July 30-August 2, 2008
Society for Mathematical Biology Conference

hosted by the Centre for Mathematical Medicine, Fields Institute
held at University of Toronto, Medical Sciences Bldg


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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:

Robert Smith? (Ottawa)
Stanca Ciupe (Duke)
Catherine Beauchemin (Ryerson)
Jane Heffernan (York)


Speaker: Robert Smith?
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.

Speaker: Stanca Ciupe
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.

Speaker: Jane Heffernan
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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