| A control theory model for radiotherapy treatment of cancer, based on the Lotka-Voltera competition system, is created to analyze the dynamics of interaction of 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 cancer cell concentration. Furthermore, four different methods of radiation delivery are modelled with four different control mechanisms. Perturbation analysis is used to model the side-effects and accidental harvesting of healthy cells by radiation. Finally, the model is validated with numerical examples with the use of a Matlab differential equation solver. |
