Mixed Immunotherapy and Chemotherapy of Tumors: Modeling, Applications and Biological Interpretations

Document Type



Mathematics (Pomona), Mathematics (HMC)

Publication Date



Mathematical modeling, Chemotherapy, Immunotherapy, Vaccine, Cancer, Tumor


We develop and analyze a mathematical model, in the form of a system of ordinary differential equations (ODEs), governing cancer growth on a cell population level with combination immune, vaccine and chemotherapy treatments. We characterize the ODE system dynamics by locating equilibrium points, determining stability properties, performing a bifurcation analysis, and identifying basins of attraction. These system characteristics are useful not only to gain a broad understanding of the specific system dynamics, but also to help guide the development of combination therapies. Numerical simulations of mixed chemo-immuno and vaccine therapy using both mouse and human parameters are presented. We illustrate situations for which neither chemotherapy nor immunotherapy alone are sufficient to control tumor growth, but in combination the therapies are able to eliminate the entire tumor.

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© 2005 Elsevier B.V.

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