Exercise 3

Wheldon's model of chronic granuloctic leukemia [8] has the form
y1(t)
=
a
1 + b y1(t-t)g
- l y1(t)
1 + m y2(t)d
y2(t)
=
l y1(t)
1 + m y2(t)d
- w y2(t)
Code the equations for general values of the parameters to make it easy to experiment with the model. Remember that if you do not set any options, you must use a placeholder of [] for the options argument. Solve the problem on [0,200] with history y1(t) = 100, y2(t) = 100 for t 0 and parameter values a = 1.1 ×1010,b = 10-12,g = 1.25, d = 1, l = 10, m = 4 ×10-8, w = 2.43 that you set in the main program. Compare the solutions you obtain with t = 7 and t = 20 . You could code this as

 for tau = [7, 20]
    sol = dde23('exer3f',tau,...
    ...
 end
You should find that the solution is oscillatory in both cases. In the first, the oscillations are damped quickly and in the second, they are not.

Reference

[8]
N. MacDonald, Time Lags in Biological Models, Springer-Verlag, Berlin, 1978.