Workshop on Modeling the Rapid Evolution of Infectious Diseases:
Epidemiology and Treatment Strategies (back to
home page)
May 14-17, 2005
Abstracts
Troy Day, Queens University
The Evolution of Endemic and pandemic Influenza
I will discuss some theoretical work that explores the evolution
of endemic strains of influenza as well as the evolution of periodic
influenza pandemics. Two main long-term goals are to:
(1) explore the potential evolutionary consequences of flu vaccines,
and
(2) explore the extent to which genetic reassortment is a crucial ingredient
in the occurrence of pandemics.
David Earn, McMaster
Emerging infectious diseases: ecology, evolution and control
Zhilan Julie Feng, Purdue
Dynamics of two-strain influenza with isolation and partial immunity
A mathematical model is used to study the evolution of influenza
A pathogens driven by coevolutionary interactions between human hosts
and competing strains of the virus. We establish that cross-immunity
and host isolation lead to recurrent outbreaks in the two-strain system.
Sub-threshold conexistence is possible even when the reproductive number
of one stain is below one. Conditions that guarantee a winning type
or coexistence are established in general. Oscillatory coexistence is
established via Hopf-bifurcation theory and confirmed via numerical
simulations.
Fabio Milner, Purdue
What is missing in TB modeling?
We shall present a detailed description of what is known about the disease
and a historical perspective of mathematical modeling of TB. We shall
present theoretical results about the models and mention epidemiological
consequences. Finally, we shall focus on what is not known about TB
and speculate about possible new models.
Patrick Nelson, University of Michigan
Back to the basics to improve our ability to model infectious diseases
Infectious disease modeling has become one of the hottest topics in
mathematical biology, but as I will show many of the models are suspect
as certain basic mathematical techniques are overlooked. I will focus
on models for HIV dynamics and show the ways that we can improve upon
our modeling of diseases. For instance, numerous models have been used
to predict parameters from patient data in HIV but applying a simple
technique from algebra, called model identifiability, I have been able
to show that the models we have been using are not identifiable to the
parameters. Hence, we have begun to explore ways of putting modeling
of ID on solid ground using techniques such as identifiability, sensitivity,
and selection; also techniques from statistical methods such as bootstrapping
and monte carlo.
I will comment on the progress that we have been making in these areas
and also comment on improvements that we have found in modeling using
delay differential equations
Robert J. Smith, Erin N. Bodine, David
P. Wilson, Sally M. Blower(UCLA)
The epidemiological impact of low efficacy HIV prevention methods.
New methods of preventing or reducing HIV transmission hold great hope
for containing the spread of the disease. However, such methods are
likely to have poor efficacy, at least initially, and may result in
a net increase in infections.We explores two low efficacy methods and
their impact on the spread of the virus. For many years, the holy grail
of HIV research has been the vaccine. The World Health Organisation
recently declared that a vaccine with efficacy as low as 35% would be
acceptable. Vaccines that are on the market initially are most likely
to be disease-modifying vaccines that allow for reduced transmission,
but give additional years of life to the patient. We show that disease-modifying
vaccines that do not substantially reduce the
per-partnership transmission probability may ultimately lead to a net
increase in secondary infections. Furthermore, if risky behaviour changes,
due to the perception that a vaccine is fully protective, the epidemiological
impact could be severe. Due to the difficulty in vaccine development,
research has recently turn to microbicides - an anti-HIV gel that can
be applied topically to the vagina, the rectum or added to condoms.
While microbicides are not expected to replace condoms, their ease of
use may have the net effect of reducing condom use in favour of a much
less effective microbicide. We show that, unlike vaccines, low efficacy
microbicides are likely to be beneficial, so long as they are used with
sufficient frequency. Thus, the introduction of low efficacy prevention
methods such as vaccines and microbicides should be tightly linked to
behavioural intervention strategies.
P. van den Driessche, Department of Mathematics
and Statistics, University of Victoria
Patch Models for Disease Spread
To account for spatial heterogenity, a general disease transmission
model is formulated, with travel rates between patches depending on
disease status. An expression for the basic reproduction number $R_0$
is derived, and the disease-free equilibrium shown to be globally asymptotically
stable if $R_0 <1$. For a disease with short exposed and immune periods
(e.g., gonorrhea) in an environment with 2 patches, the model is analyzed
in more detail. In the case that travel rates of infectious and susceptible
individuals are the same, $R_0$ is a sharp threshold, with the disease
approaching an endemic equilibrium in both patches if $R_0>1$. If
infectious individuals are too sick to travel or are restricted in travel,
then the disease can become endemic in one patch, but die out in the
other. Results illustrate that a patchy environment and travel between
patches can influence disease spread in a complicated way.
Hulin Wu, Department of Biostatistics and Computational
Biology, University of Rochester
Can We Model/Simulate AIDS Clinical Trials and Predict Its Outcomes?
Computer simulations have been evolved rapidly into all areas of scientific
research and our daily life. In the past decade, effort has been made,
by pharmaceuticals and academic researchers, to simulate is very complex.
Computer simulations may help clinicians to select the optimal treatment
strategies. We have made our effort to develop mathematical models,
statistical methods and computer codes to simulate the treatment response
of antiretroviral therapy. In our models, we consider the drug exposure,
drug resistance and adherence as well as biological mechanisms of HIV
infection. The first step, we need to
identify the unknown parameters in the developed models and simulation
systems. We employ hierarchical Bayesian modeling approach for this
purpose. We implemented our Bayesian approach using the Markov chain
Monte Carlo (MCMC) procedure consisting of a series of Gibbs sampling
and Metropolis-Hastings algorithms. The convergence of the MCMC algorithms
was carefully monitored. Secondly, we need to use the estimated parameters
to predict the response of antiviral treatment for different scenarios.
We will discuss the methodologies involved in the predictions.
Examples based on AIDS clinical trial data will be presented to illustrate
the methodologies.
Jianhong Wu, Department of Mathematics
and Statistics, York University
Lessons Learned from SARS and the 1918 Influenza Pandemic about
the Age of Infection: Its Critical Role and Modeling
This is based on the joint work with Glenn Webb (Vanderbilt University),
Yin Hsieh (National Chung Hsing University), Chwan-Chuan King (National
Taiwan University), Jiunn-Shyan JulianWu (Center for Disease Control)
and Chuan Jen Chyan (Tamkang University).
The objectives of the project are to construct a model to describe the
effects of viral-specific interventions on the transmission dynamics
of SARS and influenza, using age of infection of infected individuals
to describe the pre-infectious, infectious, pre-symptomatic, and symptomatic
periods. We considered two special cases where the infectious and symptomatic
periods coincide, and where the infectious period precedes the on-set
of symptoms.
Back to top
Back to Workshop page
