Optimal control in cancer immunotherapy by the application of particle swarm optimization

Abstract

In this article, a well-known mathematical model of cancer immunotherapy is discussed and used to represent therapeutic protocols for cancer treatment. The optimal control problem is formulated based on the Pontryagin maximum principle to deal with adoptive cellular immunotherapy, then the problem has been solved by the application of particle swarm optimization (PSO) in combination with regular methods of solutions to optimal control problems. The results are compared with those of other researchers. It is explained how the PSO algorithm could be enlisted to obtain the optimal controls, then the obtained optimal controls are demonstrated to be more appropriate to the elimination of cancer cells by using fewer amounts of external sources of medicine.