# American Institute of Mathematical Sciences

June  2013, 18(4): 1017-1030. doi: 10.3934/dcdsb.2013.18.1017

## A mathematical model for the immunotherapeutic control of the Th1/Th2 imbalance in melanoma

 1 10 Hate'ena St., P.O.B. 282, Bene Ataroth 60991, Israel, Israel, Israel

Received  May 2012 Revised  August 2012 Published  February 2013

Aggressive cancers develop immune suppression mechanisms, allowing them to evade specific immune responses. Patients with active melanoma are polarized towards a T helper (Th) 2-type immune phenotype, which subverts effective anticancer Th1-type cellular immunity. The pro-inflammatory factor, interleukin (IL)-12, can potentially restore Th1 responses in such patients, but still shows limited clinical efficacy and substantial side effects. We developed a model for the Th1/Th2 imbalance in melanoma patients and its regulation via IL-12 treatment. The model focuses on the interactions between the two Th cell types as mediated by their respective key cytokines, interferon (IFN)-$\gamma$ and IL-10. Theoretical and numerical analysis showed a landscape consisting of a single, globally attracting steady state, which is stable under large ranges of relevant parameter values. Our results suggest that in melanoma, the cellular arm of the immune system cannot reverse tumor immunotolerance naturally, and that immunotherapy may be the only way to overturn tumor dominance. We have shown that given a toxicity threshold for IFN$\gamma$, the maximal allowable IL-12 concentration to yield a Th1-polarized state can be estimated. Moreover, our analysis pinpoints the IL-10 secretion rate as a significant factor influencing the Th1:Th2 balance, suggesting its use as a personal immunomarker for prognosis.
Citation: Yuri Kogan, Zvia Agur, Moran Elishmereni. A mathematical model for the immunotherapeutic control of the Th1/Th2 imbalance in melanoma. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 1017-1030. doi: 10.3934/dcdsb.2013.18.1017
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