RADIOTHERAPY EFFECTS IN TUMOR TREATMENT: A PIECEWISE MODEL WITH DETERMINISTIC AND STOCHASTIC APPROACHES

Abstract

This paper presents a mathematical model to investigate the effects of radiation on tumor growth, which is modified using piecewise differential operators. The model incorporates classical derivatives in one interval, fractional derivatives (such as Caputo and Caputo-Fabrizio) in another, and stochastic components in yet another. The incorporation of fractional derivatives allows for the modeling of memory effects and non-local interactions, while the stochastic elements capture random fluctuations and uncertainties in tumor behavior. The study explores both deterministic and stochastic behaviors of the model under these different derivative types, focusing on how fractional and stochastic components influence the model's dynamics. The effects of deterministic, fractional, and stochastic approaches on the model's output are thoroughly analyzed. The piecewise model is solved using the sequential midpoint method, and simulations are provided to illustrate the model's predictions and the impact of these advanced derivative techniques on tumor growth dynamics under radiation treatment.