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13)
Mathematical
immunology and infectious disease
Principal organiser: Dr. Jane Heffernan
Short
summary:
The
aim of mathematical immunology is to aid in the understanding
of the complexities of the immune system through mathematical
modeling. In the context of infectious diseases, mathematical
immunology is concerned with studying the dynamics of an infectious
agent as it spreads from cell to cell within an infected host.
Insights into the mechanisms of disease progression are acquired
by focusing on the interactions between a pathogen and the
immune system. This type of study has implications for public
health, providing a rational basis for vaccine distribution,
drug delivery, and suppression of drug resistance. In this
minisymposium, new mathematical models describing the dynamics
of the immune system and infectious disease dynamics will
be highlighted. Models combining immunological and epidemiological
characteristics will have a special focus. Such models have
great potential to provide new insights into the mechanism
of pathogen growth, suggest new lines of research, and produce
guidelines for the development of new drug therapies or vaccination
protocols.
Confirmed
Speakers:
Catherine
Beauchemin (Ryerson)
Predicting
the potential impact of a cytotoxic T-lymphocyte HIV vaccine:
How often should you vaccinate and how strong should the vaccine
be?
To
stimulate the immune system’s natural defenses, a post-infection
HIV vaccination program to regularly boost cytotoxic T-lymphocytes
has been proposed. We develop a mathematical model to describe
such a vaccination program, where the strength of the vaccine
and the vaccination intervals are constant. We apply the theory
of impulsive differential equations to show that the model
has an orbitally asymptotically stable periodic orbit, with
the property of asymptotic phase. We show that, on this orbit,
the vaccination frequency can be chosen so that the average
number of infected CD4+ T cells can be made arbitrarily low.
We illustrate the results with numerical simulations and show
that the model is robust with respect to both the parameter
choices and the formulation of the model as a system of impulsive
differential equations.
The
dynamics of T-cell receptor repertoire diversity following
thymus transplantation for DiGeorge Anomaly
The
immune responses to infectious agents involves the presence
and maintenance of a large number of T cells with highly variable
antigen receptors. We explain the mechanisms underlying the
establishment and maintenance of T-cell receptor diversity
and T cell population homeostasis using mathematical models
and statistical analysis of data from DiGeorge syndrome patients
undergoing thymus transplantation. We provide insight into
how competition for specific and non-specific limiting resources
leads to establishment of a mature and diverse T cell repertoire.
We note that the T lymphocyte repertoire is not dominated
by a few best-competing clones, but populated by a high variety
of T cell lineages.
Speaker:
Catherine Beauchemin
Theoretical
modelling of influenza viral infections
Since
the influenza virus was first isolated in 1933, much attention
has been given to its structure, its genome, the immune response
it elicits, vaccines to protect against it, and its epidemiology.
Information concerning the kinetics of influenza during an
infection within an individual, however, is limited. For example,
key parameters such as the rate at which flu-infected cells
produce virus, the fraction of these viruses that are productively
infectious, are still unknown. Mathematical and computer models
have been proposed to try and answer these questions. In this
talk, I will review what we understand of influenza dynamics.
I will then present various mathematical and computational
models which have been developed in order to investigate specific
aspects of influenza infections.
Measles
Vaccination and Waning Immunity
In
spite of advances in medical technologies, the predicted eradication
of certain pathogens by vaccination has not been achieved
(i.e. measles). Mathematical epidemiological studies have
shed some light on this, however, there remain many cases
in which epidemiological models have failed to precisely predict
the spread of the disease at the population level. In-host
models can provide quantitative predictions of immune status
and can thus offer valuable insights into the factors that
influence transmission between individuals and the effectiveness
of vaccination protocols with respect to individual immunity.
We have developed an in-host model of measles infection (carefully
parameterized to match the available data). We have found
that both the /in-host /dynamics between a pathogen and the
immune system and the immune status of individuals should
have profound impacts on the prevalence of measles in a population
(i.e. a correlation between immunity and transmissibility).
To explore the effect of acquired immunity on measles epidemics,
we have developed a comprehensive model of measles infection
in which both immunological and epidemiological considerations
are included. The comprehensive model predicts large scale
oscillations of measles if vaccination levels are high and
acquired immunity wanes in a moderate period of time. It also
predicts far larger epidemics than previously predicted by
standard models if measles is introduced into a population
after a long disease free period. These results have clear
implications for public health protocols.
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