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This paper provides a survey of mathematical models and methods dealing with the analysis and simulation of tumor dynamics in competition with the immune system. The characteristic scales of the phenomena are identified and the mathematical literature on models and problems developed on each scale is reviewed and critically analyzed. Moreover, this paper… (More)

This paper deals with the qualitative analysis of a model describing the competition among cell populations each of them expressing a peculiar cooperating and organizing behaviour. The mathematical framework in which the model has been developed is the kinetic theory for active particles. The main result of this paper is concerned with the analysis of the… (More)

This paper deals with the qualitative analysis of a model related to the description of two medical therapies which have been intensively developed in recent years. In particular, we refer to the modeling of the actions applied by proteins, to activate the immune defense, and to the control of angiogenesis, to contrast the growth of tumour cells by… (More)

This paper deals with the derivation of macroscopic equations for a class of equations modelling complex multicellular systems. Cellular interactions generate both modification of biological functions and proliferative/destructive events. The asymptotic analysis refers to the derivation of hyperbolic models focused on the influence of existence of a global… (More)

- Elena De Angelis, Marcello Delitala
- Mathematical and Computer Modelling
- 2006

- Elena De Angelis, Bertrand Lods
- Mathematical and Computer Modelling
- 2008

This paper deals with the qualitative analysis of a model describing the competition between tumor and immune cells. Such competition is characterized by proliferation–destruction phenomena and the interacting entities are characterized by a microscopic state which is modified by interactions. The model also includes the description of the natural trend of… (More)

- Elena De Angelis, Roberto Revelli, Luca Ridolfi
- Computers & Mathematics with Applications
- 2009

- Luisa Arlotti, Elena De Angelis, Luisa Fermo, Miroslaw Lachowicz, Nicola Bellomo
- Appl. Math. Lett.
- 2012

- Luisa Arlotti, Elena De Angelis
- Appl. Math. Lett.
- 2011

- Elena De Angelis, Cecil Pompiliu Grünfeld
- Appl. Math. Lett.
- 2001