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.