On the global dynamics of a model for  tumor immunotherapy

Denise E. Kirschner; Alexei Tsygvintsev; Denise E. Kirschner; Alexei Tsygvintsev

doi:10.3934/mbe.2009.6.573

Mathematical Biosciences and Engineering

2009, Volume 6, Issue 3: 573-583. doi: 10.3934/mbe.2009.6.573

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On the global dynamics of a model for tumor immunotherapy

1.
Department of Microbiology and Immunology, The University of Michigan Medical School, Ann Arbor, MI 48109-0620
2.
Unité de mathématiques pures et appliquées, Ecole Normale Supérieure de Lyon, Lyon, F-69364 LYON Cedex 07

Received: 01 January 2009 Accepted: 29 June 2018 Published: 01 June 2009
MSC : Primary: 37N25, 62P10; Secondary: 35B40.

Understanding the dynamics of human hosts and tumors is of critical importance. A mathematical model was developed that explored the immune response to tumors that was used to study a special type of treatment [3]. This treatment approach uses elements of the host to boost its immune response in the hopes that the host can clear the tumor. This model was extensively studied using numerical simulation, however no global analytical results were originally presented. In this work we explore the global dynamics to show under what conditions tumor clearance can be achieved.
- cancer,
- Lyapunov functions,
- immunotherapy,
- dynamical systems.
Citation: Denise E. Kirschner, Alexei Tsygvintsev. On the global dynamics of a model for tumor immunotherapy[J]. Mathematical Biosciences and Engineering, 2009, 6(3): 573-583. doi: 10.3934/mbe.2009.6.573

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Abstract

Understanding the dynamics of human hosts and tumors is of critical importance. A mathematical model was developed that explored the immune response to tumors that was used to study a special type of treatment [3]. This treatment approach uses elements of the host to boost its immune response in the hopes that the host can clear the tumor. This model was extensively studied using numerical simulation, however no global analytical results were originally presented. In this work we explore the global dynamics to show under what conditions tumor clearance can be achieved.
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