THEMATIC PROGRAMS

December 19, 2014

July 19-30, 2010
Mathematical Immunology

Talk Titles and Abstracts

Murray Alexander (National Research Council Canada)
Control of influenza A virus infection by varying death rates of infected cells: Analysis of a spatial model

Influenza A virus infection of the respiratory epithelium triggers an antiviral innate immune response. This entails secretion of type-1 interferons, INF-a/b, from infected epithelial cells and release of an array of inflammatory and chemotactic cytokines from alveolar macrophages and wandering neutrophils and dendritic cells upon phagocytosis of newly-synthesized virus particles produced by the infected epithelial cells. The process leads to activation of natural killer (NK) cells and gives rise to viral antigen-bearing macrophages and dendritic cells that, in turn, activate and clonally expand multiple influenza A-specific cytotoxic T lymphocytes (CTLs). Activated NK cells can kill newly-infected epithelial cells whereas anti-influenza CTLs destroy virus-producing epithelial cells. We present a simple spatial model for the influenza virus infection of respiratory epithelium, represented as a hexagonal (maximally close-packed) lattice, to describe a previously undefined relationship between the rate of death of infected epithelial cells due to (i) virus replication, (ii) activated NK cells, and (iii) CTLs, and the spread of infection in respiratory tract. Without modelling the detailed kinetics of various processes, it is possible to gain valuable insights into critical mechanisms implicit in the control of virus infection. We analyze this model for linear stability and show how the same techniques may be extended to a more comprehensive model of immune response, including conditions that would prevent the generation of unwanted “cytokine storm” and ensuing inflammation in the respiratory tract.

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Vahid Anvari (York University)
The Artificial Immune Systems Algorithm Inspired by Dendritic Cells

Artificial Immune Systems (AIS) are adaptive systems involving the translation of structures and functionality of human immune system into feasible computational algorithms to tackle variety of problems in engineering particularly information technology. The Dendritic Cell Algorithm (DCA) is an example of immune inspired algorithm which granulates the information at different layers, achieved through multi-scale processing. The DCA is abstracted and implemented through a process of examining and modeling various aspects of Dendritic Cell function, from the cellular level to the systemic level. This talk presents a brief overview of the algorithm and the processes used for its development. The talk also provides a brief description of an implemented DCA highlighting signal and antigen processing as granular computation.

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Catherine Beauchemin (Ryerson University)
In-host influenza

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Stanca Ciupe (University of Louisiana at Lafayette)
Modeling antibody responses during viral infections

During the course of an individual viral infection, the virus population may consist of a distribution of different variants produced by mutation and selection. Consequently, the immune system attemps to build a response that is broad enough to handle the diversity of virus strains present. We design novel mathematical models of virus-antibody interaction and focus on the roles of cross-reactivity among neutralizing antibodies, viral evolution and the role of non-neutralizing antibodies

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Jessica Conway (University of British Columbia)
Branching process model of viral load and viral blips in individuals on treatment for HIV

We will discuss continuous-time, multi-type branching model of HIV viral dynamics in the blood stream. We are motivated by observations of viral load in HIV+ patients on anti-retroviral treatment (ART). While on ART for HIV,  an infected individual's viral load remains non-zero, though it is very low and undetectable by routine testing. Further, blood tests show occasional viral blips: very short periods of detectable viral load. We hypothesize that this very low viral load can be explained principally by the activation of cells latently infected by HIV before the initiation of treatment. Viral blips then represent large deviations from the mean. Modeling this system as a branching process, we derive equations for the probability generating function. Using a novel numerical approach we extract probability distributions for viral load yielding blip amplitudes consistent with patient data. We then compute distributions on duration of these blips through direct numerical simulation. Finally we discuss the implications of our hypothesis on mechanisms of emerging drug resistance, and model extensions intended to address them.

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Odo Diekmann (Utrecht University)
The interplay of within-host immunology and population level transmission

Infectious agents have to cope with the immune system of their hosts. In particular, it is the immune system that records past exposures as
well as vaccination history. As a consequence, the interaction between various strains of a pathogen is mediated by the immune status of the individual hosts. We therefore need nested models, i.e., models for transmission at the population level that have models for within host parasite-immune system interaction as a building block. The aim of this talk is to sketch (in wishful thinking spirit) a possible top-down approach based on the delay equation formulation of physiologically structure population models. (By 'top-down' I mean that specification of a submodel for within-host processes is postponed.)

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Hana Dobrovolny (Ryerson University)
Neuraminidase inhibitor treatment of seasonal and severe influenza

Treatment of seasonal influenza viral infections using antivirals such as neuraminidase inhibitors (NAIs) has been proven effective if administered within 48 h post-infection. However, there is growing evidence that antiviral treatment of infections with avian-derived strains even as late as 6 days post-infection (dpi) can significantly reduce infection severity and duration. Using a mathematical model of in-host influenza viral infections which can capture the kinetics of both a short-lived, typical, seasonal infection and a severe infection exhibiting sustained viral titer, we explore differences in the effects of NAI treatment on both types of influenza viral infections.

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Venkata Duvvuri (York University)
Highly conserved cross-reactive CD4+ T-cell Hemagglutinin epitopes of seasonal and the 2009 pandemic influenza viruses and their role in the infection dynamics

Blunt severity of infection caused by swine-origin H1N1 influenza virus (nH1N1) in a vast majority of individuals highlights the importance of pre-existing immune memory. Due to the evident lack of cross-reactive antibody responses in a large segment of the population, reduced illness may be attributed to pre-existing T-cell immunity directed against epitopes shared between nH1N1 virus and previously circulating strains of inter-pandemic influenza A virus. We sought to identify these epitopes and determine the level of cross-reactivity conferred by CD4+ T cell immune responses. We investigated the degree of CD4+ T cell cross-reactivity between seasonal influenza A (sH1N1 and H3N2) from 1968-2009 and nH1N1 strains. Large scale MHC II based epitope prediction and conservancy analysis on Hemagglutinin (HA) proteins performed by NETMHCIIPAN server and Epitope Conservancy tool, respectively. HA protein sequences used in this analysis were obtained from the Influenza Virus Resource at NCBI. Eighteen MHC II strong binders identified were conserved among the sH1N1 and nH1N1. Each epitope was examined against all the protein sequences that correspond to sH1N1, H3N2 and nH1N1 available in the NCBI. T cell cross-reactivity was estimated about to be ~52%, and maximum conservancy was found between sH1N1 and nH1N1 with a significant correlation (p < 0.05) These results are incorporated into a stochastic continuous time Monte-Carlo Markov-Chain model to simulate the effect of T-cell cross reactivity on disease transmission dynamics. We observed that a prolonged incubation period due to pre-existing immunity could decelerate disease spread, decrease the number of secondary infections, and result in a longer delay in the illness peak of the epidemic. This study demonstrates that prior exposure to sH1N1 strains has conferred substantial level of T-cell cross-reactivity against nH1N1 strains. The findings provide critical information that can be used for vaccine production to cover a broader spectrum of epitopes specific to nH1N1 strains.

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Raluca Eftemie (McMaster University)
Mathematical modeling of cancer immunotherapies: the anti-tumor effect of immune cells versus the anti-tumor effect of oncolytic viruses

Many of the oncolytic viruses used in cancer therapies are rapidly eliminated by the immune response of the host (tumor-bearing hosts may have partially intact immune antiviral mechanisms). This diminishes their anti-tumor effect. However, recent experimental results have shown that the treatment of a particular type of skin cancer with two viruses that express the same tumor associated antigen, extends the survival rate of mice. Here, we derive a mathematical model to investigate the interactions among immune cells, cancer cells, and two different viruses. We use experimental data from our lab to validate the model and estimate parameter values. This allows us to discuss conditions that lead to tumor growth and to propose hypotheses for tumor elimination which can be tested experimentally. In particular, we suggest that the use of oncolytic viruses can only ensure a temporary elimination of cancer cells. Complete cancer elimination can happen only in the presence of activated immune cells.

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Jonathan Forde (Hobart and William Smith Colleges)
Modeling Hepatitis Delta Infection

Hepatitis Delta Virus (HDV) is a satellite of Hepatitis B Virus (HBV), and can only reproduce in hepatocytes which are simultaneously infected with HBV.  Patients chronically infected with both HBV and HDV are more likely to experience liver failure, hepatocellular carcinoma, and cirrhosis than those infected with HBV alone.  We develop a model of HBV-HDV infection to explore the roles of the two infections, their interactions, and the immune response in patient outcomes.

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Mike Gilchrist (University of Tennessee)
Nested Models of Disease Evolution and Its Implications for Understanding Drug Resistance

Mathematical models of within-host processes can be nested within and higher-scale, epidemiological or between-host processes. Nested approaches are useful, in part, because they force biologists to think about and describe how biological processes interact between scales. One important insight from nested models is that, under simple scenarios, an understanding of how within- and between-host selection on pathogen replication rates interact. I will present an outline of these types of models and will suggest that a similar approach could be developed to aid our understanding the short and long-term evolutionary implications of the trade-offs involved in the evolution of drug resistance.

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Andreas Handel (University of Georgia)
How sticky should a virus be? The impact of attachment and detachment rates on virus fitness using influenza as an example

Budding viruses face a trade-off: Virions need to efficiently attach to and enter uninfected cells. At the same time, newly generated virions need to efficiently bud and detach from infected cells. This suggests that the virus needs to find a balance with regard to its ability to stick to a target cell, i.e. there should be an optimal level of stickiness. We investigate this issue using influenza A as an example. We show that an optimal level of stickiness does exist, and show how it changes in the presence of the immune response. We also show how the optimal values for detachment and attachment depend on other properties of the virus and host, such as virion production rate and target-cell death rate.

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Ben Holder (Ryerson University)
Non-exponential delays in the influenza infection cycle: evidence from in vitro experiments

When a human is infected with influenza, the amount of virus produced in the upper respiratory tract increases exponentially for 1-2 days and then declines exponentially.  This simple dynamic can be reproduced by a wide variety of mathematical models of viral infection which, when utilized to fit the data, will predict different values for the underlying infection kinetics parameters. We analyze in vitro influenza infection experimental data from the literature, specifically that of single-cycle viral yield experiments, to narrow the range of applicable models. In particular, we demonstrate the viability of using normal or lognormal distributions to characterize the time a cell will spend in a given infection state (e.g., the time spent by a newly infected cell in the latent state before it begins to produce virus), and the shortcomings of using delta distributions or the exponential distributions implicit to ordinary differential equation models.

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Shingo Iwami (Japan Science and Technology Agency (JST))
Estimate of viral productivity and infectivity in vitro

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Abdolamir Landi (VIDO)
Maturation of Dendritic Cells: Potentials for Mathematical Modelling

Dendritic cells (DCs) play a central role in the immune defense. They take up foreign antigens, process and present them to the T cells for a specific immune response. In order to be able to properly perform this function, DCs undergo a well-programmed process called maturation. Nowadays, the concept of maturation is becoming the centre of attention since it has been suggested that inhibition of maturation could be the reason for evasion of some infectious agents as well as tumor cells from the immune system. However, all aspects of this process are not well known, and mature DCs are being generated by using different methods to be used as vaccine carriers for infectious diseases or cancer immunotherapy. Here we present this biological process in order to have a mathematical model designed for the level of maturity as an approach to simplify and standardize this process for better comparison between laboratories and interpretation or prediction of results in experiments and trials.

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Neal Madras (York University)
Stochastic Modeling of Pathogen Mutation and CTL Escape

Cytotoxic T lymphocytes (CTLs) are key to the antiviral immune response. For a given virus, a typical host has several kinds of CTLs that are each specific for a different epitope of the virus. RNA viruses often exhibit high rates of mutation, and mutation in the viral epitopes is an important mechanism by which these viruses may escape the CTLs. We would like to know the probability that a wild-type virus will accumulate mutations in all recognizable epitopes before being eliminated by CTLs. We present a stochastic model that enables efficient calculation of this probability.  Our results are compared with the behaviour of an analogous deterministic model.

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Seyed Moghadas (University of Winnipeg)
Within-Host Dynamics of Influenza Drug-Resistance

Compensatory mutations during viral replication can result in the generation of escape mutants from immune recognition or in the emergence of transmissible drug resistant viruses. We discuss the interplay between host-immune responses and the evolution of drug resistance viral mutations in the context of influenza infection. We develop a basic modelling framework to illustrate the effects of timing in start of antiviral treatment and the efficacy of drugs in viral inhibition in the absence/presence of pre-existing immunity.

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Shinji Nakaoka (University of Tokyo)
A mathematical model for cell division, death and differentiation of CD4 positive T cells

Several well-known quantitative mathematical models which describe division/death processes of activated CD4 positive T cells can be equivalently reformulated by a system of delay equations. Based on this finding, I show some stochastic simulation results for cell division, death and differentiation of CD4 positive T cells. Our method can be used to investigate the dynamics of cell population growth both qualitatively and quantitatively. In the workshop, I would like to discuss possibility of contribution of our method to experimental studies on CD4 positive T cell division and differentiation.

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Redouane Qesmi (York University)
HIV Infection Through Breastfeeding Model with Threshold Delay

Promotion of breastfeeding has contributed significantly in that it provides optimum nutrition. However, HIV transmission in breastfed infants can occur through multiple exposures to lower doses of virus. In this talk, we will present a mathematical model with threshold-type delay describing this phenomena. A detailed stability analysis is performed. A sufficient condition for the global asymptotic stability of the disease free equilibrium (DFE) is obtained using a Lyapunov-Razumikhin function. Endemic equilibria (EE) are shown to appear through transcritical bifurcation as well as backward bifurcation of the DFE. The analysis of the EE behavior, through the study of a first order exponential polynomial characteristic equation, concludes to the existence of a Hopf bifurcation and gives criteria for stability switches.

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Tim Reluga (Pennsylvania State University)
A Homeostasis Hypothesis for Hepatitis C Treatment Dynamics

Approximately 200 million people worldwide are persistently infected with the hepatitis C virus (HCV) and are at risk of developing chronic liver disease, cirrhosis and hepatocellular carcinoma. HCV can be treated using antiviral therapy, but the response to therapy is heterogeneous. Some patients clear infection, some patients remain chronically infected, and some patients exhibiting an intermediate plateau in viral load before clearing infection. One hypothesis for this diversity of therapy responses is that the homeostatic proliferation of hepatocytes may preserve infection through vertical transmission. In this talk, I will present some results of a mathematical analysis of the homeostasis hypothesis and discuss the implications.

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Beni Sahai (Cadham Provincial Laboratory & University of Winnipeg)
Principles of Immunological Control of Antiviral Drug Resistance

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Robert Smith? (University of Ottawa)
Modelling mutation to a cytotoxic T-lymphocyte HIV vaccine

Resistance to a post-infection 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 out-compete the other strain. Imperfect adherence may result in the persistance of the mutant, while fluctuations in the vaccination time - even if no vaccines are missed - may result in the mutant out-competing the wild type.

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Naveen Vaidya (Los Alamos National Laboratory)
Immunologic Benefits of Enfuvirtide despite Virologic Failure due to the Emergence of Resistance

Enfuvirtide (ENF/T-20), the first FDA approved HIV-1 fusion inhibitor, exhibits both high efficacy and low toxicity. However, due to the emergence of resistance to ENF, treatment strategies involving ENF interruption to allow drug sensitive virus to grow, followed by ENF re-administration have been examined. In this talk, I will present a mathematical model to study the dynamics of plasma viral RNA level and the competition between ENF-sensitive and ENF-resistant viruses during ENF interruption and ENF re-administration. Our result accounts for the increased CD4+ T cell count observed during ENF re-administration in the absence of viral load decrease. We found that the plasma viral RNA level does not depend upon the fitness cost of the resistant virus or the drug efficacy, but does depend on a number of other viral dynamic parameters. The combined effect of the fitness loss of ENF-resistant virus and its initial proportion are the main factors determining the dominance of the drug sensitive virus population during ENF interruption, while the efficacy of ENF against ENF-resistant viruses also plays a role in determining the dominance of the virus population during ENF re-administration.

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Sylvia van den Hurk (University of Saskatchewan)
The role of Th1/Th2 polarization in RESPIRATORY SYNCYTIAL VIRUS disease and vaccination

Respiratory syncytial virus (RSV) is the most common respiratory pathogen in infants and children under 2 years of age with 64 million infections per year. The goal of our research is to develop a vaccine against RSV, using novel adjuvant formulations that are expected to induce high-affinity neutralizing antibodies and cell-mediated immune responses to RSV, leading to protection from RSV infection. Since an inappropriate, unbalanced immune response may result in immunopathology as opposed to protection, it is critical that a RSV vaccine induces the appropriate, protective, immune response. If a mathematical model could be designed to correlate the quality and magnitude of RSV vaccine-induced immune responses to protective immunity as opposed to immunopathology, this then might be used to predict the efficacy, and most importantly safety, of RSV vaccine candidates and possibly reduce the number of trials and animal models needed prior to clinical studies. Such a model would have the potential to more rapidly move the development of a RSV vaccine forward.

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Lindi Wahl (University of Western Ontario)
Understanding drug resistance in evolving populations of fungus: theory and experiment

Populations of filamentous fungus, such as Aspergillus nidulans, offer a powerful experimental system in which the evolution of drug resistance, and the emergence of mutations which compensate for drug resistance, have been well studied.  Each spore in the inoculum which founds such a population produces a circular colony which grows radially at a constant rate.  When a de novo beneficial mutation occurs, it produces a visible sector or wedge in the colony which grows at a faster rate.  We have derived mathematical predictions for the shape of this mutant region, the expected mutant and wildtype spore counts over time, and ultimately the extinction probability for beneficial mutations. This work has been developed in tandem with experimental efforts; preliminary data will be  presented.

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