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

Document Type : Original Paper


1 Department of Operations Research, Faculty of Mathematics, Shiraz University of Technology, Shiraz, IRAN.

2 Department of Operations Research, Faculty of Mathematical, Shiraz University of Technology, Shiraz, Iran

3 Department of Numerical Analysis, Faculty of Mathematical, Shiraz University of Technology, Shiraz, Iran


Cells in all tissues of the body are constantly growing and dividing

into new cells. Abnormal proliferation of tissues outside the body leads to

cancer. In all tissues of the body, a type of cell, called a stem cell, is found

that has the ability to become specialized cells in the same tissue to be able to

compensate for damage in tissue disorders. In this paper, based on the existing

mathematical model, the optimal control model is very effective for inhibiting

this growth in exchange for prescribing a specific drug (doxorubicin) is presented.

In order to minimize the number of cancer cells over time, the cancer control

strategy has been modeled as a problem from the theory of optimal control

during 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 the

help of the maximum principle of Pontriagin and then the analytical solution of

the first-order differential equations, the optimal solution has been determined.

In order to provide the optimal dose of the drug to the patient, the proposed

solution is simulated numerically. This numerical implementation shows how by

applying this amount of drug with a specific dose, how the number of cancer

cells decreases over time, they will be.


Main Subjects

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Volume 12, Issue 4 - Serial Number 28
January 2022
Pages 535-547
  • Receive Date: 23 January 2022
  • Revise Date: 22 May 2022
  • Accept Date: 05 December 2022
  • First Publish Date: 22 December 2022