A model of tumor and lymphocyte interactions

The interactions between a solid tumor and the immune systemare described both prior to and after neovascularizationby a predator-prey model, and predictions about tumor behaviorin a host are made. Trajectory analysis of phase-planeportraits as well as standard perturbation analysis showthat most system steady states are unstable but thatstability is theoretically possible. Reasonable parametervalue estimation enables meaningful analysis of systembehavior, and Mathematica is used to simulate modeldynamics. The model accounts for many observed tumorbehaviors, and regions of uncontrolled tumor growth,tumor extinction in finite time, and irreversible lymphocytedecline are found either analytically or numerically. Abetter understanding of tumor-immune dynamics is obtained,allowing for improved research on treatment specifically inthe area of immunotherapy.