Modeling Tumor–Immune Interactions Under Immuno-Chemotherapy: Stability Analysis and Numerical Simulation

Advancements in tumor immunology and immunotherapy demonstrate that the immune system plays a crucial role in protecting the body against tumors and may be utilized to prevent or treat them. To investigate this further, we propose a mathematical model to study the complex dynamics of tumor–immune interactions under combined treatment: immunotherapy and chemotherapy. The proposed model consists of six coupled nonlinear ordinary differential equations (ODEs) describing the interaction of tumor cells with specific immune system components (immunostimulatory and immunosuppressive intermediates) and the effects of chemotherapy and immunotherapy. The antigen-presenting cells (APCs), specifically dendritic cells, are incorporated as the immunotherapy. We examine the essential characteristics of the system’s solutions, including existence, boundedness, and positivity. Furthermore, we investigate the presence and stability of equilibrium in two scenarios: intervention of immunotherapy alone and combined use of chemotherapy and immunotherapy. Each model exhibits two equilibria: a tumor-free equilibrium and a tumorous equilibrium. The stability analysis outlines the dynamic behavior associated with each equilibrium point. Additionally, we performed a sensitivity analysis and numerical simulations to validate our theoretical findings empirically. Using numerical simulations and stability analysis, we investigated the effects of treatments on tumor–immune dynamics.