# Biology Outside the Box

Have you ever wondered how epidemics such as West Nile fever might be controlled, how cells signal each other, whether a new invasive species will decimate an ecosystem, or how to treat cancer patients optimally? All of these questions have something in common: Researchers at the University of Alberta are using mathematics to answer them. Work on these and related problems goes on at the University of Alberta's Centre for Mathematical Biology, a place dedicated to approaching biological sciences with mathematical and computer methods.

Working As a Group

Working groups, including both mathematicians and biologists, tackle these problems. Their success depends on collaboration and dialogue between group members, many of whom have different skills and training.

For example, our recent project at the centre on controlling West Nile virus involved collaboration between a postdoctoral researcher in biology (Marjorie Wonham), a graduate student trained in computer science (Tomas de-Camino-Beck), and myself (a mathematical biology faculty member). Initially, Marjorie researched the biological problem, which involved details about the dynamics between the two main disease carriers: birds and mosquitoes. The model, to which we all contributed, was written as a system of differential equations.

I spearheaded the mathematical analysis of the equations, and Tomas programmed the equations on the computer. Later, Marjorie collected data for the model, and Tomas and I compared the model's predictions. Using our model we could provide guidelines for controlling the virus. In the end, our research process was truly collaborative--none of us would have succeeded alone.

Why Use Math?

Why use mathematics at all? The aforementioned problems--control of epidemics, cell signalling, invading species, cancer treatment--are tremendously complex and influenced by many possible factors. Behaviours may be unpredictable, important factors may be left out or even underestimated, and models are not guaranteed to work the first time. Without careful tracking and analysis of the complex dynamics, we cannot hope to find answers. Research in mathematical biology involves a constant iteration of model development, analysis, prediction, and comparison with data. A common reward for mathematicians is the discovery of new, interesting mathematical problems that are fun to solve.

Sharing the Fun

Part of the fun also comes from sharing discoveries and ideas with students. One successful program developed at the University of Alberta is the Mathematical Biology Summer Workshop. This 10-day event held in May includes lectures, problem solving, computer labs, and collaborative group projects. The subjects covered in the group projects are often open-ended and leave plenty of room for individual creativity and discovery. The summer school finishes with presentations by each group and then a barbecue. The Pacific Institute for the Mathematical Sciences ( PIMS) funds the summer workshop, and it is a great way to start the summer break.

Math in the Mountains

Another place where mathematical biology is taken to new heights is at the Banff International Research Station (BIRS), nestled in the town of Banff and surrounded by the Rocky Mountains. The purpose of BIRS is to foster new and original mathematical research in key areas. Mathematical biology has been the feature of workshops, weekend retreats, and focused research group projects at BIRS. The quiet mountain atmosphere and outstanding facilities make it a great place to get work done and to collaborate.

A Worldwide Field

It is evident to anyone attending meetings such as those at BIRS that the problems that mathematical biologists work on span time zones and international borders. For example, several people at the centre are involved in a working group that uses dynamical systems to model the ecological and economic impacts of invasive species (such as zebra mussels) in the Great Lakes of North America. This group includes biologists from the universities of Notre Dame and Windsor, economists from Florida and Wyoming, and mathematical biologists from Alberta. Although the Internet facilitates easy communication among group members, nothing works as well as face-to-face collaboration on a project. So the centre at Alberta hosts about 10 international visitors each year and about the same number from other Canadian research institutions.

The field of mathematical biology is growing worldwide, and there are centres of excellence in many countries. International groups, such as the Society for Mathematical Biology (SMB), play an important role in building the mathematical biology community by holding annual meetings and mentoring young researchers.

Funding Is Key

The health of mathematical biology at the centre and elsewhere depends on funding. Several programs in Canada support mathematical biology. The Natural Sciences and Engineering Research Council (NSERC) gives operating grants to faculty members, and many faculty members apply through NSERC's interdisciplinary program. NSERC and PIMS also fund undergraduate, graduate, and postdoctoral researchers through individual fellowships. PIMS also generously supports a mathematical biology seminar series and activities of a collaborative research group within mathematical biology. The Mathematics of Information Technology and Complex Systems National Centre of Excellence provides matching funds for groups including researchers from academia, industry, and government. Other sources of funding include the Canadian Foundation for Innovation, the Canada Research Chairs program, the Alberta Government, and possible subcontracts from the U.S. National Science Foundation.

Careers in Mathematical Biology

Students come to mathematical biology with a wide variety of backgrounds, including math, biology, and other quantitative sciences. Through mathematical biology, math students gain an opportunity to tackle real-world problems and biology students gain a new set of tools and a framework for thought that gives an edge in the research process.

Over the last decade, the number of academic jobs involving mathematical biology has increased, particularly in math departments, as recognition of the field grows. Those with training in mathematical biology have a set of skills (quantitative methods, computing, teamwork, collaboration) that are also valuable to employers in government and private industry.

Getting Involved

If you are interested in further information about the Centre for Mathematical Biology and opportunities there, see our Web site. We would love to hear from you.

SMB provides an excellent Web page with resources for those who would like to get involved. Membership is only \$50 per year (\$25 for students) and includes a subscription to the Bulletin of Mathematical Biology, a top journal.

There are many opportunities for graduate and postdoctoral work in mathematical biology, which are occasionally listed with faculty jobs on SMB's job page. Alternatively, you can subscribe for free to an e-mail newsletter that contains job information and details on upcoming meetings, news, and educational opportunities (see SMB's Publications section). Finally, opportunities for education in mathematical biology, including both graduate and undergraduate programs, are available online.

Because the discipline of mathematical biology is still young and constantly developing, there are great opportunities for young scientists to contribute to the field if they are willing to learn, communicate, and think outside the box.

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