# American Institute of Mathematical Sciences

February  2004, 4(1): 39-58. doi: 10.3934/dcdsb.2004.4.39

## A mathematical model of tumor-immune evasion and siRNA treatment

 1 Department of Mathematics, University of Michigan, Ann Arbor, Michigan, United States, United States 2 Department of Microbiology and Immunology, University of Michigan, Ann Arbor, Michigan, United States

Received  December 2002 Revised  June 2003 Published  November 2003

In this paper a mathematical model is presented that describes growth, immune escape, and siRNA treatment of tumors. The model consists of a system of nonlinear, ordinary differential equations describing tumor cells and immune effectors, as well as the immuno-stimulatory and suppressive cytokines IL-2 and TGF-$\beta$. TGF-$\beta$ suppresses the immune system by inhibiting the activation of effector cells and reducing tumor antigen expression. It also stimulates tumor growth by promoting angiogenesis, explaining the inclusion of an angiogenic switch mechanism for TGF-$\beta$ activity. The model predicts that increasing the rate of TGF-$\beta$ production for reasonable values of tumor antigenicity enhances tumor growth and its ability to escape host detection. The model is then extended to include siRNA treatment which suppresses TGF-$\beta$ production by targeting the mRNA that codes for TGF-$\beta$, thereby reducing the presence and effect of TGF-$\beta$ in tumor cells. Comparison of tumor response to multiple injections of siRNA with behavior of untreated tumors demonstrates the effectiveness of this proposed treatment strategy. A second administration method, continuous infusion, is included to contrast the ideal outcome of siRNA treatment. The model's results predict conditions under which siRNA treatment can be successful in returning an aggressive, TGF-$\beta$ producing tumor to its passive, non-immune evading state.
Citation: J.C. Arciero, T.L. Jackson, D.E. Kirschner. A mathematical model of tumor-immune evasion and siRNA treatment. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 39-58. doi: 10.3934/dcdsb.2004.4.39
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