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Mathematical Medicine and Biology Advance Access originally published online on July 25, 2007
Mathematical Medicine and Biology 2007 24(3):287-300; doi:10.1093/imammb/dqm003
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Assessment of cancer immunotherapy outcome in terms of the immune response time features

D. Rodríguez-Pérez{dagger}, Oscar Sotolongo-Grau and Ramón Espinosa Riquelme

Departamento de Física Matemática y de Fluidos, UNED, PO Box 60141, 28080 Madrid, Spain

Oscar Sotolongo-Costa

Department of Theoretical Physics, Henry Poincaré Group of Complex Systems, Havana University, Havana, Cuba

J. Antonio Santos Miranda

Servicio de Oncología Radioterápica, H.G.U. Gregorio Marañón, Madrid, Spain

J. C. Antoranz

Departamento de Física Matemática y Fluidos, UNED, 28080 Madrid, Spain and Department of Theoretical Physics, Henry Poincaré Group of Complex Systems, Havana University, Havana, Cuba

{dagger} Email: daniel{at}dfmf.uned.es

Received on July 28, 2006. Revised on March 26, 2007.

A cytokine-based periodic immunotherapy treatment is included in a model of tumour growth with a delay. The effects of dose schedule are studied in the case of a weak immune system and a growing tumour. We find the existence of ‘metastable’ states (that may last for tens of years) induced by the treatment and also potentially adverse effects of the dosage frequency on the stabilization of the tumour. These two effects depend on the delay between the tumour growth and the immune system response, the cytokine dose burden, and other parameters considered in the model.

Keywords: tumour growth; delay differential equations; immunotherapy; immunodepression


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