Math and Medicine: Homework Assignment Week 6
Due on February 19
1. We worked out numbers based on a patient with a T cell count of 400, assuming that 1000
is a normal count. But how do we get patients with different counts?
a. Use the values of c and δ for each of the patients in Table 1 of the paper, and assume
that T̄ = 5.0 × 109 and σ = 0.1. What value of k would you estimate for each patient
based on their T cell count? Do they seem reasonable?
b. Suppose a treatment could change k, c or δ by a factor of 2. Which would be the most
effective in increasing the T cell count?
c. Which would be most rapidly overcome by evolution of resistance?
2. The set of programs centered around Vdriver.R on the web site numerically solve the differential equations in the model.
a. Use the parameters from the first problem and see what happens.
b. Using the basic parameters, what happens if you decrease σ, the rate of replacement of
T cells?
c. How much would you need to change each parameter by to have the disease go extinct?
d. Extra Credit: Add something to the model that mimics a long-lived reservoir of
infected cells. What happens when you have a treatment that would have otherwise
eliminated the disease? Would you still expect rapid evolution of resistance?