Mathematical Modeling and Analysis of Tumor Growth Models Integrating Treatment Therapy

This study presents a comparative analysis of tumor growth models based on logistic, exponential, and Gompertz formulations. Their response to therapeutic intervention is examined to identify which model shows better behavior with minimal decline of immune cells. The framework incorporates three main cell populations as follows: natural killer cells, cytotoxic T cells, and tumor cells, along with treatment effects. Dynamical properties such as positive invariance, existence, boundedness, and equilibrium stability are investigated. Numerical simulations indicate that the logistic model gives more favorable treatment outcomes compared to the exponential and Gompertz models. The results also show a faster decline of immune cell populations in the exponential and Gompertz models than in the logistic model under varying drug flux.