When severe acute respiratory syndrome (SARS) arrived in the
Canadian cities of Vancouver and Toronto last spring, its first
cases looked remarkably similar. Both came from individuals who
were infected at the Metropole Hotel in Hong Kong and then flew
home to Canada. In Vancouver, however, no additional cases grew
out of the initial infection. In Toronto, that single case sparked
a huge outbreak where ultimately hundreds of people were infected.
Why did such different scenarios grow out of nearly identical situations?

Dr. Lauren Ancel Meyers helps create mathematical
models that not only predict the spread of disease but can
also simulate various interventions strategies to determine
the one that might be most effective.

“It sounds intuitive, but the key difference between these
scenarios is that the infected individuals had very different contact
patterns,” says
Dr. Lauren Ancel Meyers, an assistant professor of integrative
biology at The University of Texas at Austin. “In the Vancouver
case, the man lived alone with his wife, and he went immediately
to a hospital where he was isolated and where caregivers took significant
precautions while treating him. In the Toronto case, the woman
was from a large multigenerational family. She died at home as
an undiagnosed case of SARS, meanwhile exposing many people in
her family who later went on to expose other people.
“So the contact patterns of the first few cases can make
all the difference as to whether you get a big outbreak or epidemic
or
none at all.”
Understanding the contact patterns in a community
is central to Meyers’ research. She uses mathematical modeling
to track and predict the spread of infectious diseases in a community.
Earlier
this year the University of British Columbia Centre for Disease
Control (UBC CDC) asked her to help them understand the spread
of SARS in Canada and worldwide and to determine the most appropriate
intervention strategies to stem the disease.
Meyers worked with
Dr. Babak Pourbohloul, director of mathematical modeling at the
UBC CDC, and members of the Scientific Investigators’ Vaccine Initiative
(SIVI) to create a mathematical model that describes the spread
of SARS through
a
city. Using demographic
and census data from Vancouver, they built a model of the patterns
of interaction in the city. Household size, the number of houses,
distribution of schools and hospitals and other data allowed them
to construct a network that represents the way individuals actually
interact in the community. Once they understand those interactions,
they can predict how rapidly a disease will spread, what parts
of the city are most at risk and what preventions are most effective
in stopping it.
Using mathematical models to analyze the spread
of the disease isn’t new, but Meyers and other researchers
are approaching modeling in a new way, using network theory.
In
the past, most mathematical modeling of epidemics was undertaken
by separating a population into three or more distinct groups:
those who are susceptible to a disease, those who are already infected
and those who have recovered. It assumed that there was some probability
that those who are susceptible would come into contact with those
who were infected, that those who were infected would recover,
and that in some cases, those who recovered would once again become
susceptible.
“This doesn’t take into account the true heterogeneity
of contact patterns that underlie the spread of disease,” says
Meyers.

Traditional mathematical modeling of epidemics
(top) places individuals in large groups and tries to predict
the probability of movement from one group to the next.
Network theory (bottom) allows researchers to build more
complex models that take into consideration the contact
patterns of individuals.

In reality, all susceptible people do not face the same
risk of contracting a disease. An elderly person living alone
at home is
much less likely to come into contact with an infected person
than someone who works in a large office building or a hospital,
for
example. In the initial Canadian SARS cases, it is clear that
living in a large family increased the chance of contracting a
disease.
The type and frequency of interactions that a person has with
others is key to determining who may become infected.
“Using network theory, instead of grouping people into populations,
we take into account every single person, and every single person
becomes a point in a network,” says Meyers. “Now let’s
say a person brings a disease like SARS into a community. We can
predict what parts of the community—the network—will
be infected, how quickly it will spread, and how best to stop it
.”
Network theory is often used by researchers investigating
social interactions, and it’s become popularized in the past
decade through the concept of “six degrees of separation.” “Six
degrees of separation” asserts that each person on the planet
is at the most removed from every other person by six degrees,
or six connections with others. The term was popularized by the
playwright John Guare, who wrote a play of the same name which
was later made into a movie. And a few years ago some college students
in Pennsylvania created a “six degrees of Kevin Bacon” game
that become an instant fad, asking players to link the ubiquitous
actor to other actors in a maximum of six steps.
The mathematical
models Meyers builds borrow from sociological approaches. The models
account for the points of connection between individuals.
“Each person within a community is represented as a point
in the network,” Meyers explains. “The edges that connect
a person to other people represent interactions that take place
inside or outside of the home, including interactions that take
place at school or work, while shopping or dining, while at a hospital,
etc. The network thereby captures the diversity of human contacts
that underlie the spread of disease.”
Some people may come
into contact with very few people, but others may have many strands
connecting them to other people in the community
through their work or social habits. If this person becomes sick,
he or she has the potential to become what researchers call a “superspreader,” someone
who spreads disease to a lot of people in the community. Identifying
potential superspreaders is one step in curbing an outbreak.
This
type of mathematical modeling may have important implications
for public health officials. When the SARS outbreak began, officials
were in a quandary. They needed to act quickly to control the
spread
of the disease, yet they lacked the information necessary to
determine which interventions would be most effective. Would they
be best
served by closing schools or by supplying health care workers
with better face masks, by limiting air travel or by waiting for
a vaccine?
Such decisions may be easier to make in the future, thanks to
advances in mathematical modeling.

This shows a municipal contact network. In
a city, SARS can spread within households, schools, workplaces,
hospitals and public spaces. The lines between the dots
represent contacts between individuals that could potentially
lead to disease transmission.

“Mathematical models allow us to simulate the spread of
diseases through different kinds of settings and test different
kinds of
interventions,” says Meyers. “This can give policymakers
the tools and confidence to make educated decisions.”
Meyers
first started working on mathematical models in the spread of infectious
diseases while doing postdoctoral research in Atlanta and at the
Santa Fe Institute. She collaborated with Mark Newman from the
University of Michigan, one of the pioneers of epidemiological
network modeling,
and some
researchers at the Centers for Disease Control and Prevention (CDC)
who were trying to figure out how to stop the spread of mycoplasma
pneumonia—known as walking pneumonia—in hospital
wards, military barracks, college campuses and other places where
individuals come into close contact.
“Before we began this project, the CDC hadn’t yet
determined the best strategies for controlling the spread walking
pneumonia
because they can rarely do experiments when an outbreak is in progress,” Meyers
explains. “They can’t treat half the population and
not the other half. It is also difficult to compare the success
of interventions on different outbreaks because the settings in
which they take place are often quite distinct.”
Meyers and
her collaborators developed a mathematical model of a psychiatric
institution in Indiana, building a network that accounted
for everyone who works or lives in the facility. She found that
while the focus is generally on preventing the spread of walking
pneumonia from patient to patient, caregivers play a much more
important role in the largescale spread of respiratory infections
across such a facility. Caregivers pick it up in one ward and spread
it to the next, and because of their diverse patient load, a few
infected caregivers can potentially lead to the infection hundreds
of patients.
“Looking at this from a network modeling perspective allowed
us to see how important changing the behavior of caregivers is
to
stopping an outbreak,” Meyers says.
The models then enable
researchers to simulate a change in caregiver behavior and project
the response in the spread of disease. This
allows policymakers to test possible interventions before investing
time and money into them.
And should SARS or another respiratoryborne
illness threaten Vancouver, policymakers there will similarly
be able to test possible interventions
before implementing them.

Air travel can enable illnesses like SARS and
flu to cross international borders. Meyers is working on
a model of global disease transmission based on flights in
and out of American cities.

Because contact patterns differ from community
to community, mathematical modeling requires that a model be built
for each individual community.
Meyers and Pourbohloul are currently working with a large team
of Canadian epidemiologists and infectious disease experts to
build network models of four Canadian hospitals and two communities—one
rural and the other urban. Once good network models of these hospitals
and communities are in place, they can be used to predict and control
the spread of all kinds of diseases.
At the same time, modeling
these distinct communities will allow researchers to look to see
if they can draw any generalizations
across communities. They hope to be able to say that, in general,
one type of intervention works better than another. Ideally, however,
each community, be it a large city like Toronto or a community
like The University of Texas at Austin campus, would have its own
model to use as a tool for preventing the spread of disease.
Meyers
likes the idea of building some models closer to home, be it for
Texas or Austin or the university campus. In the meantime,
she’s working on Canada and beginning to build a network
model of global disease transmission based on the flights in and
out of American cities. This kind of larger scale model would be
extremely helpful for diseases like SARS and flu that cross international
borders.
When reflecting on networks, Meyers calls to mind one of
this year’s
other big news stories: the big power outage.
“You can think about electricity spreading along a grid like disease
spreading through a population,” she says. “But our
goals for electricity and epidemiology are opposite. With electricity,
you want to make sure your network is built so that if something
happens to cut down one of your links, the whole system is not
going to crash. In the case of disease, you want to break the connections
through vaccinations or other interventions that most effectively
stop its spread.”
Vivé Griffith
Photos: Marsha
Miller
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