A switching control law approach for cancer immunotherapy of an evolutionary tumor growth model.

We propose a new approach for tumor immunotherapy which is based on a switching control strategy defined on domains of attraction of equilibria of interest. For this, we consider a recently derived model which captures the effects of the tumor cells on the immune system and viceversa, through predator-prey competition terms. Additionally, it incorporates the immune system's mechanism for producing hunting immune cells, which makes the model suitable for immunotherapy strategies analysis and design. For computing domains of attraction for the tumor nonlinear dynamics, and thus, for deriving immunotherapeutic strategies we employ rational Lyapunov functions. Finally, we apply the switching control strategy to destabilize an invasive tumor equilibrium and steer the system trajectories to tumor dormancy.