An optimal control approach for the interaction of immune checkpoints, immune system, and BCG in the treatment of superficial bladder cancer

Abstract

One of the major setbacks in BCG immunotherapy of bladder cancer is the action of immune checkpoints on the immune system. They suppress the activated immune cells from spreading, detecting and attacking cancer cells. Moreover, the excessive side effects and toxicity of the BCG to normal cells are quite alarming. We propose a mathematical model that studies this dynamics and uses an optimal control approach to suggest the optimal BCG dose required to minimize the cancer cells and action of the immune checkpoints, as well as maximizing the number of immune and normal cells in the bladder. Numerical simulations of the controlled system reveal that the optimal BCG dosage (control function) shows that the number of immune cells rises, the cancer cells are eliminated, the activities of the checkpoints are reduced, and normal cells stay high maintaining the threshold level.