Abstract
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.