Today, immunotherapy is one of the effective treatments along with chemotherapy. This is especially true in cancers, which cause the immune system’s failure. As a valuable tool, a mathematical model is developed in the form of ordinary differential equations (ODEs) to show the immune-tumor cells interaction. The macrophages polarization and cytokine dynamics are also regarded using standard pharmacokinetics-pharmacodynamics assumptions for better presenting the tumor-immune cells interaction. Its lack in researches of chemo-immunotherapy of cancer is what motivated us to come with an ODE model. The positivity of solutions, the equilibrium points, and their stabilities are studied. Moreover, the sensitivity of the final tumor population and response time to initial conditions and parameters’ values are investigated. Initial conditions of the adaptive immune system and the parameters related to tumor cells proliferation, tumor carrying capacity, and exponent of fractional tumor cell kill by CD8+T cells have more effect on the final tumor population and the response time of tumor growth. Then, numerical simulations for pulsed chemotherapy, pulsed immunotherapy, and chemo-immunotherapy are presented and compared. Three patients with different immune responses are regarded to show the effect of immune response on treatment strategy. Numerical simulations show the effectiveness of the immunotherapy along with chemotherapy for cancer treatment. Also, it is shown that the immune system’s strength has a remarkable role in cancer cure.

A mixed immunotherapy-chemotherapy treatment protocol is developed for cancer treatment. Immunotherapy alters the dynamics of the system by affecting on the parameters of the system, and then chemotherapy pushes the trajectory of the system toward the tumor-free equilibrium point. The chemotherapy protocol is derived using the pseudo-spectral controller. In this method, an infinite-horizon optimal control problem is proposed for a nonlinear cancer model. Then, the infinite-horizon optimal control of cancer is transformed into a nonlinear programming (NLP) problem. The efficient Legendre pseudo-spectral (LPS) scheme is suggested to solve the proposed problem. Moreover, to restrict the upper limit of the chemo-drug dose based on the age of the patients a Mamdani fuzzy system is designed. Simulation results on three cases; i.e. young, middle-aged and old patients, show the efficiency of the proposed treatment strategy. In each case the dynamics of the system is modified by immunotherapy, and then chemotherapy guides the trajectory of the system toward the tumor-free equilibrium point. After stopping the treatment, the trajectory of the system converges to this point due to the correction in the dynamics of the system.