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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Recognition and learning in a mathematical model for immune response against cancer

Pages: 891 - 914, Volume 18, Issue 4, June 2013      doi:10.3934/dcdsb.2013.18.891

 
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Marcello Delitala - Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (email)
Tommaso Lorenzi - Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (email)

Abstract: This paper presents a mathematical model for immune response against cancer aimed at reproducing emerging phenomena arising from the interactions between tumor and immune cells. The model is stated in terms of integro-differential equations and describes the dynamics of tumor cells, characterized by heterogeneous antigenic expressions, antigen-presenting cells and T-cells. Asymptotic analysis and simulations, developed with an exploratory aim, are addressed to verify the consistency of the model outputs as well as to provide biological insights into the mechanisms that rule tumor-immune interactions. In particular, the present model seems able to mimic the recognition, learning and memory aspects of immune response and highlights how the immune system might act as an additional selective pressure leading, eventually, to the selection for the most resistant cancer clones.

Keywords:  Modeling tumor-immune interactions, structured populations, recognition and learning, selective pressure, asymptotic analysis.
Mathematics Subject Classification:  Primary: 92B05, 45K05; Secondary: 92D25.

Received: August 2012;      Revised: September 2012;      Available Online: February 2013.

 References