IA (HL) Maths IA HL - Is the SIR model and disease spread a good topic?

[The Angelus]

Hello

 

I have been looking for topics for my Maths IA, and I plan on doing it during the Easter holidays to get it over with.

 

I want to study medicine, and thus I wanted to choose a topic that would somehow be part of that, to show personal engagement. I looked at disease spread and found the SIR model. It involves calculus, but I am afraid that it is not indepth enough.

 

What I was looking to do is to try to show how I derived the SIR model, then to use real data and try to create a model and compare with the real life data (although I am not sure where I could find the data for a particular disease). I also wanted to include herd immunity and how changing certain factors can change the spread of disease, such as vaccinations. I would also include the Kermack-McKendrick theory, and perhaps try to prove it to make the maths more sophisticated. 

 

I would like to ask if I am going in the right direction or what changes you would suggest to my approach. I do want to get a 7 from this, so that I can comfortably get a 7 on the exams from maths HL. I am having doubts as to where this topic is leading.

 

Thanks,

 

Atham

Edited March 28, 2015 by Atham

[IbTrojan]

I don't know much about HL Math but I'll tell you this, there were quite a few SL Math kids in my school (and I'm sure in plenty of other schools) that decided to do this topic as well...so unless you have a different approach with a higher level of mathematics, I wouldn't suggest it

[The Angelus]

Since I will be using a model, I would have to somehow equate it to some real life example, right? I am unsure where to get this information however, since not all the variables I need will be available. 

 

For example, for a particular outbreak, it will be very difficult to find the statistics for the number of people that are immune, since vaccinated does not equate immune. 

 

EDIT: I found some data on ebola, but even before that I realized that the SIR is way too simplistic to be used to compare with actual data.

Edited March 28, 2015 by Atham

[Vioh]

Since I will be using a model, I would have to somehow equate it to some real life example, right? I am unsure where to get this information however, since not all the variables I need will be available. 

 

For example, for a particular outbreak, it will be very difficult to find the statistics for the number of people that are immune, since vaccinated does not equate immune. 

 

EDIT: I found some data on ebola, but even before that I realized that the SIR is way too simplistic to be used to compare with actual data.

 

Yes, SIR is too simplistic, especially as you are a HL student. One way of expanding it would be to use SEIR model instead. Still, I would listen to IBTrojan if I were you. There have been so many people doing this topic this year. In fact, 2 of my closest friends just finished their math IA on ebola & epidemiology. So you should do it only if you have a different approach! otherwise, you’ll just repeat what other people have done.

 

Also, there’re lots of things relating to medicines & biology that you can do. You can talk about genetics as it contains quite a lot of maths (e.g. a friend of mine did her IA on Hardy-Weinberg principle). Or you can make a mathematical model of divisions of cells (e.g. another friend of mine even intended to model the growth of tumors, which I think is a super cool idea). I myself didn’t take biology, but I think that you should be more open to other possible ideas. It’s not like ebola is the only thing that you can do with biology & math.

[The Angelus]

Well this pretty much sets me back to square one.  I was considering the SEIR model, as having the SIR as a first model, and then the SEIR model as a second model in the exploration. 

 

I was thinking of taking it the route of modelling the spread of "zombie apocalypse" but that has no practical use or anyway to prove or disprove a model.

 

For the Hardy Weinberg principle, was that a HL IA? I am looking at the growth of tumours as well. There seem to be different types of models there. I would have to somehow derive these models for a good exploration, correct? I may need to find some patient data to justify a model.

 

EDIT: I was looking at this article: http://ddd.uab.cat/pub/matmat/matmat_a2013/matmat_a2013a3.pdf

 and I thought that if I talked about vaccination and immunity that it may get a bit more complicated. However, I think I will just abandon the idea.

Edited March 29, 2015 by Atham