A Control Model for the Growth of Cancer Stem and Non-StemCells for the Administration of Doxorubicin

Cells in all tissues of the body are constantly growing and dividinginto new cells. Abnormal proliferation of tissues outside the body leads tocancer. In all tissues of the body, a type of cell, called a stem cell, is foundthat has the ability to become specialized cells in the same tissue to be able tocompensate for damage in tissue disorders. In this paper, based on the existingmathematical model, the optimal control model is very effective for inhibitingthis growth in exchange for prescribing a specific drug (doxorubicin) is presented.In order to minimize the number of cancer cells over time, the cancer controlstrategy has been modeled as a problem from the theory of optimal controlduring the effect of a specific drug on non-cancerous stem cells in this model.To solve this problem and prescribe the optimal dose of the drug, first with thehelp of the maximum principle of Pontriagin and then the analytical solution ofthe first-order differential equations, the optimal solution has been determined.In order to provide the optimal dose of the drug to the patient, the proposedsolution is simulated numerically. This numerical implementation shows how byapplying this amount of drug with a specific dose, how the number of cancercells decreases over time, they will be.