Mathematical analysis of a tumor suppression model incorporating vitamin intake

Cancer is the second leading cause of death worldwide and occurs when cells uncontrollably divide, grow, and invade surrounding tissue. Several treatment strategies have been introduced to increase survival rates; however, each approach has potential side effects. Consequently, demand for alternative treatment approaches, such as immune system enhancement with vitamins, is growing. Here, we introduce a mathematical framework based on ordinary differential equations to examine the interactions among nutrients, immune cells, and cancer cells. Unlike many existing tumor–immune models, the proposed framework reveals that variations in nutrient levels can induce qualitative changes in system dynamics, including bistability and regime transitions between tumor-dominant and immune-controlled states. Long-term behavior, stability, and bifurcation techniques are employed. Numerical simulations are performed using the odeint solver in SciPy, which is based on the LSODA algorithm and is capable of handling both stiff and non-stiff systems. Our results suggest that optimizing nutrient levels can enhance the immune response, potentially leading to safer cancer treatment strategies.