By Angus McClure
This summer, together with my supervisor Prof Geoff Mercer, I have been working on constructing mathematical models describing the spread of a disease caused by the bacteria Clostridium Difficile (C. Diff). This bacteria colonises people’s guts and when it’s present in large numbers starts to produce toxins which give their host diarrhea and intestinal damage. The disease is usually not much worse than normal diarrhea, but can be hard to get rid of and sometimes lethal.
Inside of every human’s gut are billions of bacteria. They are mostly harmless, and a lot of them are essential for good digestion and a healthy immune system. When you take antibiotics a lot of the bacteria in your gut are killed. The bacteria in your gut will eventually grow back but for a period your gut is unclaimed territory. This creates room for other bacteria like C. Diff, which is resistant to some of the most common antibiotics. So, unfortunately, while antibiotics are the best way to treat many bacterial infections, taking some antibiotics put you at risk of getting a C. Diff infection.
But why would I want to make a mathematical model of C Diff?
I was asked speak at a school to a group of Year 10 students to convince them that they should all study maths and tell them what I’d be studying over the summer. One student asked, “How do you study how the disease spreads? Do you infect some people and see what happens?”
No. The Ethics Committee would not approve. It would also be pretty hard to find some willing volunteers for the study. But, ethics aside, this might actually be the best way to study the spread of a disease. Because you could control who gets sick and who they contact, you would be able to figure out each aspect of the spread of the disease. Repeated experiments would provide all sorts of insights into the factors, which accelerate or decelerate the spread, and tell us what sort of things we could do to prevent the disease from causing lasting damage. However, human lives are valuable so we have to find some other way.
This is where mathematical models come in. Using mathematical models we can create simple simulations, which mimic these experiments, or a hospital or community, without putting any human life at risk.
Creating a model is like creating a game. You write out a set of rules describing the sorts of things that can be done in the game. With the right set of rules the game might mirror real life giving you insight into the rules, which underpin our world. Once you’ve figured out a realistic set of rules you can tweak them and see what happens. This gives us an idea for what sort of things we might do differently in real life to change the world the way we want.
Over the summer we made a couple such models using the language of mathematics to write the rules. I then wrote a program that gets a computer to follow these rules to produce a simulation of a hospital as C. Diff spreads through it. We had a number of promising results. Though currently giving more people more antibiotics just increases the number of cases of C. Diff infections, our model showed that modest improvements in the antibiotics could drastically decrease the number of C. Diff cases.
A lot more research needs to be done before we can connect what we observed in our model to more effective treatment, but the result shows that controlling C. Diff may be easier than we thought.
Angus McClure was one of the recipients of a 2013/14 AMSI Vacation Research Scholarship.