Numerical investigation of the impact of neural stem cells on brain tumors

Malignant brain tumors, including glioblastoma and medulloblastoma, remain highly treatment-resistant. Neural stem cells (NSCs) are being investigated as tumor-tropic therapeutic vectors, but the temporal interaction between tumor and NSC populations requires quantitative characterization before model-based treatment hypotheses can be interpreted reliably. This study aimed to develop and numerically evaluate a reproducible 2-population model of tumor–NSC dynamics and to quantify the influence of NSC persistence and NSC-mediated tumor killing on simulated tumor burden. A normalized system of 2 coupled nonlinear ordinary differential equations was used: dT / dt = rT (1 − T ) − β T N and d N/ dt = αN(1 − N) − γ T N. The baseline simulation used r = 0.20000 day −1 , α = 0.05000 day −1 , β = 0.35000 day −1 , γ = 0.30000 day −1 , T 0 = 0.50000, and N 0 = 0.40000. Explicit Euler integration was performed with Δ t = 0.01 day over 20 days. A descriptive nonlinear regression fit, Fourier spectral analysis, 1-parameter sensitivity analyses, and joint α–β sensitivity analysis were applied to the simulated trajectory. In the baseline simulation, tumor density decreased from 0.5000 to a minimum of 0.4772 at day 2.59 (4.57% below the initial value) and subsequently increased to T 20 = 0.8273, while NSC density declined from 0.4000 to N 20 = 0.0247. The descriptive regression reproduced the simulated tumor trajectory with R 2 = 0.9973 and root mean square error = 0.00590. Increasing α from 0.05 to 0.10 day −1 reduced T 20 by 12.6% relative to baseline, and increasing β from 0.35 to 0.50 day −1 reduced T 20 by 19.9%. Jointly setting α = 0.10 and β = 0.50 day −1 yielded T 20 = 0.4427, 46.5% below the baseline terminal tumor density. The Fourier spectrum was dominated by the zero and low-frequency components, with no distinct oscillatory peak over the 20-day window. The model indicates that NSC persistence and NSC-mediated tumor killing materially influence terminal tumor burden, but the baseline parameterization produces only transient early suppression followed by tumor regrowth as the NSC population declines. The results are population-level, model-based estimates rather than tumor-type-specific clinical efficacy measures. Tumour-specific calibration, spatial migration, immune interactions, and experimental validation are required before translational conclusions can be drawn.