A mathematical model of cancer treatment by radiotherapy.
COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2014;
2014:172923. [PMID:
25478002 PMCID:
PMC4247922 DOI:
10.1155/2014/172923]
[Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/22/2014] [Revised: 10/14/2014] [Accepted: 10/25/2014] [Indexed: 11/29/2022]
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.
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