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Computational and Mathematical Methods in Medicine
Volume 2014, Article ID 206287, 13 pages
http://dx.doi.org/10.1155/2014/206287
Research Article

Optimal Treatment Strategy for a Tumor Model under Immune Suppression

Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea

Received 24 January 2014; Revised 2 May 2014; Accepted 18 May 2014; Published 23 July 2014

Academic Editor: Shenyong Chen

Copyright © 2014 Kwang Su Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a mathematical model describing tumor-immune interactions under immune suppression. These days evidences indicate that the immune suppression related to cancer contributes to its progression. The mathematical model for tumor-immune interactions would provide a new methodology for more sophisticated treatment options of cancer. To do this we have developed a system of 11 ordinary differential equations including the movement, interaction, and activation of NK cells, CD8+T-cells, CD4+T cells, regulatory T cells, and dendritic cells under the presence of tumor and cytokines and the immune interactions. In addition, we apply two control therapies, immunotherapy and chemotherapy to the model in order to control growth of tumor. Using optimal control theory and numerical simulations, we obtain appropriate treatment strategies according to the ratio of the cost for two therapies, which suggest an optimal timing of each administration for the two types of models, without and with immunosuppressive effects. These results mean that the immune suppression can have an influence on treatment strategies for cancer.