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

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. (c) 2007 Elsevier Ltd. All rights reserved.