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Computational and Mathematical Methods in Medicine
Volume 2014 (2014), Article ID 172923, 12 pages
http://dx.doi.org/10.1155/2014/172923
Research Article

A Mathematical Model of Cancer Treatment by Radiotherapy

1School of Science, Chongqing Jiaotong University, Chongqing 400074, China
2Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China
3School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China

Received 22 July 2014; Revised 14 October 2014; Accepted 25 October 2014; Published 13 November 2014

Academic Editor: Huaguang Zhang

Copyright © 2014 Zijian Liu and Chenxue Yang. 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

A periodic mathematical model of cancer treatment by radiotherapy is presented and studied in this paper. Conditions on the coexistence of the healthy and cancer cells are obtained. Furthermore, sufficient conditions on the existence and globally asymptotic stability of the positive periodic solution, the cancer eradication periodic solution, and the cancer win periodic solution are established. Some numerical examples are shown to verify the validity of the results. A discussion is presented for further study.