Numerical Solution of Mathematical Model of Tumor Immune Response using Runge-Kutta Fourth Order Method

Abstract

This study focuses on solving the mathematical model of tumor immune response using the Runge-Kutta fourth order method, a robust numerical approach for ordinary differential equations. The research aims to analyse the dynamic interactions between tumor cells and the immune system, addressing the limitations of analytical methods by applying a numerical solution using MATLAB R2024b software. The Runge-Kutta fourth order method is implemented on the system of ordinary differential equations with specified parameters and initial conditions, providing a numerical solution over a defined time frame. The results reveal that the tumor cell population decreases significantly while the mature lymphocyte population stabilizes, leading to a tumor-free equilibrium. This demonstrates the immune system's effectiveness in eliminating tumor growth under optimal conditions and highlights the accuracy and stability of Runge-Kutta fourth order method in modelling complex biological systems. The study emphasizes the importance of numerical methods in predicting tumor-immune dynamics, offering valuable insights for future applications in immunotherapy and cancer research.