Suboptimal mixed vaccine and chemotherapy in finite duration cancer treatment: state-dependent Riccati equation control

Abstract The aim of this paper is to propose an optimal finite duration treatment method for avoiding tumor growth. For this purpose, a mathematical model in the form of ordinary differential equations is modified with combination vaccine therapy and chemotherapy treatments. Numerical simulations, using human parameters, show that there are two equilibrium points. The tumor-free equilibrium point is unstable while the high-tumor equilibrium point is stable. Hence, the dynamics of the cancer model must be changed to have finite duration treatment. Therefore, the vaccine therapy is used to change the parameters of the system and the chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. It is shown that any treatment method without changing the dynamics of the system around the tumor-free equilibrium point is not an appropriate treatment method. For optimal chemotherapy, the State-Dependent Riccati Equation based optimal control is used to the nonlinear model. Different weighting matrices are used to show the flexibility of this method in design. Simulation results show that the performance of the treatment would be better if the matrix was state dependent. In this paper, the input weighting matrix depends on the tumor cell population. If the input matrix becomes less in the beginning of the treatment causes more tumor cells eradication. Also, the present study states that a proper treatment method should not only reduce the population of tumor cells, but also change the dynamics of the cancer.