COMPARATIVE STUDY OF CANCER GROWTH MODELING USING LOGISTIC AND FRACTIONAL DIFFERENTIAL EQUATION MODEL

Abstract

This study presents a comparative analysis of breast cancer tumor growth using two mathematical approaches: the classical first-order logistic ordinary differential equation (ODE) and a fractional ODE formulation. Using fixed parameter values (intrinsic growth rate α = 0.3, intra-specific coefficient β = 0.1) and an initial tumor volume of 8 m³, numerical simulations were performed over a 0–70 day interval (step = 7 days) to obtain solution trajectories for each model. Results show that both models predict a monotonic decline in relative tumor volume over the simulated interval, but the fractional ODE consistently predicts substantially larger tumor volumes than the logistic ODE (e.g., fractional: 6.9078 → 5.2209 m³; logistic: 3.2494 → 2.9994 m³). The percentage difference between model predictions decreases over time, from about 52.96% at day 7 to about 42.55% at day 70, indicating closer agreement as the system approaches steady behavior. The paper discusses the qualitative behavior of the two model families and highlights the greater persistence of tumor volume predicted by the fractional model. Recommendations include sensitivity analyses on growth-rate and interaction coefficients to inform clinical dosing strategies and further exploration of fractional dynamics in tumor modeling.