Qualitative analysis of second-order models of tumor–immune system competition |
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Authors: | C. Cattani A. Ciancio |
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Affiliation: | aDiFarma, University of Salerno, Via Ponte Don Melillo, 84084 I-Fisciano (SA), Italy;bDepartment of Mathematics, University of Messina, Salita Sperone 31, 98166 I-Messina, Italy |
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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. |
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Keywords: | Dynamical systems Population models Asymptotic analysis Nonlinearity |
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