Math and Medicine: Homework Assignment Week 11
Due on April 2
1. Astoundingly, I found that the fitness measure of a strain based on the model we derived in
class is exactly what we had with our basic model, but with β replaced by α/γ.
a. Try to explain why this actually makes sense.
b. Use this to write the condition for when the resistant type should be able to win out.
c. Find some parameter values for which the two types have equal fitness when q = 0.5.
Using numbers between 0 and 1 might prevent things from blowing up.
d. Use the program SRdriver.R on the web site to test this. That is, change the α’s and
γ’s to match your values and see what happens as you vary q.
2. Our model had a very simple approach to the fraction treated.
a. Sketch a model where people aren’t treated immediately. Do you think that that the
speed with which treatment begins will act sort of like q?
b. What if people give up on their treatment too early? Do you think this model would
lead to more evolution of resistance?
c. Extra Credit: The programs do not include mutation. Add in a small level of mutation
and see what happens to the results from problem 1.