Thanks for coming!

Special thanks to James Lane and Callum McDougall for participating in a trial run of the talk and providing useful feedback. Thanks also to The Archimedeans (Cambridge University Mathematical Society) for hosting me.

Video

Feedback Form

I’d really appreciate it if you could fill up the following feedback form: https://forms.gle/CZj4TJXqazohsaPE8

Whether positive or negative, it helps a lot to know what works and what doesn’t, and especially what I should improve the next time.

RESOURCEs:

I think there are many fascinating and really important* areas of research at the intersection of maths and biology, and I would love to see more maths students going into this stuff. I’m super excited by it, as anyone who knows me in real life can verify. I hope I made a good case for that (at least for epidemiology) but here I have also included some general math-bio resources. Feel free to contact me if you have any questions on that, or the talk.

Index:

• Slides
• Code for graphs and simulations
• Short version advice for those interested
• Papers (a bit of random selection)
• Recommended books
• Recommended courses to take
• Other related fields I’d like to learn more about
• Interest form

*I hope the coronavirus pandemic has been enough to convince you that this is important, but here is some content on that (from a more practical perspective).

Slides:

For this talk:

For the previous talk:

Code for graphs and simulations:

https://github.com/meryjoy99/mathematical_modelling_infectious_diseases based on http://homepages.warwick.ac.uk/~masfz/ModelingInfectiousDiseases/index.html (figures also taken from there)

Short version advice for those interested:

• Read this essay by Cohen on Mathematics and Biology (first one listed below )
• Sign up to my ‘interested’ list (at the bottom of this page )
• Take/learn Part II Mathematical Biology (more courses recommended here )

Papers (a bit of random selection)

• (Essay:) Cohen JE (2004) Mathematics Is Biology’s Next Microscope, Only Better; Biology Is Mathematics’ Next Physics, Only Better. PLoS Biol 2(12): e439. https://doi.org/10.1371/journal.pbio.0020439
• Heffernan J.M, Smith R.J, Wahl L.M. (2005) Perspectives on the basic reproductive ratio J. R. Soc. Interface. 2281–293 http://doi.org/10.1098/rsif.2005.0042
• (For the pure mathematicians:) Reed, Mary. (1997). Algebraic structure of genetic inheritance. Bulletin of The American Mathematical Society – BULL AMER MATH SOC. 34. 107-131. 10.1090/S0273-0979-97-00712-X. Link here.
• Gross K., & Snyder-Beattie, A. (2015) Core mathematics to support new theory for distributions of biological diversity along environmental gradients Link here.

Recommended books:

Many on my to-read list will hopefully be added here as I read them, but so far:

• Modelling Infectious Diseases on Human and Animals, by Keeling and Rohani. It does exactly what the title says. I based my talk almost entirely on it, although I completely skipped the chapter on Multi-Host Multi-Pathogens Models and there are many other interesting things I did not touch on. It also has many applications to use the models with real epidemiological data.
• Mathematical Biology, by J.D. Murray. This is the canonical introductory textbook on math bio (there are actually two volumes), so it covers much more than epidemic models.

Both are freely available online (use iDiscover if needed).

Recommended courses to take:

(These are from Cambridge Maths, sorry if anyone from other university is reading this!)

Apart from basic applied courses, like Differential Equations, Vectors & Matrices, Vector Calculus (and Probability) in IA, and Methods in IB:

• Mathematical Biology (Part II): This is obviously the most related course to take. I’d recommend the set of notes available here. It doesn’t have a lot prerequisites other than basic applied stuff (I know puremos who took it and enjoyed it.)
• Dynamical Systems (Part II): This course covers the theoretical background needed for most of math bio, and it is also very mathematically interesting on its own (chaos theory!). (I realise there aren’t any good recent set of notes online – if people request it I’ll consider making mine publicly available.)
• Statistics in Medicine? (Part III): I don’t know much about it, but I’ll be taking it this year, so I’ll update that at some point in 2021 (do let me know if I don’t!). According to its description, there are at least a bunch of lectures on epidemiology, while others may go more into genetics and medical trials.
• CATAM/Programming: My impression is that computational methods are very important in mathematical biology, at the very least for numerical solutions. Although don’t worry if you didn’t enjoy CATAM, almost nobody does. While I thought it was okay and I got better at it over time, I now enjoy programming much more (learning Python has been a good change from MATLAB).

Other: I suppose Stats/Probability are always useful (in particular, I’m told Part II Applied Probability has overlapping stuff with the master equations from Part II MB), and so may some applied numerical analysis. Fluids seems to be helpful when it comes down to the modelling, but there is no content needed from there (unless you want to do biophysics/biofluids). I’m also trying Part III Perturbation Methods this year, so we’ll see how useful it proves to be.

If that doesn’t quite fit your course choice…
Don’t worry! I’m half mathematical biologist half theoretical physicist so I’ve taken many courses outside of that list and I haven’t done applicable or fluids since IB.

As you see, there aren’t many obvious pre-requesites for epidemiology/mathematical biology, and I think that is great! If you’re interested in one topic, you can read the relevant chapter of a good textbook/set of notes and then read current papers, unlike in (say) physics (where you have to learn many part II & III courses before that). Because of that, I was able to do a summer research project after IB (so even before having taken the math bio course!), which is something I’d definitely recommend to anyone considering an academic/research career.

Other related fields I’d like to learn more about:

(Not sure how much they intersect:)

• Biostatistics, Mathematical genetics
• Systems biology
• Bioinformatics, Computational biology
• Synthetic biology
• Genetic engineering

Interest Form

I’d like to come up with an exciting way for myself to keep learning about math-bio and to see how interesting (or not) this is to people, so I’ve got a few ideas. It is quite experimental, but if you may be interested in any of the following:

• More talks on Mathematical Biology, Epidemiology or related topics
• Suscribing to a mailing list with interesting content on these areas
• Joining a (likely online) study/reading group on these areas

or have any other math-bio ideas, do fill up this form!