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

Reference

[8]

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