MAST90011: Modelling: Mathematical Biology

3x assignments, 25% each. Two-hour exam, 25%.

This is a great subject, highly recommended for anyone interested in real-world applications of maths! It's called "Mathematical Biology" but you could argue that it's really a course in modelling scientific problems using maths, where all of the examples just happen to come from biology. This a nice break from most of what's called "applied maths", where the problems come from physics and engineering. There's no biology knowledge assumed, and if you're expecting any highly-specific models of particular biological systems, you're in the wrong place. It's also not a pure maths subject, so if you love theorems and proofs, you're also in the wrong place.

Lectures: Kerry is a great lecturer. She's very enthusiastic and this subject is directly connected to her research interests. The lectures are quite old-school, in that everything important goes on the whiteboard and you have to copy it down. Ideally with multiple colours and a ruler, since the diagrams are an important part of understanding the concepts in the course. At the end of every 2-hour lecture, I emerged with three pages full of maths and pictures and my head spinning with new ideas. (If you've done lots of applied maths before, the general techniques will be slightly less new, but still enough to be interesting and exciting.) This is the only subject I did this semester where I didn't miss a single lecture.

Course content: I feel like this course was teaching "how to be an applied mathematician" on a few levels simultaneously, although the connections didn't really click until I got to the end of the semester. The overarching idea is that you can take a description of a biological system, distill it down into the most important bits and write it out in the form of equations. Usually the equations are nonlinear and have no exact solution, and a numerical/computational solution might not give you the insight you want. But through a bunch of clever tricks, you can still figure out the qualitative behaviour of the system: what are the equilibrium points and long-term behaviour? Is the system stable after small perturbations? What happens when you change parameter values? Sometimes highly simplified mathematical models have inspired biological experiments to prove or disprove particular hypotheses. There was an emphasis on relating properties you'd deduced about the mathematical system back to the real-world problem.

On the maths side, the tools of choice are discrete-time models (two weeks), ordinary differential equations (two weeks), partial differential equations (six weeks), stochastic models (one week) and cellular automata (one week). That's a lot of differential equations. I hope you like them.

On the biology side, it was almost a new topic every week. We covered: simple population models, host-parasitoid systems, insect outbreaks, epidemics and infectious disease models (including the maths behind vaccination and herd immunity), "invasion" processes (on a cell and population level), chemotaxis, morphogenesis and cancer modelling. There were often surprising parallels to the maths describing cell-level and population-level phenomena, which I thought was cool.

Assessment: Unfortunately, I'm not so much of a fan of Kerry's marking. I'm not complaining about any particular marks I got, but it was sometimes hard to know what was expected in assignments. People had marks deducted for being "inelegant", not writing enough or writing too much. Most people's marks improved dramatically after the first assignment. The exam is only worth 25%, and the one this year was ... surprisingly pleasant. No really nasty calculations, lots of sketching diagrams and discussing qualitative aspects of biological systems.

Nope.

Professor Kerry Landman

Nope.

5/5

There are two recommended textbooks: "Mathematical Models in Biology", L. Edelstein-Keshet (1987); and "Mathematical Biology", J. D. Murray (2003). No need to buy either of them.

1x two-hour lecture, 1x one-hour computer lab / tutorial

2014, Semester 2

H1

3 assignments (worth 25% each), 1x2hour exam (worth 25%)

I thoroughly enjoyed this subject. Kerry is a great lecturer and you get a taste of what mathematical biology actually is, and what it tackles.

Mathematical biology is a relatively new field of maths, and in this subject you'll look at:

- population growth
- epidemic modelling
- biological invasion
- pattern formation
- tumour modelling

At the start you look at discrete models (e.g. the discrete logistic equation )
To be expanded on

No

Kerry Landman

No

5/5

Edelstein-Keshet, L. Mathematical Models in Biology. McGraw Hill, 1987.
Murray, J. D. Mathematical Biology. Springer Verlag, 1990 (or the new 2 Volume Third edition, 2003).
Britton, N. F. Essential Mathematical Biology, Springer, 2003.
Dr Vries, G., Hillen T., Lewis, M., Muller, J. and Schonfisch, B. A Course in Mathematical Biology. SIAM, 2006.

These are only recommended for learning a bit extra on the material.

1x2hour lecture per week, 1x1 hour practice class

2012, Semester 2

Will release once results are released