Disease, Heart Attacks and Grizzly Bears: An Introduction to Mathematical Biology

As I've mentioned in a previous post, I'm currently completing a master's degree in mathematical biology. Since this isn't the first thing people see opening up the newspaper or gossip magazines, I thought I'd give you an idea of what exactly mathbio is and what it entails.

The short version is that mathematical biology is exactly what it sounds like: using mathematical methods and techniques to solve problems in biology. What kinds of problems, you ask? Almost all areas of biology can be found in a mathematical context, from ecosystem management to immunology to pure evolutionary theory. Pretty much any area you could study in biology has had someone, somewhere look at things from a mathematical perspective.

Personally, I think that this is a great thing, both on the biological side and the mathematical side. The biology community gets new angles to view problems from and hard quantitative results that can be the basis for experiments and further hypotheses. The mathematical community gets motivation for problems and for more pure mathematical research areas. And everyone gets solutions which could potentially save lives and better the understanding of the world we live in. Mathematical biology is undergoing a revolution of sorts, which began earlier in the 20th Century, and whose fruits are being realized now at larger scales, and not just in the ivory tower. Let me give you a few examples to illustrate this.

Take mathematical epidemiology. In Canada, this seems to be the largest subfield of mathbio (but I could be wrong). This area looks at the study of infectious diseases and epidemics and tries to model them using equations. The goal is to better understand how epidemics begin, persist, and what can be done to prevent or constrain them. Using mathematical models allows researchers and medical professionals to consider different scenarios and look at specific factors and their impact, without any risk or harm to the general population. For example, I've seen models looking at factors causing and preventing Mad Cow disease in livestock, of HPV (human papillomavirus ) and the effectiveness of potential vaccination regimes, and of the spread of HIV in parts of sub-Saharan Africa. These are certainly real issues with real consequences, and solutions are being developed by applied mathematicians and health researchers.

Or perhaps you'd be more interested in mathematical ecology. Ecology is the study of how species interact on a macro level in ecosystems, and what affects the population growth or decline of species. Modelling predator-prey or competing species interactions are classic examples of mathematical biology. One of the most studied examples is the dynamics of lynx-hare populations in the Canadian Arctic. The hare is prey for the lynx, and as one population changes, so does the other. Salmon are an example of competing species. Salmon farms are usually situated near wild salmon habitats, so they use some of the same resources, and there is a chance that either the farm or wild salmon could wipe out the other, each case with negative consequences. I have seen papers and presentations of both ecological situations. Even more interesting is the fact that such ecological modelling has yielded some rich mathematics, specifically for the fields of dynamical systems and chaos theory. Perhaps this shows nature has much to show us about the intricacies of mathematics.

If neither of those took your fancy, perhaps you'd be interested in mathematical physiology and medicine. This area sees the mathematical modelling of physiological processes and medical treatments, and attempts to use math to gain a better understanding how the human body works and how we can better heal it. One big area of research here is tumour development and growth. Here, mathematics and related methods are used to study how tumours grow and sustain themselves and how they can be stopped or at least controlled. Related to this is the study of cancer and how it begins at the cellular level. I have also seen research done on causes of heart attacks and irregular heartbeats and how a to design a better kidney dialysis machine, both using good old mathematics. This I think could be the most promising area of mathbio research, since it could benefit almost everyone by furthering our understanding of medical treatments without using real patients or scarce medical resources. And again it could also give more insight to underlying maths that are used to model such problems.

I should mention that my research isn't really in any of these research areas. I'm more into evolutionary game theory and the evolution of cooperation, which is a pretty cool topic in itself, loosely based the question "Why bother helping others out when you just free load instead?". I'll give more insight to this question and my rears later on. But I hope that I've at least shed a little light on this thing called mathematical biology. But there's lots more than what I've written above. From tropical diseases to why we have sex, a mathbio researcher has used math to understand it.