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

Ben  Sheller; Domenico  D'Alessandro

doi:10.3934/mbe.2015.12.1037

Article Contents

2015, Volume 12, Issue 5: 1037-1053. Doi: 10.3934/mbe.2015.12.1037

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

Ben Sheller^1, and
Domenico D'Alessandro^1,

1.
Department of Mathematics, Iowa State University, Ames, IA 50011

Received: June 30, 2014

Revised: January 31, 2015

Published: May 2015

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Abstract

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.

Keywords:

Modeling of immuno-therapy,
application of control theory to cancer therapy,
Lyapunov stability.

Mathematics Subject Classification: Primary: 92C50, 93C10; Secondary: 93D05.

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