
Nonlinear systems 97
points E
3
and E
2
, it is possible to verify that, if
α <
2rβ
s
1 −
d
1
βk
2
− d
2
, (3.37)
the density of malignant cells in E
3
is lower than in E
2
.
There is a biological interpretation for the equilibrium points E
2
and E
3
lying in the positive orthant. In particular, if only E
2
belongs to the positive
orthant, a mechanism for converting resting pr e dator cells to hunting preda-
tor cells does not exist. Conversely, when E
3
belongs to the positive orthant
it is po ssible to control the steady-state density of the tumour by varying
α. Therefor e, it is of significant clinical interest to determine the region of
attraction surrounding E
3
, since