Computational Modeling of Prostate Cancer Growth with Tumor– Immune Interactions and Treatment Optimization Using Euler's Method

Abstract Prostate cancer remains one of the leading causes of cancer-related mortality worldwide, necessitating improved mathematical tools for understanding tumor progression and optimizing treatment strategies. This study presents a computational model for prostate cancer growth incorporating tumor–immune interactions and treatment optimization using Euler’s method implemented in MATLAB. The model is formulated as a system of coupled ordinary differential equations describing the dynamic interactions between tumor cells, immune cells, and therapeutic agents. Tumor proliferation, immune-mediated suppression, and treatment-induced reduction in cancer cell population are incorporated into the model together with an optimal treatment control parameter. Euler’s numerical method is applied in MATLAB to obtain approximate solutions of the governing equations and simulate the temporal evolution of tumor dynamics under varying treatment conditions. The results are presented using tables and graphical methods, including plots of tumor cell population, immune response, and treatment effects against time to illustrate the behavior of the system. Numerical simulations are used to investigate the influence of treatment intensity, immune response strength, and model parameters on prostate cancer progression. The results demonstrate that optimized treatment strategies combined with strong immune response can significantly reduce tumor growth and improve treatment outcomes. The proposed computational framework provides a useful tool for analyzing prostate cancer dynamics and offers potential applications in treatment planning, prediction, and therapeutic decision-making.