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.

"I'm Thinking of Going to Grad School"

So, you're thinking of going to grad school. I think that's great, because in some ways, being a graduate student is terrific. However, in some ways, being a graduate student is a bit of a crappy career path. It really depends on your motivation, your career goals, and your opinions on education in general. It's not a trivial decision.

Basically, my opinion is this: if you don't like school or "academia", don't go to grad school. You probably won't like it, and will likely hate it. If you enjoy school and are good at it, you might like grad school, but there are other considerations to be had too.

So, without further ado, here's the breakdown of reasons to go and not go to grad school:

Reasons to Go:

• Pursuing an academic career: This one is pretty obvious. If you want to have a job in academia as a professor or researcher, you'll need to start you journey in grad school. Doing some postgraduate work is a good way to figure out if going down this path is right for you. Talking to other grad students or professors is also a good idea. The academic life is something of a calling, but look into it if you think it's for you.
  
• Gaining experience for a particular career: While a Bachelor's degree is a good thing to have on your resume, there are a few jobs that typically look for more. For example, some jobs in finance or investment banking look for individuals with Master's or PhD degrees. Some administrative positions in education require at least a Master's. And I've also heard that you'll be taken more seriously as an author with an advanced degree. In some disciplines such as mathematics, graduate level education is much different from undergraduate, and employers may be looking for something specific. In all of these cases, the knowledge and skills you'll acquire in graduate work will be helpful, and be put to good use.
  
• Continuing previous work done: This is perhaps an unusual reason, but still a valid one. You may have done some work for a professor or researcher during your undergrad, as a research assistant, programmer or TA. If it went well, and there's still more work to be done, maybe they'd take you on as a graduate student. You gain a good reference and an advanced degree for your resume. They get continuation on their work and an established collaborator. For some people, this is a win-win situation. I personally think this benefits everyone involved, and can foster strong professional relationships.

Reasons to Not Go:

• "Couldn't think of what else to do": This is hands down the worst reason to go to grad school. Indifference is a terrible thing to have in academia. If you're not "into" your research, it will show. It is hard to be motivated and take initiative to read current journal articles on narrow topics such as pair approximation methods in lattice-based population dynamics models. It'll also be hard to prepare for tutorials for dozens of first year engineering students, some of which are wondering why they lost marks on that one question they knew they got right, and others of which get up and leave noisily as you try to demonstrate how to compute a matrix inverse. Believe me, if you really turn your nose up at either of these situations, perhaps graduate work is not for you.
  
• No interest in research: If you don't like the idea of doing hardcore academic research, perhaps consider another career option. Research is the order of the day as a graduate student (and in turn as a professor). If you're writing a thesis, you must come up with some original research to publish. If you're taking a course-based degree, you will still have to read academic papers and books. In any case, graduate study is much more independent than undergrad. Even if you like the teaching aspect, disliking research will not make for a good time in grad school.
• Money: It has to be said: If you want to make a lot of money, don't go to grad school. You will be poor. Even if you score a major grant or scholarship, you will make less than entry level wages. People who want a corner office on the top floor and a posh urban loft typically don't go to grad school. They go to the so-called "corporate" world, right after college or university. Wanting to make a lot of money isn't bad and I'm making no judgments here, but I can say that you probably not enjoy the grad school life. I certainly know people who went to work right after their first diploma/degree, and they couldn't be happier for it. You just have to know yourself and what you want. The upside here is that your career prospects may improve if you have an advanced degree, so you may need to do a cost-benefit analysis to see if it's worth a few years of have a "lower" income.
  

This list is by no means exhaustive, but hopefully it paints a picture of what the grad school life is like. I can say that I think I make a good decision for myself. On the whole, I love what I'm doing right now.