Fuzzy-optimal control of cancer by considering bifurcation and age of the patients using mixed immune-chemotherapy treatment

Due to the side effects and drug resistance, it is impossible to impose a long term treatment. Therefore, it is desirable to provide a method for the treatment of cancer in a limited time. So, mixed chemo-immunotherapy treatment has been presented, and the mathematical model has been extended based on this new treatment protocol. The immunotherapy modifies the dynamics of the system, and the chemotherapy guides the trajectory of the system toward the preferred equilibrium point. For identifying the effective parameters on the modification of the system dynamics, the stability and the bifurcation of the system have been studied. Since the patient’s age is effective in providing treatment, a fuzzy system, based on physiological considerations, has been used to adjust the maximum dose for a young patient more than a child one and for a child patient more than an old. The simulations on three different age patients, 8, 22, and 60 years old, indicates the necessity of the provided treatment. The treatment duration in the old and child patients is shorter than the young one due to the stronger immune system assumption that shows the importance of the immunotherapy besides the chemotherapy.