# American Institute of Mathematical Sciences

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2015, 12(5): 1037-1053. doi: 10.3934/mbe.2015.12.1037

## Analysis of a cancer dormancy model and control of immuno-therapy

 1 Department of Mathematics, Iowa State University, Ames, IA 50011, United States, United States

Received  July 2014 Revised  February 2015 Published  June 2015

The goal of this paper is to analyze a model of cancer-immune system interactions from [16], and to show how the introduction of control in this model can dramatically improve the hypothetical patient response and in effect prevent the cancer from growing. We examine all the equilibrium points of the model and classify them according to their stability properties. We identify an equilibrium point corresponding to a survivable amount of cancer cells which are exactly balanced by the immune response. This situation corresponds to cancer dormancy. By using Lyapunov stability theory we estimate the region of attraction of this equilibrium and propose two control laws which are able to stabilize the system effectively, improving the results of [16]. Ultimately, the analysis presented in this paper reveals that a slower, continuous introduction of antibodies over a short time scale, as opposed to mere inoculation, may lead to more efficient and safer treatments.
Citation: Ben Sheller, Domenico D'Alessandro. Analysis of a cancer dormancy model and control of immuno-therapy. Mathematical Biosciences & Engineering, 2015, 12 (5) : 1037-1053. doi: 10.3934/mbe.2015.12.1037
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