Chapter 5
Analysis of the Model
In this chapter, we will go back to the optimal control problem OC formulated in Chapter
2 and apply to it the tools of optimal control theory presented in Chapter 4. For the
convenience of the reader, we recall the problem and the notation:
p(t) represents the volume of primary tumor cells at a given time t
q(t) represents the carrying capacity of the vasculature at a given time t
u(t)describes the amount of drug administered at a given time t:
For a free terminal time T, we want to minimize the value
Z T
p(T) + k u(t)dt (5.1)
0
over all piecewise continuous
u : [0;T] ! [0;a]
subject to the following dynamics
 

pp = pln ; p(0) = p
q 0 (5.2) 

2q = bp  + dp
3 q Guq; q(0) = q0: (5.3)
24
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