Liz Davis's Web Page at DIMACS
|Email: LDavis12@cornellcollege.edu |
I am currently a participant in the DIMACS REU program.
Over the summer, I'll be researching epidemiology, especially focusing on preventative measures.
So far, I'm just working on getting my hands into some of the models commonly used in epidemiology.
I'm especially interested in the juxtaposition of economics and epidemiology: how do we best use limited resources to curtail the spread of disease?
Originally, I was thinking of working on some questions regarding dengue fever, but after speaking a bit to Dr. Fefferman, it seems that that's going to be a bit too difficult for a single summer.
Instead, I'm going to be working on analyzing a model of some vector-borne illness with different transmission rates depending on whether a person is infected or not.
It seems that some diseases are quite skilled at manipulating host behavior to maximize their own spread, so that's what I'll be focusing on.
Click here to see my first presentation.
I spent a lot of time this week reviewing and learning for the first time some properties of difference equations, as well as coding the difference equations for
our model into Mathematica 7 so that I could see what they were doing over time.
The theme of this week is "Something Goes Awry with Liz's Difference Equations." I thought things were working out pretty well after meeting with Dr. Fefferman and
clearly defining one of our parameters as a function of the vector population and the host population, but then I had a case where it was possible for a single vector (mosquito, in this model)
to produce any real number amount of eggs, which is clearly not realistic... bad world, when mosquitoes can have 15000 babies per week if there are enough birds.
I think I've fixed the issue with epic numbers of new mosquitoes, after using a different equation for the parameter. I have to check it through with Dr. Fefferman for
conceptual accuracy, but I'm feeling pretty good with it. In other news, I *finally* understand what bifurcation diagrams are drawing a picture of, and I've coded it in Mathematica 7,
so hopefully I'll be able to give the project some solid pictures of what's going on in the system with a change in parameters. The issue is still, as usual, trying to understand this process
for a nine-dimensional system (we've got groups of well birds, sick birds, sick mosquitoes [1-3], well mosquitoes[1-3], and new-born mosquitoes]. Not many resources I've found deal with bifurcations
of such high dimensional systems, so I'll have to feel this one out.
I not only figured out how to make a bifurcation diagram in Mathematica for a system of difference equations (which, to tell the truth, wasn't as terrifying as I thought), but I also in the same week
managed to break that picture. Some things were going wrong (always with the same parameter), so I had to run to Dr. Fefferman to make sure I was using the right process.
Here's what I'm thinking: it all comes down that single parameter. Everything that is wrong in the equations with the long-term projections comes down to that singular parameter. Fortunately, Dr. Fefferman and I seem to have fixed it this week,
so hopefully we'll actually have the final equations and be able to start writing the paper.
Just finishing some business here at Rutgers before heading back home. I found another parameter in the equations that's not doing quite what I want it to... the physical behavior of the system isn't accurately
represented by the parameter. Hopefully, Dr. Fefferman and I will be able to fix this long distance, and then we can begin writing the paper!!!
Last modification 7/22/2010