Mathematical modeling and analysis of cancer immunotherapy

Cancer Immunotherapy is one of the innovative cancer treatment modalities currently being used for eradication of disseminated cancer cells after surgical debunking of the primary tumor. A system of nonlinear deterministic differential equations was used to construct a phenomenological model of cancer pathodynamics during exogenous immunological therapy. The model incorporates all the basic and essential physiological interactions between cancer cells, normal cells, and adoptively--transferred exogenous cytolytic immune cells. The mathematical tools used include: Dynamical Systems Theory, Nonlinear Analysis, and Hartmann-Grobman Theory. In particular, clinically plausible therapeutic criteria are derived under which cancer cells exhibit persistence recurrence, or annihilation of normal cells. Clinically applicable therapeutic scenarios are described which are of importance to the clinical oncologists and the medical doctors working with cancer patients. Investigative computer simulations are exhibited which elucidate some clinical aspects of cancer immunotherapy