Qualitative analysis of second-order models of tumor–immune system competition

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Abstract

This paper deals with the qualitative analysis, existence of equilibria and asymptotic behavior of some second-order models of the competition between tumor and immune cells. The background model belongs to d’Onofrio [A. d’Onofrio, A general framework for modeling tumor–immune system competition and immunotherapy: Mathematical analysis and biomedical inferences, Physica D 208 (2005) 220–235; A. d’Onofrio, Tumor–immune system interaction: Modelig the tumor-stimulated proliferation of effectors and immunotherapy, Math. Models Methods Appl. Sci. 16 (2006) 1375–1401]. Various developments proposed in this paper are focussed on the hiding–learning dynamics, followed by the qualitative analysis.

Keywords

Dynamical systems
Population models
Asymptotic analysis
Nonlinearity

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Partially supported by Marie Curie Network MRTN-CT-2004-503661 - Modeling, Mathematical Methods and Computer Simulations of Tumor Growth and Therapy and by Regione Campania LR 28/5/02 n. 5, Finanziamenti 2003 - Modelli nonlineari di materiali compositi per applicazioni di nanotecnologia chimica-biomedica.