Modified model for cancer treatment

Abstract

This paper proposes an optimal method for eradicating cancer, such that it cannot be relapsed. The major issue is that from the dynamical point of view, the tumour free equilibrium point at the end of chemotherapy is still unstable. Mathematically it means that when the chemotherapy is stopped, the dynamic behaviour of the system moves away from the tumour free equilibrium point and the tumour cells starts increasing. To overcome this problem, the stabilisation of the equilibrium point is proposed. According to this method, the vaccine therapy changes the dynamics of the system around the tumour free equilibrium point, and the chemotherapy pushes the system to the domain of attraction of the desired point. It is shown, that, according to the simulation results, after completing the chemotherapy process, the dynamic of the system becomes stable and the cancerous cells converges to zero.