
Math
Biology and Medicine 

Theme
Organizers: Siv Sivaloganathan (Waterloo) and Pauline van den Driessche
(UVic)
This
broad theme will bring together experts from several distinct
areas of research in mathematical biology and medicine. Two areas
of particular focus will be cancer modelling and transmission
dynamics and spread of infectious diseases. Mathematical modelling
is gradually becoming an integral part of research in the biomedical
sciences as an essential tool that can help in developing a deeper
understanding of biological systems. The aim is to bring together
leading researchers in these areas to provide stateoftheart
reviews, report on current cuttingedge research and open problems,
as well as to provide a nexus for both senior and junior researchers
(both in the biomedical and mathematical sciences) to interact
in an informal and congenial atmosphere. It is also hoped that
bringing together researchers from the different subthemes will
lead to a crossfertilization of ideas and an exploration of mathematical
commonalities and challenges.

Speakers
in Infectious Diseases Theme

Speakers
in Cancer Modelling Theme

Julien
Arino (Manitoba)
Lydia Bourouiba (MIT)
Jacques Belair (Montreal)
Guihong Fan (Arizona State)
Rongsong Liu (Wyoming)
Connell McCluskey, (Wilfrid Laurier)
Zhisheng Shuai (UVic)
Edward Thommes (Guelph)
Yanyu Xiao (Western Ontario)
Ping Yan (PHAC)*

Helen
Byrne (Oxford)
Corina Drapaca (Penn State)
Raluca Eftimie (Dundee)
Rudy Gunawan (Pharsight Corp.)*
Mansoor Haider (N. Carolina State)
Thomas Hillen (Alberta)
Amirali Masoudi (Alzahra)
Colin Phipps (Waterloo)
Gibin Powathil (Dundee)
Kathleen Wilkie
(CCSB, Tufts)
*tentative


Speakers
in Infectious Diseases Theme
Julien
Arino, University of Manitoba
A model for mass gatherings
Mass
gatherings are socially motivated occasional or periodic convergences
of a large number of individuals to one location. Examples include
sport events such as the Summer and Winter Olympic Games and the
FIFA World Cup every four years, religious pilgrimages such as the
Hajj every year and Kumbh Mela every six years, large music festivals,
etc.
The
specific nature of each mass gathering varies. However, there are
common characteristics, the most important of which being that they
occur in three phases: convergence to the mass gathering site, actual
event and return of individuals to their homes.
I
will present deterministic and stochastic metapopulation infectious
disease models used to evaluate the consequences of the cooccurrence
of a mass gathering and an infectious disease outbreak. This work
in the context of the Bio.Diaspora Project is joint with my student
Liliana Menjivar.
Lydia
Bourouiba, Massachusetts Institute of Technology
Coauthors: John W. M. Bush
Insights from the fluid dynamics of disease transmission
The
emergence and spread of infections diseases is a problem of global
interest with enormous human and economic consequences. Population
and network disease models yield insight into, and guide policy
aimed at mitigating, the spread of these public health threats.
In such models, the central notion of contact greatly influences
the disease epidemic outcomes, but its definition remains nebulous.
We discuss how a combination of theoretical and experimental biofluid
dynamics approaches can assist in revisiting the dynamics of contact
and transmission of infectious diseases
Jacques
Bélair, Université de Montréal
Coauthors: Yuan Yuan, Memorial University of Newfoundland
Distribution of delays in a model with both latency and temporary
immunity
A
disease transmission model of SEIRS type with distributed delays
in latent and temporary immune periods is presented. With general
probability distributions in both of these periods, we address
the threshold property of the reproductive number R0 and the dynamical
properties of the diseasefree/endemic equilibrium points present
in the model. More specifically, we discuss the dependence of
R0 on the probability distribution in the latent period and the
independence of R0 from the distribution in the temporary immunity,
and establsh conditions for the global asymptotical stability
of the respective equilibria. Conditions for the existence of
oscillatory solutions through Hopf bifurcations will also be given.
Guihong Fan, Arizona State University
Coauthors: Prof. Huaiping Zhu (York University)
Modelling vectorborne diseases with discrete time delay
Vectorborne
diseases are a typical infectious disease which can cause severe
illness in humans or animals. Vectors like mosquitoes or ticks play
a critical rule in the transmission and spread of the diseases.
To investigate the role of vectors, we formulate a system of delay
differential equations to model the transmission dynamics of the
diseases between vectors and their hosts. Analytical analyses show
that vectors alone can force the system to oscillate. The interaction
between vector and amplification host is unlikely responsible for
oscillatory behaviors of the system. Case studies for West Nile
virus and malaria are presented.
Rongsong Liu, University of Wyoming
Coauthors: Stephen Gourley
Resistance to larvicides in mosquito populations and its implications
for malaria control
We
model larviciding of mosquitoes taking into account the evolution
of resistance to the larvicides, the evolutionary costs of resistance
and the implications for malaria control. There is evidence that
resistance comes with various costs one of which is reduced adult
longevity for resistant mutants. The mosquito adult lifespan is
one of the most crucial parameters in malaria transmission due to
a long developmental time for the malaria parasite in the insect.
A possible malaria control strategy is therefore to shorten this
adult lifespan by larviciding with a potent larvicide to which mosquitoes
become resistant. This novel strategy is studied using a mathematical
model for the wild type and resistant mutants and by incorporating
the malaria disease dynamics using an SEI type model with standard
incidence that incorporates the latency period of the parasite in
wild type and resistant mosquitoes. We consider the linear stability
of the malaria–free equilibrium in which the resistant strain
is dominant and derive a condition for the global eradication of
malaria. Numerical simulations are presented which offer further
insights. The parameter to which the analysis is most sensitive
is the per–capita death rate of adult resistant mosquitoes.
Increasing this parameter dramatically reduces the basic reproduction
number R0. However, increasing it too much causes the wild type
to outcompete the resistant mutants and the control strategy fails.
Exploitation of costs of resistance to larvicides thus offers a
possible malaria control measure if the larvicide is sufficiently
potent and costs of resistance are neither too great not too small.
Connell
McCluskey, Wilfrid Laurier University
Coauthors: Pierre Magal (Bordeaux 2)
An agestructured model for nosocomial infections
In
a hospital setting, certain pathogens are passed back and forth
between health care workers (HCW) and patients. HCWs remain contaminated
on a timescale related to the length of a hospital shift. Patients
remain infected on a timescale related to the duration of their
stay in the hospital. Often, these infections are drugresistant
and so their control is very important. Nevertheless, such infections
remain common.
We
study a two group SIR model, with continuous agestructure in the
infected classes. We allow that infectivity and recovery may depend
on the ageofinfection. The resulting model is a PDE, which includes
delay models and ODE models as special cases.
We
study the issue of persistence of the disease versus extinction,
as well as global stability through the use of a Lyapunov functional.
Zhisheng
Shuai, University of Victoria
Coauthors: Pauline van den Driessche (University of Victoria)
Global
dynamics of a multigroup cholera model
Cholera
is a bacterial disease that can be transmitted to humans directly
by persontoperson contact or indirectly via the environment (mainly
contaminated water). A multigroup cholera model is formulated that
incorporates direct and indirect transmission with nonlinear incidence,
as well as spatial or host heterogeneity. The basic reproduction
number R0 is determined and shown to give a sharp threshold. If
R0 = 1, then the diseasefree equilibrium is globally asymptotically
stable and cholera dies out from all groups; whereas if R0 >
1, then the unique endemic equilibrium is globally asymptotically
stable and the disease persists at an endemic level in each group.
The proof of global stability utilizes a graphtheoretic approach
and a new combinatorial identity.
Edward
Thommes, University of Guelph
Coauthors: Chris Bauch (University of Guelph), Ayman Chit, Genevieve
Meier (GlaxoSmithKline)
A new multistrain dynamic influenza model
We
present a new compartmental influenza model, designed to follow
the dynamics of four influenza strains (two A, two B) within
an agestratified, evolving population over many years. Mixing
among age groups is implemented via a contact matrix. Population
birth and death rates can vary over time, as can vaccination
strategies and vaccine efficacy. Crossprotection is modeled
between the A strains, and between the B strains. We describe
our solutions to some problems intrinsic to multistrain compartmental
models, and also discuss our approach to parameter fitting.
Yanyu
Xiao, University of Western Ontario, York University
Coauthors: Xingfu Zou
Modeling malaria transmission in a patchy environment
A
mathematical model is derived to describe the transmission and spread
of malaria over a patchy environment. The model incorporates two
factors: disease latencies in both humans and mosquitoes, and dispersal
of humans between patches. We derived the basic reproduction number
R_0 for the structured disease model. The dynamics ofthe model is
investigated in terms of R_0. It is shown that the disease dies
out if R_0<1; and the disease is endemic if R_0>1. For the
case of two patches, some more explicit conditions are obtained,
and impacts of dispersal rates in all different compartments on
R_0 are also explored. Some numerical simulations are performed
which show that the impacts could be very complicated: in a certain
range of the parameters, R_0 is increasing with respect to a dispersal
rate while in another range, it can be decreasing with respect to
the same dispersal rate.
Ping
Yan, Centre for Communicable Diseases and Infection Control, Public
Health Agency of Canada
A discussion on synthesizing stochastic and deterministic disease
transmission models
This
presentation attempts to synthesize stochastic and deterministic
disease transmission models and to put them in a statistical context,
such as parameter estimation and prediction. It starts with brief
reviews of the univariate and bivariate birthdeath Markov processes
used as SIS and SIR models (Allen, 2011, second edition) and compare
them against their deterministic counterparts. In a finite population
setting, the deterministic models can be regarded as ordinary
differential equation models for the stochastic mean values of
the birthdeath processes under an extreme case of the moment
closure framework by setting the second order moments to zero.
Alternatively, the deterministic models are often regarded as
approximations to the ODE models for the stochastic mean values
as the population size approaches infinity. Therefore, the presentation
proceeds with the discussions of the contexts under which the
stochastic models do and do not “average out” to their
deterministic counterparts, in infinitely large populations. These
further lead to the statistical implication for estimating parameters
in disease models, where data, even in the perfect suitable of
continuous and complete observation, tend to arise from a single
realization of the sample paths of an inherently stochastic event.
The final part of the presentation will discuss the notion of
“heterogeneity” in disease models and the proposal of
formulating such a concept in terms of stochastic orders, along
with some application results from recent publications in the
study of the initial growth and evaluation of effectives of certain
infectious disease control measures.
Speakers
in Cancer Modelling Theme

Helen Byrne (University of Oxford)
Multiscale modeling of the intestinal crypt and early colorectal
cancer
The
luminal surface of the gut is lined with a monolayer of epithelial
cells that acts as a nutrient absorptive engine and a protective
barrier. To maintain its integrity and functionality, the epithelium
is renewed every few days. A range of theoretical approaches has
been proposed to model crypt homeostasis and neoplasia. For example,
subcellular models of the Wnt signaling pathway can be coupled to
models of the cell cycle in order to predict how changes in the
extracellular Wnt stimulus affect a cell's ability to proliferate
and how mutations in the Wnt signaling pathway lead to hyperproliferation.
Equally, continuum models can provide a coarsegrained description
of the spatiotemporal dynamics of entire crypts. Multiscale models
occupy the middle ground, permitting a detailed description of the
interplay between processes acting on the subcellular, cellular
and tissue scales. In this talk, I will introduce a simple model
of the Wnt signaling pathway and show how its integration within
a cellbased model can provide new insight into the cellular dynamics
of healthy and neoplastic crypts.

Corina Drapaca (Penn State)
Mathematical Modeling of Tumors Classification
The
US National Center for Health Statistics reported recently that
cancer is about to become the deadliest disease of modern times.
The advancements in medicine of the last decade have reduced considerably
the death rates of serious diseases such as heart disease, stroke,
and pneumonia, but unfortunately similar progress has not happen
yet with cancer. Theoretical models capable of explaining the fundamental
mechanisms of tumor growth and making reliable predictions are essential
in the design of optimal, personalized therapies that will maximize
treatment outcomes and reduce health care costs. In this talk we
will present a mathematical model that is able to differentiate
not only between healthy and pathologic tissues, but, more importantly,
between benign and malignant tumors. Our multiscale triphasic model
for biological tissues couples biochemical processes that take place
in tissue's microstructure and tissue's mechanics and thus could
explain for instance the role played by the stiffness of a tumor
and its microenvironment in the transition from a low (benign) to
a high (malignant) grade tumor. The multiscaling is based on a recently
developed homogenization technique for materials with evolving microstructure.

Raluca Eftimie, University of Dundee
Coauthors: David J.D. Earn, Jonathan Dushoff, Jonathan L. Bramson
Using viruses to eliminate tumours: the role of multistability
and multiinstability phenomena
Recent
advances in virology, gene therapy and molecular and cell biology
have provided insight into the mechanisms through which viruses
can boost the antitumour immune response, or can infect and kill
directly tumour cells. Here, we derive a mathematical model to investigate
the antitumour effect of two viruses and their interactions with
the immune cells. We then discuss the role of virus persistence
on the elimination of tumour cells. To this end, we focus on multistability
and multiinstability, two complex phenomena that can cause abrupt
transitions between different states in biological and physical
systems. In the context of cancer immunotherapies, the transitions
between a tumourfree and a tumourpresent state were so far associated
with the multistability phenomenon. Here, we show that the multiinstability
phenomenon can lead to the formation of a homoclinic bifurcation,
which causes the system to switch from a tumourpresent to a tumourfree
state. This multiinstability phenomenon is driven by the persistence
of the virus, while the multistability phenomenon is driven by
the immune response.

Rudy Gunawan (Pharsight Corp.)*tentative

Mansoor A. Haider, Dept. of Mathematics,
North Carolina State University
Mixture Models for Cartilage Tissue Engineering in CellSeeded
Scaffolds
Articular
cartilage physiology is regulated by a single population of specialized
cells called chondrocytes. The chondroyctes are sparsely distributed
within an extracellular matrix (ECM), maintaining a state of homeostasis
in healthy tissue. ECM degeneration due to osteoarthritis can lead
to complete degradation of cartilage surfaces, necessitating total
joint replacement. Chondrocytes can be utilized to regenerate cartilage
ECM via tissue engineering approaches in which these cells are seeded
in degradable biopolymer or hydrogel scaffolds. In such systems,
biosynthetic activity of the cells in response to their nonnative
environment results in regeneration and accumulation of ECM constituents
concurrent with degradation of the surrounding scaffold material.
In this talk, mixture models are presented for interactions between
biosynthesis of ECM constituents and ECM linking in cellseeded
scaffolds. Both ODEbased (temporal) models for evolution of average
apparent densities and PDEbased (spatiotemporal) models will be
presented for variables including unlinked ECM, linked ECM and scaffold.
Of particular interest are model predictions influencing the compressive
elastic modulus of the tissue construct. These models provide a
quantitative framework for assessing and optimizing the design of
cellscaffold systems and guiding strategies for articular cartilage
tissue engineering.

Thomas Hillen, University of Alberta
Coauthors: Jiafen Gong, Mairon M. dos Santos, Chris Finlay
Are More Complicated Tumor Control Probability Models Better?
Mathematical
models for the tumor control probability (TCP) are used to estimate
the expected success of radiation treatment protocols of cancer.
There are several mathematical models in the literature and we made
the experience that simple and complex models often make the same
predictions. Here we compare six of these TCP models: the Poisson
TCP, the ZaiderMinerbo TCP, a Monte Carlo TCP, and their corresponding
cell cycle (twocompartment) models. Several clinical nonuniform
treatment protocols for prostate cancer are employed to evaluate
these models. These include fractionated external beam radiotherapies,
and high and low dose rate brachy therapies.
We
find that in realistic treatment scenarios, all onecompartment
models and all twocompartment models give basically the same results.
A difference occurs between one compartment and two compartment
models due to reduced radiosensitivity of quiescent cells. Based
on our results, we can recommend the use of the Poissonian TCP for
every day treatment planning. More complicated models should only
be used when absolutely necessary.

Amir Ali Masoudi, Department of Physics, Alzahra University,
Tehran,Iran
Coauthors: S. Hosseinabadi, J. Davoudi, M. Khorrami, M. Kohandel
Statistical Analysis of Radial Interface Growth
Recent
studies have questioned the application of standard scaling analysis
to study radially growing interfaces. We show that the radial EdwardsWilkinson
equation belongs to the same universality as that obtained in the
planar geometry. In addition, we use numerical simulations to caculate
the interface width for both random deposition with surface relaxation
and restricted solid on solid models, assuming system size increases
linearly with time(due to radial geometry). By applying appropriate
roules for each model, we show that the interface width increases
with time as t^, where the exponent is the same as those obtained
from the corresponding planar geometries.

Colin Phipps, Univesrity of Waterloo
Coauthors: Mohammad Kohandel (University of Waterloo)
Mathematical model for angiogenic behaviour in solid tumours
A
mathematical model is presented for the concentrations of proangiogenic
and antiangiogenic growth factors, and interstitial fluid pressure,
in solids tumours embedded in host tissue. In addition to production,
diffusion, and degradation of these angiogenic growth factors (AGFs),
we include interstitial convection to study the locally destabilizing
effects of interstitial fluid pressure (IFP) on the angiogenic activity
endowed by these factors. The molecular sizes of representative
AGFs and the outward flow of interstitial fluid in tumors suggest
that convection can be a significant mode of transport for these
molecules. The resulting balance or imbalance of proangiogenic and
antiangiogenic factors serves as a possible mechanism for determining
whether blood vessels are stable, developing or regressing. The
results of our modeling approach suggest that changes in the physiological
parameters that determine interstitial fluid pressure have as profound
an impact on tumor angiogenesis as those parameters controlling
production, diffusion, and degradation of AGFs. This model has predictive
potential for determining the angiogenic behavior of solid tumors
and the qualitative effects of cytotoxic and antiangiogenic therapies
on tumor angiogenesis.

Gibin Powathil, Division of Mathematics, University of Dundee,
Dundee, UK.
Coauthors: Kirsty Gordon, Lydia Hill and Mark Chaplain
A hybrid multiscale cellular automaton model for studying
the effects of cellcycle heterogeneity on tumour response to chemotherapy
The
therapeutic control of a solid tumour critically depends on the
responses of the individual cells that constitute the entire tumour
mass. From a modelling perspective, these biological cells can be
considered as discrete entities. An individual cell’s spatial
location within the tumour and its intracellular dynamics, including
the evolution of the cell cycle within each cell, has an impact
on the decision to grow and divide. There is also influence by signals
from other neighbouring cells and the local oxygen and nutrient
concentrations. Hence, it is important to take all of these “multiscale”
factors into account when modelling solid tumour growth and its
response to various cellkill therapies, including chemotherapy.
In order to address this multiscale nature of tumour growth, we
propose a hybrid, individualbased model that analyses the spatiotemporal
dynamics at the level of cells, linking individual cell behaviour
with the macroscopic behaviour of cell organisation and the microenvironment.
The evolution of tumour cells is modelled by using a cellular automaton
(CA) approach, where each cell has its own internal cell cycle,
modelled using a system of ODEs. The internal cell cycle dynamics
determine the growth strategy in the CA model, making it more predictive
and biologically relevant. It also helps us to classify the cells
according to their cell cycle states and to analyse the effect of
various cellcycle dependent cytotoxic drugs. Moreover, we have
incorporated the evolution of oxygen dynamics within this hybrid
model in order to study the effects of the microenvironment in cellcycle
regulation and tumour treatments. This is an important factor from
a treatment point of view, as the low concentration of oxygen can
result in a hypoxiainduced quiescence (G0/G1 arrest) of the cancer
cells, making them resistant to key cytotoxic drugs. Using this
multiscale model, we investigate the impact of oxygen heterogeneity
on the spatiotemporal patterning of the cell distribution and their
cell cycle status. We demonstrate that oxygen transport limitations
result in significant heterogeneity in HIF1(alpha) signalling and
cellcycle status, and when these are combined with drug transport
limitations, the efficacy of the therapy is significantly impaired.

Kathleen Wilkie, Center of Cancer Systems Biology, Steward St.
Elizabeth's Medical Center, Tufts University School of Medicine
Coauthors: Philip Hahnfeldt
A Mathematical Model of ImmuneInduced Tumor Dormancy and
the Emergence of Immune Evasion
Tumor
dormancy is a condition in which tumor cells persist in a host
for a period of time without significant growth. As the state
represents a natural forestalling in progression to manifest disease,
it is of great clinical interest. Experimental work in mice suggests
that in immuneinduced dormancy, the longer a tumor remains dormant
in a host, the more resistant the cancer cells become to cytotoxic
T cellmediated killing. In this work a mathematical model that
attempts to capture the significant interactions between a dormant
tumor and the immune system is presented. Principles of logistic
growth are used to describe the growth dynamics of both the tumor
and immune populations. The effects of an increasingly resistant
cancer population on tumor dormancy and the potential mechanisms
behind this increasing resistance are analyzed and discussed.
The mechanisms assume that the immune system selectively prunes
the tumor of immunesensitive cells to cause an initially heterogeneous
population to become a more homogeneous, and more resistant, population.
To this end, we first discuss two mathematical forms for immune
predation that allow for the development of immuneevasion: one
form assumes a timedecay of efficacy while the other form assumes
efficacy decays as a function of the cancerimmune interactions.
Next, the existence of a resistant cancer subpopulation is added
to the model. This subpopulation competes with the immunesensitive
population for nutrients, does not initiate an immune response,
and may provide protection against immune attack to the entire
tumor population. Finally, a possible populationlevel regulatory
mechanism for optimal tumor composition is explored through populationcontrolled
proliferation rates. This model demonstrates that through actions
which reduce tumor growth through the targeted removal of a tumor
subpopulation, the immune response actually progresses the tumor
to a more aggressive state.
Contributed
Talks
Shannon
Collinson,
York University
Coauthors: Jane Heffernan PhD
The effects of media on influenza infection: An agent based Monte
Carlo simulation
Media
reports affect social behaviour during epidemics and pandemics.
Changes in social behaviour, in turn, affect key epidemic measurements
such as peak magnitude, time to peak, the beginning and end of
an epidemic. The extent of this effect has not been realized.
We have developed mathematical models of influenza spread based
on a SusceptibleExposedInfectedRecovered (SEIR) model including
the effects of mass media. The models are used to evaluate different
functions representing media impact and how these functions affect
key epidemic measurements. We have also developed an agent based
Monte Carlo (ABMC) simulation of influenza infection between hosts
in order that variability in key epidemic measurements can be
determined.
Yimin
Du
York University
Coauthors: Jane Heffernan (York University) Jianhong Wu (York University)
The basic inhost model for Tuberculosis (TB)
There
are almost 2 million TBrelated deaths every year. With the HIV
epidemic and the appearance of multidrugresistant TB, TB is becoming
even more deadly. Mathematical models have been used to provide
some insight into the pathogenesis of TB infection inhost, determining
key characteristics that determine TB disease outcome (clearance,
slow progression, fast progression, latent TB or reactivation).
However, such models have been very complex with many equations
(i.e.10 or more). This does not compare to the simple and very
powerful basic model of virus dynamics (3 simple equations) that
has been used to give great insight into the pathogenesis of various
viral infections (i.e.HIV, HCV). We develop a simple mathematical
model of TB infection inhost (4 equations). The model includes
macrophages, T lymphocytes, bacteria and their interactions, and
captures all disease outcomes. Uncertainty and sensitivity analysis
and numerical simulations have given very interesting results,
including identification of key parameters that determine disease
outcome, as well as model conditions which can produce a backward
bifurcation. The model also provides a sound foundation for future
studies on the pathogenesis of drug resistant TB and HIV/TB coinfection.

Daihai
He
Hong Kong Polytechnic University
Coauthors: David Earn, Jonathan Dushoff, Troy Day, and Junling Ma
Investigating the causes of the three waves of the 1918 influenza
pandemic in England and Wales
Past
influenza pandemics appear to be characterized by multiple waves
of incidence but the mechanisms that account for this phenomenon
remain unclear. We proposed a simple epidemic model in which we
incorporate three factors that might contribute to the generation
of multiple waves: (i) schools opening and closing, (ii) temperature
changes during the outbreak, and (iii) changes in human behavior
in response to the outbreak. We fitted this model to the reported
influenza mortality data of the 1918 pandemic from 334 UK administrative
units, and estimated the epidemiological parameters. We then use
information criteria to identify which of the three factors provides
the best explanation for the multiple waves seen in the data.
Our results suggest that all three factors are important and that,
taken together, a model with these factors can produce epidemiological
dynamics that match the data well for reasonable parameter values.
Xi
Huo, Vanderbilt
University, Nashville, TN, USA
Coauthors: Glenn Webb (Vanderbilt University, Nashville, TN, USA)
An Agedependent Population Model with Contact Tracing in Epidemic
Diseases
Contact
tracing is considered to be a useful method to reduce infections
in the control of an epidemic disease. People intuitively think
that high level contact tracing results in less infection than relatively
low level contact tracing does. But that argument is not always
the case according to our deterministic model about contact tracing.
We conclude that tracing too many contacts during the contact tracing
period might just postpone the outbreak of the disease and might
NOT reduce infections effectively. I’m planning to present
our main model, simulation results with explanations and suggestions
about choosing suitable contact tracing levels.

**Yijun
Lou, Department of Mathematics and Statistics, York University
Coauthors: Jane M. Heffernan and Jianhong Wu
Costeffectiveness Evaluation of Vaccination Programs Against Sexually
Transmitted Diseases for Different Sexes
For
sexually transmitted diseases the determination of an optimal
vaccination program is not straightforward due to sexual
heterogeneity. In this talk, we will present two models
of sexually transmitted infections to evaluate the costefficacy
of vaccination programs for different sexes in the context
of STD control, with special application to potential genital
herpes vaccination programs. For both models, we find that
the stability of the system and ultimate eradication of
the disease depend explicitly on the corresponding reproduction
number. We also find that vaccinating females is more costeffective.
This is joint work with Drs. Jane Heffernan and Jianhong
Wu.
Robert
M. Miura
Department of Mathematical Sciences, New Jersey Institute of
Technology.
Coauthors: K.C. Brennan, Department of Neurology, University
of Utah;Joshua C. Chang, Department of Biomathematics, UCLA;
Thomas Chou, Department of Biomathematics, UCLA; Dongdong He,
Department of Mathematics and Statistics, York University; Huaxiong
Huang, Department of Mathematics and Statistics, York University;
Robert M. Miura, Department of Mathematical Sciences and Center
for Applied Mathematics and Statistics, New Jersey Institute
of Technology; Phillip L. Wilson, Department of Mathematics
and Statistics, University of Canterbury; Jonathan J. Wylie,
Department of Mathematics, City University of Hong Kong
Neurovascular Coupling During Cortical Spreading Depression:
A Mathematical Model
Cortical
spreading depression (CSD) is a slowly propagating wave
of ionic and metabolic disturbances in brain tissue. There
are massive cellular depolarizations and changes in tissue
perfusion and metabolism, which have not been modeled. A
new mathematical model for CSD is developed where oxygen
supply is modeled as flow through a lumped vascular tree
that is controlled by extracellular potassium concentration.
Our key findings are that the metabolic activity of the
cortex during CSD exceeds the physiological limits on oxygen
delivery and that perfusion changes during CSD strengthen
the intensity and elongate the event. The vascular changes
from our CSD model reflect experimental findings. Combined
modeling and experimentation should accelerate understanding
of the mechanisms of CSD.

Andreea
Rimbu Pruncut, Université de Montréal
Coauthors: Jacques Bélair, Université de Montréal
Model of ChemotherapyInduced Myelosuppression with Distributed
Delays
We
discuss a model of chemotherapyinduced myelosupression
using differential equations with distributed
delays. Our model generalizes an existing semimechanistic
pharmacokineticpharmacodynamic model developed
by Friberg et al (2002). The original model uses
a chain of transit compartments to take into account
the delay between administration of the drug and
the observed effect. We replace the equations
of the transit compartments by a single differential
equation with a bimodal distribution of delays,
and discuss the stability of the new system. A
stability chart displaying the boundary of the
region of stability in the plane of two parameters
of the system is presented.
*Schehrazad
Selmane (USTHB)
Modeling the Behavioral and Immunological Resistance against
Syphilis
Syphilis is a sexually transmitted infection that can be successfully
controlled by public health measures due to the availability
of a highly sensitive diagnostic test and a highly effective
and affordable treatment and effective prevention measures,
nevertheless its continuing occurrence illustrates that the
control efforts need to reevaluate. A modified SIR epidemic
model for syphilis describing behavioural and immunological
resistance that is only temporary is proposed. The determinations
of the reproduction number, the existence of equilibria, stability
analysis of the disease free equilibrium and conditions for
backward bifurcation to occur are presented. Numerical simulations
for the model are provided.

Naveen
K. Vaidya
Department of Applied Mathematics, University of Western Ontario,
London, Canada
Coauthors: Lindi M. Wahl
Benefit Analysis of HIV1 Treatment in the Face of Drug
Resistance
For
many HIV1 infected patients, drug resistance can cause therapy
to fail. It is critical to understand the benefits of continuing
therapy in the face of resistance. Using mathematical models,
I show that although drug therapy cannot suppress the viral
load, it can alter the viral fitness resulting in an increase
in CD4+ T cell count, which should yield clinical benefits.
Further analysis reveals that this benefit depends on the
cell proliferation rate, which, in some situations, produces
sustained Tcell oscillations. I will also explore the analysis
of extended models incorporating more than two viral species,
including compensatory mutants.
**Estefanía
Ruiz Vargas
Department of Applied Mathematics, University of Western Ontario,
London, ON, Canada N6A 5B7
Coauthors: S.G. Greening, D.G.V. Mitchell and L.M. Wahl
Modular structure of brain networks
Understanding
the modular structure of the brain can help us build reliable cognitive
models in which brain functions are distributed across diverse regions.
We analyze weighted networks calculated from fMRI data acquired
during task performance, retaining all of the connections between
all of the voxels. We analyze the modular structure of the resultant
network, comparing against known functional regions putatively involved
in the task. We also examine how the modules are modified when a
fraction of the connections in the whole network are weakened, which
can give insight into the structural changes caused by brain injuries
such as concussions.
Fei
Xu, Department of Mathematics,
Wilfrid Laurier University
Coauthors: C. Connell McCluskey, Ross Cressman
Spatial Spread of an Epidemic through Public Transportation
Systems with a Hub
In
this talk, we investigate an epidemic spreading among several locations
through a transportation system, with a hub connecting these locations.
Public transportation is not only a bridge through which infections
travel from one location to another but also a place where infections
occur since individuals are typically in close proximity to each
other due to the limited space in these systems.
A mathematical model is constructed to study the spread of an infectious
disease through such systems. A variant of the next generation method
is proposed and used to provide upper and lower bounds of the basic
reproduction number for the model.
Xiangsheng
Wang, York University,
Threshold dynamics of avian influenza spread

Hongying
Shu, University of New Brunswick
The immunsuppressive infection: oscillations and chaos
