Avoiding healthy cells extinction in a cancer model

- The dynamics of three interacting cell populations of tumor cells, healthy host cells and immune effector cells is discussed.
- Transient chaotic behavior for a certain choice of parameters takes place before extinction of healthy and immune cells.
- The method of partial control is applied to avoid the extinction of the healthy tissue.
- The difficulties of applying such control method at the present state-of-the-art of cancer therapies are discussed.

We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. For certain parameter choice, the dynamical system displays chaotic motion and by decreasing the response of the immune system to the tumor cells, a boundary crisis leading to transient chaotic dynamics is observed. This means that the system behaves chaotically for a finite amount of time until the unavoidable extinction of the healthy and immune cell populations occurs. Our main goal here is to apply a control method to avoid extinction. For that purpose, we apply the partial control method, which aims to control transient chaotic dynamics in the presence of external disturbances. As a result, we have succeeded to avoid the uncontrolled growth of tumor cells and the extinction of healthy tissue. The possibility of using this method compared to the frequently used therapies is discussed.