Workshop on Mathematical Models for the Study of the Infection Dynamics of Emergent and Re-emergent Diseases in Humans
(22 - 26 Oct 2007)
~ Abstracts ~
Singapore modelling of pandemic
flu
Vernon Lee, Public Health Physician, Singapore
The three pandemics of the 20th Century resulted in
substantial worldwide impact and there is concern about the
impact of the next pandemic. To influence policy decision
making in developing preparedness plans, modeling is an
important tool to provide quantitative and visual
representations on the possible impact of the future event.
For example, economic models enable policy makers to
consider the cost-effectiveness of various strategies.
Anti-viral treatment in Singapore was shown to be
cost-effective compared to no action across the board, while
mass prophylaxis was cost-effective only in high-risk
sub-populations. Models on disease spread also describe the
pandemic’s impact, and suggest how interventions may reduce
the impact. For example, treatment and optimal prophylaxis
of healthcare workers, together with reducing their
exposures through infection control, will prevent
absenteeism. Many preventive and control measures such as
school closures, social distancing, travel restrictions, and
other interventions were used in previous pandemics to
varying effectiveness levels. Mathematical models suggest
how these public health measures may affect the pandemic’s
spread. These models, together with economic and feasibility
considerations, assist policy makers in determining the
possible effectiveness of different public health measures.
As we prepare for a future pandemic, modeling tools together
with historical lessons will provide us with evidence for
action.
Modelling of antibiotic
resistance: R0 for MRSA and options for control
Martin Bootsma, Utrecht University, The Netherlands
I will discuss to what extent the spreading capacity for
different strains of methicillin-resistant Staphylococcus
aures (MRSA) is known and what efficient options for control
are for different strains and why MRSA control work in some
countries but not in others.
Translating statistics and
mathematics into health protection: Hong Kong’s baptism
by fire since 1997
Gabriel Leung, The University of Hong Kong
Until recently, infectious disease surveillance data had
rarely been specified or used to directly inform policy
beyond simple statistical analyses to aid routine outbreak
investigations. At the same time, mathematical models of
disease transmission and control had not been taken into
serious consideration by policymakers. The 1997 H5N1 and the
2003 SARS epidemics jolted Hong Kong, situated in the
southern Chinese influenza basin and a proven epicentre of
emerging infections, into proactive consolidation of a
robust infrastructure that aims to inextricably link
together original research and the day-to-day reality of
health protection. Reviewing empirical findings from our
systematic approach to generating relevant research
questions, formulating hypotheses and specifying analyses, I
summarise our strategic development and realignment of
academic resources towards applied research in mathematical
biology and statistical epidemiology that at once satisfy
our core mission of scientific innovation and the service
imperative of public health action.
Transmission trees as causal
models of epidemics
Jacco Wallinga, National Institutes of Public Health and
the Environment, The Netherlands
Mathematical epidemic models, deterministic or
stochastic, typically describe the unobservable events of
the infection process, such as making contact, being
infected, becoming infectious and acquiring immunity. The
conceptual clarity of such models comes at a price: it is
hard to relate the value of key epidemiological variables,
such as reproduction numbers and generation times, directly
to observable events, such as for example the distribution
of times of symptom onset and variation in DNA/RNA sequences
of isolated pathogens.
Here, we represent the cases and the infectious relations
between them during an epidemic as a directed acyclic graph,
and we call such a graph a transmission trees (or
transmission forests). Because infectious relations have a
causal interpretation, a transmission tree can be viewed as
a causal model of an epidemic. The structure of the
transmission tree determines the likelihood of observing
attributes of the epidemic, such as the distribution of
times of symptom onset and variation in pathogen molecular
sequences. Therefore, we can use these observable attributes
directly to assign a likelihood to all possible transmission
trees that are consistent with an observed epidemic. Perhaps
surprisingly, this likelihood-on-transmission-tree-space can
yield simple estimating equations for real-time monitoring
of key epidemiological variables, such as reproduction
numbers and generation times.
The tempo and mode of evolution
of mosquito transposable elements as revealed by molecular
phylogenies
Claudio Struchiner, PROCC, FIOCRUZ, Rio de Janeiro,
Brazil
We here present estimates of key parameters guiding
transposable elements(TE) invasion dynamics as revealed by
molecular phylogenies reconstructed from Anopheles gambiae
and Aedes aegypti mosquito genome projects. Our analysis
follows four steps: (i) mining the two mosquito genomes
currently available in search of TE families; (ii) fitting,
to selected families found in (i), a phylogeny tree under
the general time-reversible (GTR) nucleotide substitution
model with an uncorrelated lognormal relaxed clock (UCLN)
and a non-parametric demographic model; (iii) fitting a
non-parametric coalescent model to the tree generated in
(ii); (iv) fitting parametric models motivated by ecological
theories to the curve generated in (iii).
The demographic component implied by this approach is of
great epidemiological interest since it can help in
identifying the molecular and ecological approximate
conditions under which transposable elements will spread
through a host population. By exploring the analytic
potential of coalescence models fitted to data generated by
genome projects, we address the lack of empirical data
against which putative models developed in the past could be
fitted and checked.
Statistical methods for
estimating the incubation distribution of SARS
Ben Cowling, The University of Hong Kong
Accurate and precise estimates of the incubation
distribution of novel, emerging infectious diseases are
vital to inform public health policy decisions. Alternative
methods of estimating the incubation distribution of an
infectious disease are discussed, allowing for
interval-censored exposure times. The methods are applied to
data on patients infected with Severe Acute Respiratory
Syndrome (SARS) in Hong Kong, Toronto, Taiwan and Beijing.
Finally, regression models are used to investigate potential
heterogeneities in the incubation period between patient
subgroups.
Pandemic influenza forecasting:
does past performance indicate future performance?
Julian Wei-Tze Tang, Chinese University of Hong Kong
All mathematical models require some basic assumptions,
which may govern the outcome and final conclusions derived
from such models.
In this talk, using the example of a recently published
model of the 1918 influenza pandemic, I will highlight some
of the problems inherent in extracting data from older
published infectious diseases outbreak data – exactly the
type of data used from previous influenza pandemics to
attempt to predict the behaviour of any future influenza
pandemic. These problems are more of a clinical/ diagnostic
nature, and may not be apparent to mathematicians without
any clinical background. There are always difficulties with
exactly how such outbreaks are identified, how potential
cases and contacts are ascertained, and how much impact any
interventions may have on the final outcome of the outbreak.
Using this example, I will illustrate how and why doubts may
be cast upon the values of R (or R0) estimated for past, and
predicted for future influenza pandemics.
Time evolution of disease spread
on networks with degree heterogeneity
Babak Pourbohloul, University of British Columbia,
Canada
Two crucial elements facilitate the understanding and
control of communicable disease spread within a social
setting. These components are the underlying contact
structure among individuals that determine the pattern of
disease transmission; and the evolution of this pattern over
time. Mathematical models of infectious diseases, which are
in principle analytically tractable, have taken two general
approaches in incorporating these elements. The first
approach, generally known as compartmental modeling,
addresses the time evolution of disease spread at the
expense of simplifying the pattern of transmission. On the
other hand, the second approach uses contact networks to
incorporate detailed information pertaining to the
underlying contact structure among individuals. While
providing accurate estimates on the final size of
outbreaks/epidemics, this approach, in its current
formalism, disregards the time progression during outbreaks.
So far, the only alternative to integrate both aspects of
disease spread simultaneously has been to abandon the
analytical approach and rely on computer simulations.
Powerful modern computers can perform an enormous number of
simulations at an incredibly rapid pace; however, the
complex structure of “realistic” contact networks, along
with the stochastic nature of disease spread, pose a serious
challenge to the ability of the computational techniques to
produce robust, real time analysis of disease spread in
large populations. An analytical alternative to this
approach is lacking. We offer a new analytical framework,
which incorporates both the complexity of contact network
structure and time progression of disease spread.
Furthermore, we demonstrate that this framework is equally
effective on finite- and “infinite”-size networks.
Four examples of Bayesian methods
in the analysis of infectious disease data
Ben Cooper, Health Protection Agency, UK
In recent years there has been a rapid growth in interest
in the application of Bayesian methods in infectious disease
epidemiology. Much of this interest has stemmed from a
recognition of the value of Markov chain Monte Carlo
algorithms in allowing analyses that would have been
impossible using more conventional approaches. Incorporation
of prior information or beliefs into the analysis has often
been a secondary consideration or neglected entirely.
There are many applications, however, where there are good
reasons for adopting a fully Bayesian approach and
incorporating prior information into the analysis. In this
talk four examples are presented: estimation of key
parameters for SARS transmission; quantifying the importance
of different routes of HIV transmission; real-time
forecasting of pandemic influenza; and analysis of hospital
infection data. These examples illustrate a range of
simulation-based inferential strategies for obtaining
posterior distributions.
Dynamic network modeling and its
impact on disease propagation
Kah Loon Ng, National University of Singapore
In the modeling of infectious disease spread within
explicit social contact networks, previous studies have
predominantly assumed that the effects of shifting social
associations within groups are small. These models
have utilized static approximations of contact networks. We
examine this assumption by modeling disease
spread within dynamic networks where associations shift
according to individual preference based on three
different measures of network centrality.
This is joint work with Nina Fefferman.
Strategies for controlling
antiviral resistance during the next influenza pandemic
Joseph Wu,The University of Hong Kong
Many countries are stockpiling antivirals (primarily oseltamivir) to mitigate the impact of the next influenza pandemic. Such an unprecedented massive use of antiviral may cause rapid emergence of antiviral resistance, in which case the effectiveness of antiviral stockpiles will be substantially attenuated and billions of dollars invested in antivirals will be virtually wasted. We present strategies that may reduce this threat of antiviral resistance.
The continued mystery of
regular, old, annual flu
Nina Fefferman, Rutgers University and Tufts
University, USA
Though incredibly common, and responsible for significant
mortality among children and the elderly, even in highly
developed areas of the globe, influenza still remains
incredibly poorly understood. Theories about basic
etiology, viral antigenic drift, strain mutation, and immune
memory have still failed to fully characterize all the
complexities of seasonal and annual patterns of incidence.
In this talk, we will examine some of the current theories
to explain observed seasonality in influenza incidence,
defining some basic epidemiological properties of the
disease along the way. We will end by focusing specifically
on some new theories about how social contact structure
could play its own role in observed patterns of incidence.
Bacterial antibiotic resistance
surveillance in Singapore
Li Yang Hsu, National University of Singapore
The development and spread of antibiotic-resistant
bacteria is an emerging international public health issue.
Methicillin-resistant Staphylococcus aureus epidemics in
both community and hospital settings are now well described
and studied. However, Gram-negative bacterial resistance has
had a lower "profile" yet present a more serious threat in
the long term. Rising rates of cephalosporin resistance have
been observed in Enterobacteriaceae isolates from the
community, and carbapenem resistance among common nosocomial
Gram-negative pathogens such as Enterobacteriaceae,
Pseudomonas aeruginosa, and especially Acinetobacter
baumannii have reached critical levels in many developed
countries including Singapore, which has one of the highest
rates of gram-negative antibiotic resistance in the world.
Currently, two out of every 100 patients admitted to a
public sector hospital in Singapore will develop an
infection caused by these drug-resistant bacteria, of which
almost 5% are untreatable save with highly expensive and/or
toxic agents. Because of their impact on mortality and
healthcare costs, antibiotic-resistant bacterial infections
negatively affect Singaporeʼs goal for cost-effective
healthcare delivery, and hamper our efforts to be a regional
medical hub. Yet relatively little has been done to study
the spread of these organisms locally, and models for this
internal epidemic, as well as for intervention and control
measures, have not been developed. There is considerable
scope for further work in this area.
A gravity model for metapopulation dynamics of infectious diseases
Yingcun Xia, National University of Singapore
Infectious diseases provide a particularly clear illustration of the spatio-temporal underpinnings of consumer-resource dynamics. The paradigm is provided by extremely contagious, acute, immunizing childhood infections. Partially synchronized, unstable oscillations are punctuated by local extinctions. This, in turn, can result in spatial differentiation in the timing of epidemics, and -- depending on the nature of spatial contagion -- may result in travelling waves. Measles are one of a few systems documented well enough to reveal all of these properties and how they are affected by spatio-temporal variations in population structure and demography. Based on a gravity coupling model and a time series susceptible-infected-recovered (TSIR) model for local dynamics, we propose a metapopulation model for regional measles dynamics. The model can capture all the major spatio-temporal properties in pre-vaccination epidemics of measles in England and Wales.
The quest for the epidemiological
foundations of STI models: insights from resistant gonorrhea
in the UK
Mark Chen, Tan Tock Seng Hospital, Singapore
In recent years, endemic transmission of Quinolone
Resistant Neisseria Gonorrheae (QRNG) has been documented in
multiple regions across the UK. The spread of these
resistant strains has been rapid, and yet extremely uneven.
While some population groups experienced widespread
transmission of QRNG, other populations have been relatively
spared; moreover, the incidence of QRNG in different
epidemiological sub-groups has also shown a differential
response following changes in treatment guidelines. We
suggest that these observations challenge various aspects of
the classical model of STI transmission originally proposed
by Hethcote and Yorke. We hence embarked on a quest to
rediscover the epidemiological foundations for STI models
based on our insights from gonococcal transmission. We
present work to show several aspects of importance to
modeling gonorrhea that have often been neglected, both in
classical deterministic models, as well as in network and
individual-based models; these include the importance of
modeling the “gap” between partnerships, the need to
consider possible metapopulation structures, and the role of
stochasticity. We then apply some of these concepts back to
the problem of resistant gonorrhea, to show their relevance
in explaining the epidemiology of QRNG.
Comparing hospital and
non-hospital rates of infection of SARS in Singapore
Anthony Kuk, National University of Singapore
Using a two-environment proportional intensity model, it
is shown that the rate of infection in a hospital
environment without isolation is 30 times higher than that
in a non-hospital environment. The model used allows for
heterogeneity in individual infectiousness and confounding
between infectiousness and hospitalization time. When
exposure history is taken into account, it is shown that
four of the five persons commonly regarded as
“superspreaders” actually do not have unusually high
individual infectiousness. The observed superspreading
events seem to have been caused by environmental rather than
biological factor. If time allows, I will also discuss how
the ECME algorithm (a variant of the expectation
maximization algorithm) can be used to estimate the rate of
infection nonparametrically as a function of time.
Introduction to developments in mathematical modelling
Eduardo Massad, University of São Paulo, Brazil
An overview of some of the theoretical develoments on modeling the epidemic processes will be discussed, along with some of my own research progresses
Vector-borne disease: research questions
Eduardo Massad, University of São Paulo, Brazil
A review of the models related to vector-borne diseases will be presented, highlighting the current epidemiological questions related to global warming and its impact on those infections
Why were we unable to predict the 2007 Dengue outbreak in Singapore?
Eduardo Massad, University of São Paulo, Brazil
This question will be examined at the light of our model for dengue published in the Epidemiology and Infection (2007).
The relationship between antibiotic use and antibiotic resistance; Questions more than answers....
Paul Anantharajah Tambyah, National University of Singapore
Antibiotic resistance is a global problem worldwide. Recent news reports have highlighted the extent of the problem with the mortality associated with antibiotic resistant bacteria in many countries exceeding HIV disease, tuberculosis and many other more widely publicised emerging and re-merging infectious diseases. It is widely believed that antibiotic resistance is the result of selection of antibiotic resistant microorganisms due to selection pressure from the heavy use of antibiotics. While this would appear intuitive, there has not been a clear cut formula to ensure that the right amount of antibiotics are used appropriately without selecting for the emergence of antibiotic resistant pathogens. This is complicated further by the fact that other factors including host factors and infection control measures which reduce the transmission of antibiotic resistant pathogens come into the mix. Furthermore, there are also questions about the role of specific antibiotics in the selection of antibiotic resistance and the impact of the duration of antibiotics on the selection of antibiotic resistance. There is clearly an urgent need for a major research effort to understand the relationship between antibiotic use and antibiotic resistance to address many of these quantitative issues to generate models which can be tested in clinical situations.
Random effects model: An application to spatial epidemiology
Arul Earnest, The University of Sydney, Australia
The Conditional Autoregressive (CAR) model is widely used in small-area ecological studies to map outcomes measured at some areal level and to examine associations with covariates. Most of these applications are in the field of disease mapping. In recent times, researchers have started to apply these models on infectious disease data. This talk will present some of these studies, discuss the methodological constraints and offer some possible solutions.
Is there a seasonal pattern for infectious diseases, including acute respiratory illnesses, in Singapore?
Li Wei Ang, Ministry of Health, Singapore
Trend and seasonality are important aspects of disease manifestation as well as clues to the aetiology of diseases. We seek to understand whether seasonal patterns exist in selected infectious diseases, including acute respiratory illnesses, in Singapore which has a tropical climate with limited variation in temperature. We did a retrospective study of monthly observations of selected infectious diseases, which included acute respiratory illnesses (ARI), chickenpox, hand-food-mouth disease (HFMD), dengue, melioidosis and mumps, aggregated from weekly polyclinic attendances for ARI, and MD-131 notifications for the other diseases during the 5-year period (2000 – 2004). Time series analyses were carried out using the multiplicative decomposition method, and we applied various methods to examine seasonal variability.
