Proposing a finite duration cancer treatment using multi-objective optimization

This paper proposes an optimal method for eradicating cancer, such that it can not be relapsed. The major issue, is that the tumor free equilibrium point at the end of chemotherapy is still unstable. Mathematically, it means that when the chemotherapy is stopped, the trajectory of the system moves away from the tumor free equilibrium point and the tumor cells starts increasing. To overcome this problem, we can either restart the process of chemotherapy or try to stabilize the equilibrium. In this article the dynamics of the system is changed around the tumor free equilibrium point by the use of vaccine therapy and the chemotherapy pushes the system to the domain of attraction of the desire point. For optimal chemotherapy, two objective functions optimized simultaneously in order to minimize the size of tumor as well as the side effects of the anticancer drug on the patients’ body. After removing the chemotherapy, the cancer does not relapse due to change in the dynamics of the system. Simulation results show that by applying this method, the cancer cells population approaches to zero even after cessation of chemotherapy for a long time.