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Seminars can induce a near catatonic state in some students. However, a seminar series is where Abdul-Aziz Yakubu (pictured left) saw past the often tedious details and into the widespread relevance of mathematical biology, awakening a lifelong passion. This native of Ghana, who is now a professor at Howard University in Washington, D.C., began his love affair with mathematical biology while attending doctoral seminars at North Carolina State University (NCSU) in Raleigh. John Franke and James Selgrade, two extraordinary mathematical biologists, inspired Yakubu and helped explain the bigger picture for him. "I have always had an interest in trying to apply my mathematics to help mankind as best I could," Yakubu states.

Yakubu's journey to aid mankind began in his West African homeland. A talent for mathematics placed Yakubu in one of the relatively few openings at the University of Ghana, where he received a B.S. in mathematics and computer science in 1982. Despite Ghana's excellent educational system, the economic depression left few career opportunities for researchers. So, like many of his African colleagues, he came to the United States. He received his master's degree from the University of Toledo in Ohio in 1985 and his Ph.D. from NCSU in 1990, both in applied mathematics.

At Home in Academia

Soon after completing his doctorate in 1990, Yakubu was recruited to Howard University by Fern Hunt--then a Howard University mathematics professor and now a research mathematician with the National Institute of Standards and Technology's Mathematical Modeling Group--and James Donaldson, now dean of the College of Arts and Sciences at Howard University. He quickly climbed the ranks from assistant professor to associate professor--he was tenured in 1995--and became a full professor a couple of years later.

Yakubu says, "Fern Hunt and James Donaldson provided me a home here and that made it possible for me to advance my career in a very friendly, very supportive environment. That's rare. I could not imagine a better environment for me to grow than here at Howard."

Although Howard became home, Yakubu accepted visiting professorships at NCSU, Cornell University (where he later accepted an adjunct position), the University of Minnesota, the Mathematical Sciences Research Institute at Berkeley, and Los Alamos National Laboratory. The relationships he developed at these institutions allowed him to forge collaborations with fellow experts, participate in lectures, and present papers nationally and internationally. While at the biometrics department at Cornell University (from 2000 to 2002) he worked with mathematical biologist and Next Wave feature guest editor Carlos Castillo-Chavez, as well as other biologists and physicists who helped him sharpen his biology skills and exposed him to possibilities in mathematical biology that he had not previously considered.

Modeling Biological Possibilities

Those possibilities included observing phenomena of purely mathematical interest in biological systems. It is sometimes easier, Yakubu believes, to generate interesting mathematical questions from biology than from pure mathematics. Yakubu started with ecological studies, like the effect of dispersal or migration on species persistence and the conditions under which species go extinct. "Having come from Africa," he says, noting the impact of human activities on wildlife, "I've always been interested in endangered species." He also studies questions about human interactions, the spread of disease, and epidemics, especially how they affect "developing countries and poor people everywhere."

Whether the subject is disease distributions, predator-prey interactions, specific organs and systems, sleep patterns, human locomotion, or the other myriad systems, Yakubu asserts that mathematical biology provides insight into questions that cannot be reasonably or adequately addressed in the lab or the field. Many things that were not tractable in the past--such as the patterns of epidemics--are now explicable with mathematical biology. Yakubu goes on to explain that mathematical biology allows conditions to be manipulated to extremes that would be unethical, cost prohibitive, or otherwise unwieldy. "These are exciting times for mathematical biology," says Yakubu. "I don't see an end."

When it comes to training, Yakubu believes that, while mathematical skills are important, mathematical biologists must also know as much as possible about the system(s) being modeled. Mathematical models have limitations, and Yakubu sometimes uses lab observations and/or field work to validate a model's conclusions. "In building a model one has to be careful; it is really a balance between how much complexity you allow in the model as compared to how much of the model you can analyze," Yakubu cautions. The objective, he notes, is to capture the essential features of the phenomenon being modeled without being so simplistic that its conclusions are irrelevant (see sidebar). A project headed by Yakubu's graduate student, Shari Wiley, exemplifies using simplicity. Three fish species (mackerel, herring, and sand lance) are used to begin modeling the entire food chain present at George's Banks, North Carolina.

Computer Imperfect

Yakubu notes that while computers can help to manage complex studies, it is important for mathematical biologists to be able to use pencil and paper as well as computers, because even modern, high-speed computers are subject to errors in the numerical results. These errors occur, for example, when a model is especially sensitive to initial conditions; "then for all practical purposes, the long-term behavior of the model defies numerical computation. Small errors in computation, due to round-off errors, may become magnified as time evolves. The results of numerical computation of a life history, no matter how accurate, may bear no resemblance whatsoever with the real life history." Consequently, the best results are qualitative--the kind that pencil and paper are best at producing--because they can be explained step-by-step and without approximations.

Keeping Learning Relevant

Yakubu imparts his passion to his undergraduate students and his three graduate students--whom he meets with individually every other day. "I realize the way to motivate students is to give them as much attention as you can," he says. He teaches two classes where he introduces new topics with real-world significance. The professor explains, "Once students realize the significance of what they're about to learn, they become more attentive." He personally checks their answers, and those with the best solutions present them to the class because passivity is not allowed.

"There is definitely a role for mathematical biology, and in fact, I'm hoping one of the things we're doing at Howard [is to] encourage more of our students to choose this area. New diseases are constantly developing. The more people we have, the better it is going to be for everybody." Yakubu emphasizes the discipline's career potential. "This is a very good career path. Our students all over, especially minorities, need to know this. The best brains are yet to be attracted to this field and we have a lot of top talent in our minority communities here. A lot of minorities are not attracted to mathematics because they really don't see an application that connects them to their community. With mathematical biology you can make a tremendous contribution."

For students who want to prepare themselves for careers in mathematical biology, Yakubu recommends learning differential equations, dynamic systems, bifurcation theory, statistics, and biology. But Yakubu also emphasizes the importance of picking up whatever knowledge is needed to understand a problem. His graduate students have incorporated this advice into their coursework. Shari Wiley, for example, is taking economics to understand the economic impact of fishing activities. "You learn whatever tools you need to answer the question. The rest is persistence."

Clinton Parks is a writer for MiSciNet and may be reached at cparks@aaas.org.

Clinton Parks is a writer for MiSciNet and may be reached at cparks@aaas.org.