by Jane Heffernan
Centre for Disease Modelling, York University
Coauthors: Seyed Moghadas, Centre for Disease Modelling, York University

Minisymposium Abstract:
Multidisciplinary has become the watchword of modern biology. The integration of several disciplines has created a rapidly growing multidisciplinary field of research, the so-called “Mathematical Immunology”. In simple terms, mathematical immunology attempts to uncover the biological mechanisms underlying the dynamics of pathogen-host interactions by employing mathematical, statistical, and computational models. In recent years, the field of mathematical immunology has blossomed with the availability of large and rich datasets due to the genomics revolution and increased sensitivity of laboratory and clinical tools; the development of mathematical tools capable of encapsulating complex nonlinear systems; and the advancement in computing power for large-scale calculations, simulation, and visualization. Interest in the computer simulation of biological processes to reduce complications incurred in human and animal research (such as ethical and practical considerations, costs, and risks) has also increased attention to this field. Although not old, mathematical immunology has contributed greatly to the understanding of within-host dynamics of many diseases that have been the bane of humanity for many centuries, such as Tuberculosis (TB), Influenza, Measles and Malaria, and infections that have been discovered in the past few decades including the Human Immunodeficiency Virus (HIV), and Hepatits B and C viruses (HBV and HCV).
This symposium provides an opportunity to present important contributions to the field of mathematical immunology that have been made by several members and collaborators of the York University Centre for Disease Modelling. We hope that the presentations and interactions during this symposium will lead to further collaborations in the subject area.

Jane Heffernan, York University
A two compartment model for HBV/HCV

HBV and HCV can cause chronic infections of the liver. Liver transplantation was originally thought to be a cure of chronic HBV or HCV, however, reinfection of the new liver graft would occur. This points to a second compartment of infection. We have developed a mathematical model of HBV or HCV in-host including a second compartment of infection. A backward bifurcation is found relating to production rates of the virus and the death rates of infected cells in both compartments of infection.

Robert Smith?, University of Ottawa
Modelling Mutation to a Cytotoxic T-lymphocyte HIV Vaccine

Abstract: Resistance to a postinfection HIV vaccine that stimulates cytotoxic T-lymphocytes (CTLs) depends on the relationship between the vaccine strength, the fitness cost of the mutant strain, and the rate of mutant escape. If the vaccine is strong enough, both strains of the virus should be controlled by administering the vaccine sufficiently often. However, if escape mutation to the vaccine occurs, then either the wild type or the mutant can outcompete the other strain. Imperfect adherence may result in the persistence of the mutant, while fluctuations in the vaccination time - even if no vaccines are missed - may result in the mutant outcompeting the wild type.

Glenn Webb, Vanderbilt University
Mathematical Models of Antibiotic Resistant Bacterial Infections in Hospitals

The development of drug-resistant strains of bacteria is an increasing threat to society, especially in hospital settings. Many antibiotics that were formerly effective in combating bacterial infections in hospital patients are no longer effective due to the evolution of resistant strains. The evolution of these resistant strains compromises medical care worldwide. Recent examples are vancomycin-resistant enterococci epidemics and methicillin-resistant staphylococci epidemics in US and Canadian hospitals. The objectives of this work are to investigate mathematical models to analyze the dynamic elements of patient in-host acquisition and transmission of non-resistant and resistant bacteria strains in hospital settings, and to provide understanding of measures to mitigate these epidemics.

Amy Hurford (York University)
Does the risk of inducing autoimmunity select against molecular mimicry in parasites?

Parasites that are molecular mimics capitalize on a host’s natural aversion to inflict self-harm and are more likely to evade the immune system and be transmitted. However, in the case of infection-induced autoimmunity, the immune response is to both normal host cells and to the parasite, and so parasite strains that are molecular mimics no longer have a selective advantage. In this talk, I will show that the evolution of molecular mimicry in parasites is selected against when there is a substantial risk and cost of inducing autoimmunity. I will describe characteristics of the parasite that could be identified to confirm that autoimmunity affects parasite evolution, and I will show that medical interventions intended to reduce the risk of autoimmunity may select for molecular mimicry in parasites and, paradoxically, increase the risk of infection-induced autoimmunity. This is joint work with Troy Day (Queen's).

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(withdrawn)Troy Day (Queen's University)
Theoretical Insights into the Evolution of Drug Resistance

The evolution of resistance to drugs used for combating infectious diseases has become one of the most seriouspublic health problems in modern medicine. In this talk I will present some theoretical results that explore this problem from several different perspectives, with the goal of better mitigating the emergence and spread of resistance. I will show how simple mathematical models of the within-host dynamics of pathogen replication, can contribute to this goal. I will conclude by illustrating how these theoretical results suggest a new approach for preventing the evolution of resistance.

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