Cancer treatment and control

This interactive presentation is meant to explore the role of control in the treatment of cancer with chemotherapy. The dynamical system and the cost functional are the components of a control problem. The selection of either piece directly influence the control strategy. A compartment model is used to model the evolution and growth of cancer utilizing exponential, logistic, and Gompertzian dynamics in this presentation. The cost functional for current treatment strategies can be typified as seeking to aggressively drive the cancer into remission as quickly as possible as the primary objective. Alternate forms for the cost function can be to balance the life expectancy and quality of life relative to the destruction of the cancer cells. In both forms for the cost functional, constraints are imposed on when the chemotherapy can be administered. For simplicity, the control is the time when chemotherapeutic treatment(s) are administered. The essential difference in the treatment policies is that traditional schedules use a cycle or group of treatments whereas the alternate schedule is for individual treatments. A numerical study is presented to illustrate the roles of the dynamics and cost functional.