G. Belostotski, H.I. Freedman
Department of Mathematics
School of Academic Foundations and Bridging
Northern Alberta Institute of Technology
11762-106 Street, Edmonton, Alberta, T5G 2R1, CANADA
e-mail: gb3@ualberta.ca
Department of Mathematical and Statistical Sciences,
University of Alberta
Edmonton, Alberta, T6G 2G1, CANADA
e-mail: hfreedma@math.ualberta.ca

Abstract.A control theory model for radiotherapy treatment of cancer, based on the Lotka-Voltera competition system, is created to analyze the dynamics of interactions between cancer and healthy tissues. Using standard stability analysis, the stability of the system is described and qualified as ``treatment" or ``cure". The key feature of the model is the use of a harvesting-type control term to represent radiotherapy, where radiation-induced harvesting is equivalent to the reduction of the cancer cell concentration. Furthermore, four different methods of radiation delivery are modeled with four different control mechanisms. Numerical examples using of a Matlab differential equation solver are given to illustrate each case.

Received: September 21, 2005

AMS Subject Classification: 92C50, 92D40

Key Words and Phrases: cancer modelling, cancer treatment, competition theory, controlability, ordinary differential equations, radiotherapy

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 4