A mathematical model for cancer treatment based on combination of anti-angiogenic and immune cell therapies

In this study, we investigated a mathematical model that integrated mechanisms of tumor angiogenesis and tumor-targeted cytotoxicity in immune cells. The model considered the interaction of cancer cells with the immune system and the treatment that combines unlicensed dendritic cells and anti-vascular endothelial growth factor antibodies. We proposed an unconventional treatment protocol; for now, treatment is purely theoretical and has not been practically attempted. The treatment has been described by analytical functions that depend on time and dose. This was a function of t and q, where q is the amount (dose) of the drug. A customized treatment is a significant advantage of explicit analytical functions. We compared the results obtained from the mathematical model with the proposed treatment to the clinical results and observed an almost complete match between the treatments. In addition, we applied the global quasi-linearization GQL method to the mathematical model, which enabled us to expose the hierarchy of the system and, hence, split the system into fast and slow subsystems. This decomposition enabled us to analytically compute the equilibrium points of the model and their stability, which is crucial for the application.