country lockdowns, service/business shutdowns, and possible economic
meltdown.
The world is truly in a state of emergency, a time of great uncertainty and anxiety.
Yet, as in the history of human civilization, we all should be hopeful that
humankind will be able to learn and prevail in the end. There will be no exception
this time. One of the important lessons that we can probably learn from the
Mother Nature in this global fight against COVID-19 is that only by being
united as one, as humanity, working together to remove the barriers of races,
vii
viii Preface
nation-states, political ideologies, religions, and special interests, and coexisting

harmoniously in an increasingly interconnected and interdependent world, can
human beings be saved. This also calls upon scientists to rethink their roles and
social responsibilities, to rediscover the world, and to advance sciences beyond
the usual disciplinary boundaries. Under such a unique circumstance, the theme
of this book becomes particularly appropriate, as it attempts to show how disciplines
such as computer science, systems science, and epidemiology can converge and
address some of the most pressing, socially relevant issues in eradicating diseases.
The contents presented in this book reflect part of our ongoing initiatives at Hong
Kong Baptist University (HKBU), which are aimed to address several important
problems in infectious disease epidemiology and to solve them in a systematic
way through the developed computational models, methods, tools, and case studies.
Some examples of the problems are as follows:
• How has the field of epidemiology evolved (Chap. 1)? How can data-centric
technologies be incorporated? (Chaps. 1 and 7)
• How can the heterogeneous nature of disease transmission be modeled and
characterized? (Chap. 2)
• How can we strategically plan and achieve disease interventions (Chap. 3)?
• How can we take into consideration the human (individual and social) aspects of
decision-making in disease interventions? (Chaps. 4–6)
• How can the epidemiological challenges be best addressed from a systems
perspective? (Chap. 7)
• What promises does systems epidemiology hold? What is the best way to pursue
it? (Chap. 7)
Solutions to the above problems can help governments, public health policy-
makers, scientists, and front-line practitioners in seeing the current and future global
health challenges, such as COVID-19, from a systematic, data-driven computational
modeling perspective, and hence developing the corresponding effective interven-
tion strategies. For instance, the solutions provided in this book can help respond
to the following questions in the case of COVID-19: Once a coronavirus vaccine
becomes available, what will be the best (scientifically sound and yet practically
acceptable) way to administer the limited supplies? Who will have the priorities?
Will there be enough people to take the vaccine, so that the target coverage (herd
immunity) can be achieved? How will people make their vaccination decisions?
The book is intended to serve as a reference book for researchers and practition-
ers in the fields of computer science and epidemiology, who may read Chaps. 1 and 7
of the book first, to gain a holistic view of the domain, prior to reading Chaps. 2–6
for further studies on the specific problems and issues involved.
Together with the provided references for the key concepts, methods, and
examples being introduced, the book can readily be adopted as an introductory text
for undergraduate and graduate courses in computational epidemiology as well as
systems epidemiology and as training materials for practitioners and field workers,
Preface ix
who may study the book in the regular order of Chaps. 1–7 and then revisit Chaps. 2–
6 to extend some of the topics and problems.
Hong Kong Jiming Liu

Hong Kong Shang Xia
May 2020
Acknowledgements
Jiming Liu is extremely grateful for the rigorous foundation development in

Physics that he acquired from East China Normal University in Shanghai in the
late 1970s and early 1980s and for the mind-opening education and enriched
inquiries in Philosophy, Cybernetics, and Psychology that he gained through the
most inspirational teachings of David Mitchell, Gary Boyd, and Gordon Past, as
well as other thinkers and visionaries, from Concordia University in Montreal in
the mid-1980s. Both periods have profoundly impacted him throughout his career
and life. He would like to acknowledge the amazing collegiality and friendships that
he has enjoyed in more than three decades from many of his mentors, colleagues,
collaborators, and students in Montreal before 1994, in Windsor in 2006–2007, and
in Hong Kong since 1994, who have not only accompanied, but also enlightened,
him throughout his odyssey of intellectual discovery, exploration, and wonder. For
the past ten years, he has made special efforts in developing solutions to address
real-world problems, such as global health and infectious disease epidemiology
in particular, from the novel perspectives of complex systems, network science,
machine learning, and autonomy-oriented computing. For this and other rewarding
journeys, he would like to express his heartfelt gratitude to: Xiao-Nong Zhou (as
well as dedicated colleagues) of National Institute of Parasitic Diseases (NIPD) at
Chinese Center for Disease Control and Prevention (China CDC), with whom he
co-established the Joint Research Laboratory for Intelligent Disease Surveillance
and Control; his long-time colleagues as well as collaborators and supporters at
Hong Kong Baptist University (HKBU), William Cheung, Pong Chi Yuen, Yiu-
ming Cheung, Yang Liu, among so many others; his previous postdoctoral fellows
and research collaborators, Bo Yang, Zhiwen Yu, Xiaofeng Xie, Qing Cai, Zhanwei
Du, etc.; his earlier research students, Shang Xia, Benyun Shi, Chao Gao, Li Tao,
Xiaolong Jin, Hongbing Pei, Hechang Chen, Xiaofei Yang, Shiwu Zhang, Hongjun
Qiu, Jianbing Wu, Qi Tan, Jinfu Ren, and many more. Also, he would like to thank
HKBU as a whole for the trust and opportunities to shape and contribute to the
university environment in the capacities of Chair Professor in Computer Science,
Head of Computer Science Department, Associate Dean (Research) of Faculty
of Science, Dean of Faculty of Science, and Associate Vice-President (Research)
xi
xii Acknowledgements
of the university, to make it the most conducive place for scholarship. He would
like to thank Hong Kong Research Grants Council (RGC) for the funding support
over the years; a number of grants have been awarded to specifically support his
team’s research on understanding and solving epidemiological problems through the
exciting routes of computer science, machine learning, and artificial intelligence.
Last but the foremost, he would like to express his deepest thanks to his wife
M.L. and his daughters I.Y.Y. and B.Y.X. for their long-lasting love and the most
wonderful time.
Shang Xia would like to express his sincere gratitude to Prof. Jiming Liu for his
enlightening, patience, motivation, enthusiasm, and profound knowledge. Without
his encouragement and persistence, this book could not be accomplished. He would
like to express his sincere gratefulness to Computer Science Department at Hong
Kong Baptist University (HKBU), where he acquired his PhD degree, benefited a lot
from the most inspirational guidance, and enjoyed a fulfilling campus life. For this
rewarding journey in Hong Kong, he would sincerely express his heartfelt gratitude
to Dr. Benyun Shi, Dr. Li Tao, and Dr. Yang Liu, from whom he benefited their
collaboration and support. The sincere thanks also go to Prof. Xiao-Nong Zhou and
the National Institute of Parasitic Diseases at Chinese Center for Disease Control
and Prevention for the great support for his academic career and research. Last but
not least, he would like to thank his family: his wife Yao Q.Q. and his daughters
Yoyo and Xiuxiu for their caring, love, and support in this wonderful life.
Both authors wish to express their special thanks to Dr. Yang Liu for his great
efforts in proofreading the manuscript and offering excellent editorial suggestions
and help.
Hong Kong Jiming Liu

Hong Kong Shang Xia
May 2020
Contents
1 Paradigms in Epidemiology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Methodological Paradigms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Recent Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Infectious Diseases and Vaccination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Objectives and Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.1 Modeling Infectious Disease Dynamics . . . . . . . . . . . . . . . . . . . . . . . 8
1.4.2 Modeling Vaccine Allocation Strategies. . . . . . . . . . . . . . . . . . . . . . . 8
1.4.3 Modeling Vaccination Decision-Making . . . . . . . . . . . . . . . . . . . . . . 9
1.4.4 Modeling Subjective Perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Computational Modeling in a Nutshell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Modeling Infectious Disease Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Infectious Disease Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.2 Age-Specific Disease Transmissions . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Modeling Contact Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 Empirical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.2 Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Case Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.1 Hong Kong H1N1 Influenza Epidemic . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.2 Age-Specific Contact Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4 Further Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3 Strategizing Vaccine Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1 Vaccination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.1 Herd Immunity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.2 Vaccine Allocation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Vaccination Priorities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Age-Specific Intervention Priorities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.1 Modeling Prioritized Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
xiii
xiv Contents
3.3.2 Effects of Vaccination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3.3 Effects of Contact Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.4 Integrated Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4 Case Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4.1 Hong Kong HSI Vaccination Programme . . . . . . . . . . . . . . . . . . . . . 42
3.4.2 Effects of Prioritized Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.5 Further Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4 Explaining Individuals’ Vaccination Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1 Costs and Benefits for Decision-Making. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2 Game-Theoretic Modeling of Vaccination Decision-Making . . . . . . . . . 51
4.3 Case Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3.1 Hong Kong HSI Vaccination Programme . . . . . . . . . . . . . . . . . . . . . 53
4.3.2 Vaccination Coverage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.4 Further Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5 Characterizing Socially Influenced Vaccination Decisions . . . . . . . . . . . . . . 57
5.1 Social Influences on Vaccination Decision-Making . . . . . . . . . . . . . . . . . . . 57
5.2 Case Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2.1 Vaccination Coverage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.3 Further Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6 Understanding the Effect of Social Media. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.1 Modeling Subjective Perception. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2 Subjective Perception in Vaccination Decision-Making . . . . . . . . . . . . . . 74
6.2.1 Dempster-Shafer Theory (DST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.2.2 Spread of Social Awareness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.3 Case Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.3.1 Vaccination Decision-Making in an Online Community . . . . . 78
6.3.2 Interplay of Two Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.4 Further Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7 Welcome to the Era of Systems Epidemiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.1 Systems Thinking in Epidemiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.2 Systems Modeling in Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.3 Systems Modeling in Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.4 Toward Systems Epidemiology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Abbreviations
ACIP Advisory Committee on Immunization Policy

AEFI Adverse events following immunization
BPA Basic probability assignment
CHP Centre for Health Protection
DST Dempster–Shafer theory
H1N1 Influenza A virus (H1N1)
H7N9 Avian influenza A virus (H7N9)
HSI Human swine influenza
HSIVP Human Swine Influenza Vaccination Programme
MMR Measles–mumps–rubella
NVAC National Vaccine Advisory Committee
SARS Severe acute respiratory syndrome
SEIR Susceptible–exposed–infectious–recovered
SIR Susceptible–infectious–recovered
SIS Susceptible–infectious–susceptible
SIT Social impact theory
STD Sexually transmitted disease
xv
Notation
S Population in susceptible compartment

I Population in infectious compartment
R Population in recovered compartment
N Overall population
Si Susceptible subpopulation i
Ii Infectious subpopulation i
Ri Recovered subpopulation i
Ni Overall subpopulation i
α Infectivity
β Susceptibility
λ Infection rate
μ Transmission rate
γ Recovery rate
cij Contact frequency between two subpopulations i and j
R0 Basic reproduction number
Rt Effective reproduction number
CH Contact matrix for household setting
CS Contact matrix for school setting
CW Contact matrix for workplace setting
CG Contact matrix for general community setting
C Contact matrix for overall social setting
Φ Social settings (H, S, W, G)
rH Household contact coefficient
rS School contact coefficient
rW Workplace contact coefficient
rG General community contact coefficient
K Disease reproduction matrix or next-generation matrix
A Infectivity matrix, diag (α1 , . . . , αN )
B Susceptibility matrix, diag (β1 , . . . , βN )
S Susceptible population matrix, diag (S1 , . . . , SN )
I Infectious population vector, [I1 . . . IN ]T
xvii
xviii Notation
ρ(K) Top eigenvalue of K

x1 Top left eigenvector of K
y1 Top right eigenvector of K
Nivac Number of vaccinated neighbors
Ninon Number of unvaccinated neighbors
wij Social closeness between two connected individuals i and j
λ̂i Perceived infection rate for subpopulation i
β̂ Perceived susceptibility
θ Herd immunity threshold
ζ Cost of disease infection
ξ Cost of vaccination
rc Cost ratio rc = ξ/ζ
σi Vaccination decision
σˆi Cost-minimized choice
σ˜i Social opinion from connected neighbors
ιvac
i Social influence for vaccination
ιnon
i Social influence against vaccination
ιi Influence discrepancy
ν Responsiveness to influence discrepancy in Fermi function
P (ιi ) Probability generated from Fermi function
rf Conformity rate
G Social network, G = V , L
V Network nodes (individuals)
L Network links (interactions)
Θ Universal set of vaccination decision, {Yes, No}
φ Empty set
2Θ Power set, {φ, {Y es}, {No}, Θ}
m(·) Basic probability assignment
m(Y es) Belief value of vaccination
m(No) Belief value of non-vaccination
m(Θ) Belief value of no decision (uncertainty)
mi Set of belief values
mi Updated belief values
mei Obtained awareness about negative events
medis Belief values generated by a severe disease infection
mevac Belief values generated by a vaccine adverse event
f Coefficient of awareness fading
Reporting rate of severe disease infections
κ Reporting rate of vaccine adverse effects
Chapter 1
Paradigms in Epidemiology
Epidemiology deals with “the study of the occurrence and distribution of health-
related states or events in specified populations, including the study of the deter-
minants influencing such states, and the application of this knowledge to control
the health problems” [1]. As defined by MacMahon et al. [2], epidemiology is
interdisciplinary by nature, concerning the sciences of etiology, genetics, biology,
pharmacy, geography, ecology, as well sociology and human behavior. Epidemio-
logical studies motivated by combating infectious diseases mainly focus on four
aspects of challenges, as follows: (1) pattern analysis, by investigating the spatio-
temporal distributions of the observed disease occurrences; (2) causal inference, by
identifying and evaluating associated impact factors; (3) forecasting and prediction,
by evaluating the dynamics of infectious diseases with reference to different sce-
narios; and (4) policy analytics, by exploring and conducting effective intervention
measures.
Toward these ends, the pioneers in epidemiology have provided much useful
knowledge to guide efforts in infectious disease control. As pointed out by Merrill
[3], epidemiology has evolved from supernatural practices to research based on
scientific foundations, from ad hoc reports to systematic investigations of public
health events and problems, from ignorance of the causes of diseases to a scientific
understanding of their hidden factors, determinants, and outcomes, and from lacking
feasible means for solving public health problems to having effective approaches to
disease intervention.
Developmental milestones in infectious disease epidemiology can be dated
back to the work of Hippocrates (460–377 BC), who examined the influence of
environments and attempted to explain how diseases transmit and cause infection
in a group of host individuals [3]. Other early studies include the work of John
Graunt (1620–1674), who described disease mortality rates by applying statistical
and census methods [4], and Thomas Sydenham (1624–1689), who studied disease
distribution patterns, moving from an observational to an analytical perspective [5].
In the nineteenth century, John Snow (1813–1858) traced the sources of disease
© Springer Nature Switzerland AG 2020 1

J. Liu, S. Xia, Computational Epidemiology, Health Information Science,
https://doi.org/10.1007/978-3-030-52109-7_1
2 1 Paradigms in Epidemiology
outbreaks (e.g., cholera in Soho, London, in 1854) and thereafter pointed out the
associations of disease outbreaks with social and natural environments [6]. To
more formally describe the dynamics of disease transmission, Ross (in 1911) and
MacDonald (in 1957) developed a set of mathematical equations and proposed
a threshold indicator, named the basic reproduction number, to quantitatively
characterize the extent of disease transmission [7].
1.1 Methodological Paradigms
Various methodologies have been developed to address a wide range of challenges

in infectious disease control and prevention, and these methods have been applied in
epidemiological studies in the past several decades. As stated by Zadoks [8], based
on the observation of disease occurrences, descriptive methods, such as clustering
and hot spot analysis, have been used to analyze the patterns of infectious diseases
in terms of their temporal, spatial, and demographic distributions in a population,
i.e., to answer the questions of when, where, and who. Statistical methods, such
as regression or Bayesian inference, can be used to further explore the causal
relationships between disease occurrence and the possible impact factors, i.e., to
answer the questions of why and how. Predictive methods, such as mathematical
modeling or computer-based simulation, have been developed to forecast the
dynamics of infectious diseases during an epidemic, and identify the most suitable
indicators for representing such a dynamic process. Based on these, prescriptive
methods, such as optimization, or scenario and sensitivity analyses, can be used by
public health authorities to decide how to implement the most effective intervention
strategies, such as the allocation of pharmaceutical resources (e.g., vaccines and
antivirals) and social distancing (e.g., segregation and school closures).
Infectious disease epidemiology has undergone a number of methodological
paradigm shifts throughout its development, as highlighted in Fig. 1.1. The typical
methods mentioned in the preceding paragraph, i.e., descriptive, predictive, and pre-
scriptive methods, correspond to three of those paradigms (the fourth is introduced
in the next subsection and discussed in detail in the final chapter of this book).
These three paradigms are (1) empirical investigation, (2) theoretical modeling, and
(3) computational modeling. Accordingly, we refer to the epidemiological method-
ologies based on these paradigms as (1) empirical epidemiology, (2) theoretical
epidemiology, and (3) computational epidemiology, respectively.
• Empirical Methods
The paradigm of empirical observation and investigation is well suited to the
early stage of epidemiological studies. As mentioned by Rothman et al. [9], it
typically involves (1) collecting observational data about disease transmission,
i.e., when, where, and who, and associated impact factors, e.g., the characteristics
of disease pathogens and host individuals at the microscopic scale, and of etiolog-
ical and meteorological environments at the macroscopic scale; (2) qualitatively
describing or quantitatively analyzing observational data to establish associative
1.1 Methodological Paradigms 3
Fig. 1.1 Major methodological paradigms in infectious disease epidemiology
or causal relationships between impact factors and disease transmission; and (3)
conducting further experiments or field investigations to test epidemiological
hypotheses, usually relating the proposed causes to the observed effects, the
findings of which may serve as the foundation for planning and implementing
disease intervention.
• Theoretical Methods
The theoretical paradigm in epidemiological studies involves the use of mathe-
matical tools, and is focused on generalizing and characterizing the processes of
disease transmission and their interrelationships with various impact factors [10].
Mathematical equations or models are typically constructed to quantitatively
describe the dynamics of disease transmission and estimate possible outcomes.
By evaluating different conditions under which the models reach convergent,
stable, or equilibrium states, public health authorities can potentially make long-
term projections and informed decisions on disease intervention. Theoretical
epidemiology sometimes draws on certain assumptions and simplifications about
the real processes of disease transmission. Meanwhile, it may also require
mathematical operations to derive model constructs of the behaviors of various
diseases, and use these to infer the disease dynamics and the corresponding
intervention measures.
• Computational Methods
With the developments in artificial intelligence, machine learning, data analytics,
data mining, and geographic science and information systems, the computational
paradigm has rapidly emerged in epidemiological studies. Computational meth-
ods are aimed to better characterize and understand the real processes of disease
transmission, by modeling and analyzing the patterns of transmission and quan-

titatively evaluating the potential outcomes of disease intervention [11]. Primary
computational tools that are used comprise computational modeling, simulation,
prediction, and optimization, as well as data analytics and visualization, to
make the results accessible to public health authorities and epidemiologists. This
has further expanded the scope and capabilities of epidemiology for analyzing
and predicting the dynamics of disease transmission and the effects of disease
intervention in a given population. In addition, public health authorities are now
able to more effectively conduct scenario analysis, which facilitates their strategic
decision-making.
1.2 Recent Developments
The above-mentioned methods have been in vogue for several decades and have
been used to make great contributions to our understanding and ability to combat
infectious diseases. However, there remain a number of challenges. As schemati-
cally illustrated in Fig. 1.2, these challenges come from emerging and re-emerging
infectious diseases, which are significantly correlated with multiple impact factors
and their interacting effects, such as genetic mutation of disease pathogens/parasites
[12], human socio-economic and behavioral changes [13], and environmental and
ecological conditions [14, 15].
Fig. 1.2 Some interacting components (in circles) and their associated impact factors that can
affect the transmission of infectious diseases
1.2 Recent Developments 5
Now we examine influenza as an example. It has been shown that a wide range
of factors are involved in the dynamic processes of these outbreaks [16], which may
include the following: (1) pathogenic factors, such as viral genetic recombination
and the expression of pathogens; (2) host factors, such as the immunity of people
at different ages; (3) social and behavioral factors, such as people’s movement
or travel activities; and (4) policy factors, such as disease intervention measures.
Furthermore, these factors closely interact with each other. For instance, disease
pathogens are carried by humans as they travel, which accelerates the recombination
of different types of viruses. However, the implementation of disease intervention,
e.g., school closures, changes people’s contact behaviors, effectively cutting off the
route of disease transmission.
This highlights how various factors can interrelate and interact at various scales.
Crucially, the coupling and interactive relationships among those impact factors
can determine the intrinsic (yet possibly hidden) spatial, temporal, and social
mechanisms of disease transmission. These mechanisms can involve systemic
characteristics, such as feedback, saturation, bifurcation, and chaos, thus posing new
challenges for comprehensive epidemiological investigations [17].
Effective intervention measures rely on biomedical understanding of disease
pathogens/parasites, descriptive studies of spatio-temporal patterns of disease occur-
rences, and causal analysis of impact factors. In addition, predictive explorations
of the trends of disease transmission, i.e., the mechanistic interactions among
the components of the transmission process, are also key to understanding and
combating infectious diseases. For example, an early warning system for an
emerging infectious disease, like COVID-19, requires knowledge about the possible
geographic routes of disease transmission, such as human air-travel networks
[18]. The prevention of zoonotic and vector-borne diseases, like COVID-19 and
malaria, requires both environmental and ecological changes of animal/vector
species to be addressed [19], as well as human migrant and mobile behaviors
[20]. Furthermore, the effectiveness of disease intervention measures depends on
the efficacy of resource allocation, compliance of targeted host populations, and
responsive feedback to environmental modifications.
In addition to the above-mentioned challenges, epidemiological studies also
face new opportunities in the present and future data-centric era, enabled by the
confluence of data from various sources and the development of modeling and
analytical tools in data science [21]. For example, a global disease surveillance
system connects the health agencies of its member countries and partners at
different levels, via local, regional, national, and international organizations [22].
This surveillance system can be used for managing and sharing historical records
and reports on when and where specific people have been infected by certain kinds
of diseases.
Other data sources are also helpful for analyzing and modeling potential disease
transmission. For example, remote sensing data from satellites can readily be
utilized for mapping the meteorological and ecological conditions of local or global
environments [23, 24].
Another important source of data is Internet-based media, which can serve as

an informative channel for revealing individuals’ health-related behaviors and opin-
ions. For example, Google Flu Trends was earlier used to assess the transmission
of influenza virus [25], and the use of Internet search data was demonstrated to be
effective in predicting dengue fever [26].
In view of these challenges and opportunities, it is imperative that new method-
ologies and paradigms are developed that offer novel perspectives and methods for
comprehensive investigation of disease dynamics and associated impact factors,
thus expanding our capabilities to understand, predict, control, and prevent the
transmission of infectious diseases.
1.3 Infectious Diseases and Vaccination
Faced with the threat of infectious diseases, implementing timely and effective
disease intervention measures is critical for preventing mortality and debilitating
morbidity, and reducing the socio-economic losses. Various types of intervention
measures have been widely studied and adopted for these purposes. For example,
immediate isolation/quarantine can prevent transmission during an influenza-like
epidemic [27, 28]. The mass prophylactic use of antiviral drugs can reduce the
vulnerability of susceptible individuals exposed to infectious diseases [29]. Inter-
ventions by social distancing (e.g., school closures and workplace shutdowns) can
lower the frequency of contacts among the host population and, hence, reduce the
probability of transmitting diseases between susceptible and infectious individuals
[30, 31].
Besides the above-mentioned intervention measures, vaccination has been
regarded as one of the most effective methods for preventing infectious diseases,
due to the effect of vaccine-induced herd immunity (i.e., immunizing a certain
portion of the host population provides indirect protection for the unimmunized
individuals [32]). That is to say, to prevent a potential outbreak, the vaccination
coverage in a host population needs to be above a critical level for inducing the
effect of herd immunity, known as herd immunity threshold. In practice, it remains
a continual challenge for public health authorities to achieve such a threshold of
vaccination coverage for preventing disease outbreaks.
The task is challenging due to a series of reasons. For one thing, although
significant progress has been made over the years in vaccine development, the
capacity for providing adequate and timely vaccine doses remains a concern,
especially when encountering emerging infectious diseases, e.g., 2009 influenza A
(H1N1) [33]. Supply restrictions can arise due to many factors, including the time
needed for finalizing vaccine compositions, to respond to the constantly evolution
of new disease strains [34], the limited capacity for vaccine manufacturing and
logistics [35], and the difficulties in access to and uptake of vaccines due to
poor delivery infrastructures and economic constraints, especially in developing
countries [36]. In such situations, public health authorities in charge of vaccination
1.4 Objectives and Tasks 7
programs face the question of how to allocate a finite number of available vaccine
doses to most effectively prevent disease transmission. For example, the World
Health Organization (WHO) has strongly suggested that each country should
respond to a possible shortage of vaccine supplies by deciding in advance which
groups should have access [37].
Furthermore, the public acceptance of a vaccination program will crucially affect
the actual level of vaccine uptake: any loss of confidence in vaccine safety and
efficacy will lead to huge gaps between the level of public vaccination willingness
and the level needed to contain disease transmission. Historically, societies have
experienced several events of vaccine refusal, e.g., the pertussis vaccine scare in
the 1970s [38], the decline of measles-mumps-rubella (MMR) vaccine uptake in
the 1990s [39, 40], and the rise and popularity of anti-vaccination movements [41,
42]. The rejection of vaccination and the subsequent decline of vaccine uptake have
brought about outbreaks of certain vaccine-preventable diseases that were thought
to no longer be threats to humankind [43, 44].
In view of this, an in-depth understanding of individuals’ voluntary vaccination
compliance is urgently required. It has been found that public acceptance of
vaccination, which amounts to individuals’ decisions on whether or not to take
vaccines, are affected by a mixture of cultural, behavioral, and socio-economic
factors. For example, the public may have doubts about vaccine safety and efficacy
due to scare stories around the adverse effects of vaccination [45, 46]. Or, behaving
in their own self-interest, individuals may be inclined not to get vaccinated if
enough other people have been vaccinated [47, 48]. The affordability and convenient
accessibility of new vaccines are also of importance for individuals considering
vaccination, especially in developing countries [49, 50].
Furthermore, the rapid emergence of online social media, e.g., Facebook and
Twitter, allows opinions, whether for or against vaccination, to spread broadly
and immediately among the population [51]. Therefore, social influences play an
increasingly important role in individuals’ vaccination decisions. In this regard, an
individual’s decision on whether or not to vaccinate himself/herself is no longer a
personal affair, but will affect the decisions of others, and collectively determine the
final coverage of a vaccination program.
Clearly, there exists an urgent need for more systematic studies of vaccination
at both population and individual levels, and thereby improve the efficacy of
vaccination programs for preventing the outbreak of infectious diseases.
1.4 Objectives and Tasks
In this book, we examine the dynamics of disease transmission in a host population,

in which individuals’ contact relationships are inferred from the socio-demographic
data. Based on such a description of disease transmission, we address the problem
of vaccine allocation by developing a novel prioritization method that targets certain
subpopulations to most effectively reduce disease transmission. Furthermore, to
investigate individuals’ acceptance of vaccination, we present decision models to

characterize individuals’ voluntary vaccination and evaluate the impact of social
influences and individuals’ subjective perception on the effectiveness of disease
intervention by vaccination.
1.4.1 Modeling Infectious Disease Dynamics
As aforementioned, the dynamics of disease transmission depend on many disease-

and host population-related factors. To characterize the heterogeneity of a host pop-
ulation, we need to consider its age structure, and then construct a compartmental
model to describe disease dynamics with respect to individuals’ age-specific vari-
ations, i.e., the heterogeneity in terms of age-specific infectivity and susceptibility,
as well as cross-age contact relationships, as in the case of COVID-19 transmission
[52].
For the purpose of demonstration in this book, we consider the real-world
scenario of the 2009 Hong Kong H1N1 influenza epidemic, and calibrate our
demonstration parameters with reference to the epidemiological characteristics of
influenza A (H1N1). As detailed information about the actual contacts among age-
specific subpopulations is often unavailable, we exploit a computational method to
infer the contact relationships in terms of individuals’ cross-age contact frequencies
from the census data in Hong Kong. Specifically, we represent individuals’ actual
contacts as cross-age contact frequencies within four specific social settings, i.e.,
school, household, workplace, and general community. We then estimate the overall
contacts that account for disease transmission by incorporating four setting-specific
contact frequency matrices, which are weighted with the coefficients corresponding
to the proportions of individuals’ contacts within the considered social settings.
To computationally evaluate our model, we carry out a series of simulation-
based experiments to examine its predicted disease dynamics. That is, we validate
our epidemic model by comparing the model predictions with the real-world
observations, in terms of the daily new infection cases and the age-specific attack
rates, i.e., the proportion of infected individuals in each subpopulation. In essence,
we reproduce the dynamics of disease transmission based on the heterogeneity of
the age-structured host population. The results, as we describe later, can serve as
the basis for further discussions on vaccine allocation methods and on individuals’
voluntary vaccination.
1.4.2 Modeling Vaccine Allocation Strategies
The heterogeneity of the host population means that the disease-preventing effects
of vaccination in individuals of different ages can vary markedly. An immediately
related practical question is how to allocate a finite number of vaccine doses to
most effectively reduce disease transmission; crucially, this requires knowledge

of the effectiveness of this intervention. In this book, we focus on developing a
problem-solving method for answering this question. Specifically, we develop a
computational method for identifying the relative priority of each subpopulation,
by evaluating the effectiveness of age-specific vaccination in reducing disease
transmission. We examine the effects of disease intervention on containing disease
transmission by measuring the reproduction number corresponding to the age-
specific heterogeneity of a host population. By doing so, we identify subpopulations
whose vaccination will lead to the greatest reduction in disease transmission, by
considering the marginal effects of reducing the reproduction number in cases of
age-specific vaccine allocation.
Unlike the existing optimization-based methods, this proposed vaccine allocation
method has the following distinct characteristics:
• The method utilizes prior knowledge about individuals’ age-specific susceptibil-
ity and infectivity, real-time disease prevalence in each subpopulation, and the
basic patterns of individuals’ cross-age contact frequencies within each social
setting. Moreover, it does not rely on detailed information about individuals’
actual contacts, nor the potential changes in these contacts in response to disease
transmission, which would be difficult to rapidly and accurately determine in
practice.
• The method is designed to most effectively reduce disease transmission by
allocating a finite number of vaccine doses to certain target subpopulations.
The identified vaccination priorities can be adaptively regulated based on the
dynamics of disease transmission, i.e., the number of vaccine doses suggested to
be allocated to each subpopulation can be dynamically adjusted according to the
latest progress of disease transmission and vaccine supply.
• The method incorporates the effects of other disease intervention measures
being implemented simultaneously with vaccination, e.g., individuals’ contact
reduction. Therefore, in the situation of integrated disease intervention, the
method can provide more accurate and effective solutions for vaccine allocation.
We apply above-mentioned method to the real-world scenario of the 2009 Hong
Kong H1N1 influenza epidemic to identify the relative priorities of subpopulations
for disease intervention in Hong Kong. The results show that this method of
prioritizing age-specific subpopulations for vaccine allocation and social settings
for contact reduction can readily improve the effectiveness of disease transmission-
containing efforts.
1.4.3 Modeling Vaccination Decision-Making
In a voluntary vaccination program, individuals’ decisions on whether or not to

uptake vaccine crucially affect the level of vaccination coverage and, thus, the effec-
tiveness of disease intervention. In this regard, modeling and evaluating individuals’
vaccination decision-making would provide useful information for public health

authorities on how to improve the effectiveness of vaccination programs [53].
Researchers have typically utilized payoff-based approaches to characterize
individuals’ vaccination decision-making with respect to the perceived risks and
benefits of vaccination. Moving beyond that, we consider the fact that whether
an individual does or does not get vaccinated is also influenced by the decisions
of others, i.e., social influences. We thus view individuals’ voluntary vaccination
as an integrated decision-making process that incorporates both a cost analysis of
vaccination and the impact of social influences.
Our integrated decision model is an improvement over the existing models, and
has several interesting features, as follows:
• We model an individual’s vaccination decision-making as an integrated process
that balances his/her self-initiated cost minimization and the social influences
of others’ decisions. Moreover, this model introduces a parameter, called the
conformity rate, to modulate individuals’ tendency toward two decision-making
mechanisms: an individual will adopt his/her own cost-minimized decision, or
the social opinion of his/her interconnected neighbors.
• Based on the existing studies in which the social influences on the process of
opinion formation have been addressed, we further consider the heterogeneity of
individuals’ social relationships, i.e., how individuals are socially interconnected.
Computationally, we model and characterize the effect of networked social
influences on individuals’ vaccination decisions based on Social Impact Theory
(SIT).
• Based on this new model, we examine the effects of social influences on indi-
viduals’ decisions and on the effectiveness of disease intervention (vaccination
coverage), with respect to three determinants: (1) the relative costs of vaccination
and infection; (2) individuals’ conformity to social influences, i.e., conformity
rate; and (3) individuals’ initial level of vaccination willingness.
We parameterize the integrated decision model based on the real-world sce-
nario of the 2009 Hong Kong H1N1 influenza epidemic, and perform a series
of simulation-based experiments to infer the coverage of voluntary vaccination
programs as a result of individuals’ decision-making. The results indicate that
individuals’ vaccination decision-making can be affected by both the associated
costs and their conformity to social influences. Thus, it becomes necessary for public
health authorities to estimate the level of individuals’ acceptance of vaccination
prior to the start of a voluntary vaccination program, as well as to rapidly assess
and enhance the effectiveness of their adopted vaccination policies, e.g., providing
certain financial subsidies to reduce the cost of vaccination.
1.4.4 Modeling Subjective Perception
It has long been observed that the spread of awareness about an epidemic via social
media can affect individuals’ opinions and behaviors concerning an epidemic. In the
case of an emerging infectious disease, it can be difficult for individuals to become
informed about the disease and/or a newly developed vaccine prior to their decision-
making. In such a case, the spread of awareness about disease severity and vaccine
safety could affect individuals’ subjective perception about vaccination and, hence,
substantially affect their decisions [54].
To gain a better understanding of individuals’ voluntary vaccination, we develop
a belief-based decision model to evaluate the effect of the spread of awareness
on individuals’ decision-making and on the effectiveness of disease intervention.
Compared with the existing studies on modeling individual-level vaccination
decision-making, this belief-based model has the following unique properties:
• Unlike existing decision models that represent decision-making as a binary
problem, we consider the role of uncertainty in individuals’ vaccination decision-
making. Specifically, the situation in which an individual has made no firm
decision can be considered as a state of “yet to decide”, due to uncertainty. In this
regard, we introduce three belief variables to characterize the possible decision
response from an individual, namely that he/she will accept or reject the vaccine,
or has not yet decided.
• We further consider the fact that individuals’ decisions depend on their subjective
perception about whether or not vaccination is acceptable. Moreover, awareness
of disease severity and vaccine safety can spread from person to person—akin
to a disease itself—and will substantially affect their subjective perception of
vaccination.
• To model the spread of awareness, we utilize various real-world online social
networks to characterize the structure of individuals’ social relationships. There-
after, we further extend Dempster-Shafer Theory (DST) to computationally
model the propagation and evolution of individuals’ beliefs, as well as their
decision-making, having incorporated the awareness obtained from their socially
interconnected neighbors.
We investigate the effect of the spread of awareness on individuals’ vaccination
decision-making with respect to three considered impact factors, based on a series of
simulations of the 2009 Hong Kong H1N1 influenza epidemic. First, the reporting
rates of severe infection and adverse effects of vaccination are used to represent the
frequencies of these topics, which tend to draw public attention. Next, we consider
the coefficient of awareness fading, a parameter used to quantify the information
flows among individuals. Finally, we examine the effect of disease reproduction
number, which corresponds to the severity of an epidemic.
The simulation results show that the reporting rates will determine the number of
vaccinated individuals and the time at which they receive vaccination. A higher
fading coefficient will significantly reduce individuals’ vaccination willingness.
A larger value of disease reproduction number will enhance the proportion of

vaccinated individuals, although this cannot compensate for the growth of the
infected population size resulting from a more severe disease outbreak.
1.5 Summary
In this book, we develop a computational modeling approach to evaluate and guide

the implementation of different intervention measures for controlling infectious
diseases. We focus on the following topics in the remaining chapters:
In Chap. 2, we provide a general description of the concepts and related
computational models and tools for characterizing disease transmission dynamics
in a heterogeneous host population. Specifically, we introduce the concepts of
compartmental modeling for describing disease transmission in an age-structured
host population. Then, we present a computational method for inferring the cross-
age contact patterns of the population. Finally, we parameterize and validate the
epidemic model with a real-world epidemic scenario, which serves as the basis for
our further discussions on vaccine allocation and individuals’ voluntary vaccination.
In Chap. 3, we develop a prioritization method for identifying target subpop-
ulations for vaccine allocation that would enable us to most effectively reduce
disease transmission. We walk through a series of simulation-based experiments
that evaluate the performance of such a vaccine allocation method in improving the
effectiveness of disease intervention.
In Chap. 4, we examine vaccination decision-making from the perspective of
individuals. In particular, we show how to model individuals’ decision-making
processes in response to a voluntary vaccination program. We use computational
modeling to perform a game-theoretic analysis of the costs and benefits of vacci-
nation with respect to individuals’ social relationships. Then, we experimentally
examine the level of vaccination coverage, based on this game-theoretic model,
through a series of simulations of voluntary vaccination.
In Chap. 5, we introduce an extended decision model that additionally addresses
the effect of social influences on an individual’s decision whether to undergo
voluntary vaccination. In the extended decision model, we utilize the SIT to further
characterize social influences with respect to individuals’ social relationships. We
evaluate the effect of social influences by computing the level of vaccination
coverage through a series of simulations of voluntary vaccination based on such
an integrated decision model.
In Chap. 6, we present a more complete investigation of voluntary vaccination
by modeling and examining the effect of the spread of awareness on vaccination
decision-making. In doing so, we develop a belief-based decision model, in which
individuals’ decisions are affected by their subjective perception of vaccination. In
this model, we utilize and extend DST to characterize individuals’ belief updates and
changes in vaccination decisions accordingly. We evaluate the effect of the spread of
1.5 Summary 13
awareness by carrying out simulation-based experiments to examine the time course

of vaccine administration and disease transmission.
In Chap. 7, we offer a fresh outlook on the latest methodological paradigm
in infectious disease epidemiology, which is known as systems epidemiology.
Specifically, we introduce the fundamental ingredients of systems thinking, which
are essential for viewing and addressing complex epidemiological questions holisti-
cally. We then provide detailed systems modeling principles and practical steps that
can be followed in future systems epidemiological studies.
Finally, under “References” section, we provide a detailed list of references for
further reading and research.
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It lasted nearly two years. Then Maxwell, at the conclusion of some
brutal quarrel, burst another bloodvessel, and his life was despaired of.
Mary was his nurse; he would have no other. She had to sit up with him; to
attend upon him; to submit to his petty irritability, made worse by illness; to
watch him in his restless slumbers, hoping that each time he closed his eyes
would be the last.
One night—it was the very night on which this chapter opened—she sat
by his side absorbed in gloomy thought. The candle was flaring in the
socket. Everything was still. The dying man slept peacefully. With her
hands drooping upon her lap, she sat allowing her thoughts to wander; and
they wandered into the dim future, when, released from her tyrant, she was
once more a happy woman. Long did she indulge in that sweet reverie, and
when it ceased, she turned her head mechanically to look upon the sleeper.
He was wide awake: his dull eyes were fixed intently upon her; and a shiver
ran all over her body as she met that gaze!
"I am not dead yet!" he said, as if he had interpreted her thoughts.
She trembled slightly. With a sneer, he closed his eyes again.
Silently she sat by his side, communing with her own dark thoughts. He
slept again; slept soundly. She rose, and moved about the room; it did not
awaken him. She took courage:—crept down stairs, unfastened the door—
and fled.
Fled, and left her tyrant dying;—fled, and left him without a human
being to attend upon him—left him to die there like a dog; or to recover, if
it should chance so. She cared not; her only thought was flight; and, winged
with terror, she flew from the accursed home of guilt and wretchedness; and
felt her heart beat distractedly, as, a homeless, penniless wanderer, she
urged her steps along that dusty road under the quiet shining moon.
Ten days afterwards, Meredith Vyner received a long letter from his
wife, detailing the misery of her penniless condition, and imploring
pecuniary aid. The poor, old man wept bitterly over the letter, and again
reproached himself with having been the cause of her ruin. He could not
forget that he had loved her—had been happy with her. He forgave her for
not having loved one so old as himself; and wrote to her the following
reply:—
WYTTON HALL, 2nd August, 1845.
"MY DEAR WIFE,
"We have both need of forgiveness—you have mine. I know I am not

young enough to be loved by you:
Durum! sed levius fit patientia

Quidquid corrigere est nefas,
as our favourite says—not that the quotation is very good. But if you can
have patience, as I can have; if you can forget all 'incompatibilities,' and
live quietly and not unhappily with me, come back again, and all shall be
forgotten. I will do my best to make you happy, I promise that nothing of
what has passed shall ever be recurred to. You shall again be mistress of my
house and fortune.
"But I do not wish to force you even to this. If, on deliberate reflection,
you think you cannot live comfortably with me, I have given instructions to
Messrs. Barton and Hadley to remit you, wherever you may choose to
reside, eight hundred pounds a year. Upon this you can live in all comfort in
France. With every wish for your happiness,
"Believe me, my dear Wife,

"Yours affectionately,
"H. S. MEREDITH VYNER."
This letter never reached Mrs. Vyner. Believing that her application had
been treated with the silent scorn it deserved, she left the town, and toiled
her way to a neighbouring town, where a young woman, formerly one of
her maids, kept a small magazin de modes, and offered a temporary asylum.
There she endeavoured to earn a subsistence by teaching English; and at
first, success crowned her efforts; but having been recognised by an English
traveller spending a few days there, the fact of her having eloped from her
husband became bruited about, and all her pupils left her.
She was forced to quit the place, and to seek refuge and oblivion in
Paris. What bitter humiliations, and what severe trials, she had there to
undergo may be readily conceived. A mystery hangs over her fate; she was
seen once on the Boulevard du Temple, miserably dressed, and so aged by
suffering, that every trace of beauty had disappeared; but nothing has since
been heard of her.
Concerning the other persons of this tale, I have few particulars to add.
Mrs. Langley Turner has married Lord ——, and now gives as many
parties as before, only they are fearfully dull: perhaps because so much
more "select;" for it is a very serious truth, that your high people are
anything but entertaining.
Frank Forrester has seen many ups and downs; but the last time I saw
him, his cab splashed me with mud as I lounged down St. James's-street.
Rose has two chubby children, who promise to have the spirit of the
mother; they keep the nursery in a constant uproar!
Violet has one large, dark-eyed, solemn boy, who, though not a
twelvemonth old, looks at you with such thoughtful seriousness, that you
are puzzled what to say to him; and I refrained tickling him under the chin,
lest he should consider it as unseemly trifling; and as to talking to him
about his tootsy-pootsies being vezzy pitty—that never could enter the
mind even of the most ignorant nurse.
Marmaduke continues his political career with dignity and success;

Violet cheering him on, and loving him with all her large heart, so that Rose
declares, except herself and Julius, she knows of nobody so happy as these
two;—Violet disputes the exception.
And Captain Heath? The narration of his happiness is a bonne bouche I
have reserved for the last.
The whole family were at Wytton Hall, and though so happy in

themselves, frequent were their inquiries as to when the captain was to
come down—only one person never asked that question, and that person
was Blanche; the reason of her silence I leave to be guessed.
He came at last; came not to see the mild, affectionate greeting of a

sister from his much loved Blanche, but the delight, embarrassment, and
pain of one who loved and dared not avow it. He had been absent three
months. During that absence, she discovered her love. At first, she merely
felt a certain weariness; next, succeeded melancholy; next, impatience to
see him; and finally, the yearning of her heart proclaimed she loved him.
Yes: such is the imperfection of poor human nature, that it cannot reach
the circulating library standard; with our best efforts to be forlorn and
disconsolate, we will accept of society and consolation; with the strongest
idea of the virtue of constancy, a loving heart cannot but love!
Blanche was embarrassed when she saw her lover again! and he, poor
fellow! was too modest to understand her embarrassment. In vain did they
ramble about the grounds together, not a syllable did he breathe of his love.
Blanche began to be almost fretful.
One morning they were playing with Rose Blanche together, and the
little toddler having climbed upon his knee, declared she intended to
"mazzy Captain Heath some day;" upon which her mama said a leetle
pettishly: "No, my darling, Captain Heath is not a marrying man. He is to
be an old bachelor."
Captain Heath made no reply, for he could not tell her why he was
condemned to be an old bachelor.
Yet, that very afternoon, as they were strolling through the wood
together, and the conversation turned upon her child, he was moved by
some mysterious impulse, to take her hand in his, and with a faltering voice,
to say,—
"Blanche ... dearest Blanche ... forgive me for what I am now going to
say ... refuse the offer if you will, but do not be offended with me for
making it ... Your child, Blanche, is growing up ... She will soon need a
better protector than even your love ... she ... I hope you will not
misunderstand me ... I know you cannot love me ... though I have loved you
so many years ... but I am grown used to that ... I have loved you, Blanche,
for years, scarcely ever with the hope of a return, and latterly, with the
certainty, that my love was hopeless ... But when I offer myself as a
husband ... as a protector to you, and to your child ... I do that which, if it
would not pain you, I feel to be right ... I want to have a husband's authority
for devoting my life to you. I do not ask your love...!"
Her head was turned away, and her eyes were filling with tears—tears
of exquisite pain, of inexpressible delight; as these words, "I do not ask
your love," thrilled through her, she suddenly turned and looked him full in
the face.
Was it her blushing tremor, was it her undisguised tenderness which

spoke so clearly to the yearning heart of her lover? I know not. Love has a
language of its own, untranslatable by any words of ours, and that language
in its mystic, yet unequivocal voice, told Captain Heath, that he was loved.
Printed by STEWART and MURRAY, Old Bailey.

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Computational Epidemiology From

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Bayesian Disease Mapping : Hierarchical Modeling in

Disease Mapping From Foundations to Multidimensional

Decision making Analysis and Optimization Modeling of

Lecture Notes in Computational Intelligence and

A Relevance-Theoretic Approach to Decision-Making in

Contemporary Marketing Strategy: Analyzing Consumer

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Large Group Decision Making Creating Decision Support

More information about this series at http://www.springer.com/series/11944

ISSN 2366-0988 ISSN 2366-0996 (electronic)

© Springer Nature Switzerland AG 2020

What Can We Learn from COVID-19?

To see a World in a Grain of Sand

William Blake (1757–1827) Auguries of Innocence

nation-states, political ideologies, religions, and special interests, and coexisting

Hong Kong Jiming Liu

Jiming Liu is extremely grateful for the rigorous foundation development in

Hong Kong Jiming Liu

3.3.2 Effects of Vaccination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

ACIP Advisory Committee on Immunization Policy

S Population in susceptible compartment

ρ(K) Top eigenvalue of K

© Springer Nature Switzerland AG 2020 1

1.1 Methodological Paradigms

Various methodologies have been developed to address a wide range of challenges

Fig. 1.1 Major methodological paradigms in infectious disease epidemiology

transmission, by modeling and analyzing the patterns of transmission and quan-

1.2 Recent Developments

Another important source of data is Internet-based media, which can serve as

1.3 Infectious Diseases and Vaccination

1.4 Objectives and Tasks

In this book, we examine the dynamics of disease transmission in a host population,

investigate individuals’ acceptance of vaccination, we present decision models to

1.4.1 Modeling Infectious Disease Dynamics

As aforementioned, the dynamics of disease transmission depend on many disease-

1.4.2 Modeling Vaccine Allocation Strategies

most effectively reduce disease transmission; crucially, this requires knowledge

1.4.3 Modeling Vaccination Decision-Making

In a voluntary vaccination program, individuals’ decisions on whether or not to

vaccination decision-making would provide useful information for public health

1.4.4 Modeling Subjective Perception

A larger value of disease reproduction number will enhance the proportion of

In this book, we develop a computational modeling approach to evaluate and guide

awareness by carrying out simulation-based experiments to examine the time course

"I am not dead yet!" he said, as if he had interpreted her thoughts.

She trembled slightly. With a sneer, he closed his eyes again.

WYTTON HALL, 2nd August, 1845.

"MY DEAR WIFE,

"We have both need of forgiveness—you have mine. I know I am not

Durum! sed levius fit patientia

"Believe me, my dear Wife,

Marmaduke continues his political career with dignity and success;

The whole family were at Wytton Hall, and though so happy in

He came at last; came not to see the mild, affectionate greeting of a

Was it her blushing tremor, was it her undisguised tenderness which

Printed by STEWART and MURRAY, Old Bailey.