### 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*

tba

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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

___________________________________________________

**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.)

__________________________________________________

**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.

__________________________________________________

**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.

_________________________________________________

**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.

________________________________________________

**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*

tba

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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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