Two eigenvalues of the system are \(\lambda_{1}=-\delta\)and\({\ \lambda}_{2}=\ \alpha-\frac{\sigma}{\delta}\). The first
eigenvalue is always negative and the second eigenvalue is negative
if\(\text{\ αδ}<\sigma\). The parameters \(\alpha\) and \(\sigma\) are
related to the growth rate of the tumor and immune cells, respectively,
and the parameter \(\delta\) is related to the natural death rate of the
immune cells. So, in order to have a stable tumor-free equilibrium
point, the growth rate of the cancer cells must be smaller than the
ratio of the growth rate of immune cells to their natural death rate.
Hence, the immune system should be reinforced during the treatment to
establish this target.
By using free system (1)-(2), i.e. system (1)-(2) the intersection of
the two following equations derives the cancerous equilibrium points of
the free system.