February  2004, 4(1): 241-266. doi: 10.3934/dcdsb.2004.4.241

A model of tumor and lymphocyte interactions

1. 

Department of Biopharmaceutical Sciences, University of California, San Francisco, San Francisco, CA 94143, United States

Received  November 2002 Revised  September 2003 Published  November 2003

The interactions between a solid tumor and the immune system are described both prior to and after neovascularization by a predator-prey model, and predictions about tumor behavior in a host are made. Trajectory analysis of phase-plane portraits as well as standard perturbation analysis show that most system steady states are unstable but that stability is theoretically possible. Reasonable parameter value estimation enables meaningful analysis of system behavior, and Mathematica is used to simulate model dynamics. The model accounts for many observed tumor behaviors, and regions of uncontrolled tumor growth, tumor extinction in finite time, and irreversible lymphocyte decline are found either analytically or numerically. A better understanding of tumor-immune dynamics is obtained, allowing for improved research on treatment specifically in the area of immunotherapy.
Citation: Amy H. Lin. A model of tumor and lymphocyte interactions. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 241-266. doi: 10.3934/dcdsb.2004.4.241
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