From Kinetic Theory for Active Particles to Modelling Immune Competition

2008 ◽  
pp. 1-17
Author(s):  
Abdelghani Bellouquid ◽  
Marcello Delitala
Keyword(s):  
Kinetic Theory ◽  
Active Particles

Collective learning modeling based on the kinetic theory of active particles

2016 ◽  
Vol 16 ◽  
pp. 123-139 ◽  
Author(s):  
D. Burini ◽  
S. De Lillo ◽  
L. Gibelli
Keyword(s):  
Kinetic Theory ◽  
Collective Learning ◽  
Active Particles

Hilbert method toward a multiscale analysis from kinetic to macroscopic models for active particles

2017 ◽  
Vol 27 (07) ◽  
pp. 1327-1353 ◽  
Author(s):  
D. Burini ◽  
N. Chouhad
Keyword(s):  
Kinetic Theory ◽  
Multiscale Analysis ◽  
Second Step ◽  
Theory Approach ◽  
Type Method ◽  
Macroscopic Models ◽  
Active Particles ◽  
Time Space ◽  
Large Systems ◽  
Hilbert Type

This paper develops a Hilbert type method to derive models at the macroscopic scale for large systems of several interacting living entities whose statistical dynamics at the microscopic scale is delivered by kinetic theory methods. The presentation is in three steps, where the first one presents the structures of the kinetic theory approach used toward the aforementioned analysis; the second step presents the mathematical method; while the third step provides a number of specific applications. The approach is focused on a simple system and with a binary mixture, where different time-space scalings are used. Namely, parabolic, hyperbolic, and mixed in the case of a mixture.

ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES

2012 ◽  
Vol 22 (01) ◽  
pp. 1130001 ◽  
Author(s):  
N. BELLOMO ◽  
A. BELLOUQUID ◽  
J. NIETO ◽  
J. SOLER
Keyword(s):  
Kinetic Theory ◽  
Asymptotic Analysis ◽  
Critical Analysis ◽  
Asymptotic Theory ◽  
Blow Up ◽  
Cellular Interactions ◽  
Biological Functions ◽  
Active Particles ◽  
Tissue Models ◽  
Macroscopic Equations

This paper proposes a review and critical analysis of the asymptotic limit methods focused on the derivation of macroscopic equations for a class of equations modeling complex multicellular systems by methods of the kinetic theory for active particles. Cellular interactions generate both modification of biological functions and proliferative/destructive events. The asymptotic analysis deals with suitable parabolic, hyperbolic, and mixed limits. The review includes the derivation of the classical Keller–Segel model and flux limited models that prevent non-physical blow up of solutions.

FROM THE MODELING OF THE IMMUNE HALLMARKS OF CANCER TO A BLACK SWAN IN BIOLOGY

2013 ◽  
Vol 23 (05) ◽  
pp. 949-978 ◽  
Author(s):  
ABDELGHANI BELLOUQUID ◽  
ELENA DE ANGELIS ◽  
DAMIAN KNOPOFF
Keyword(s):  
Immune System ◽  
Kinetic Theory ◽  
Biological Function ◽  
Early Stage ◽  
Black Swan ◽  
Mathematical Approach ◽  
Hallmarks Of Cancer ◽  
Active Particles ◽  
Scalar Variable ◽  
Large Systems

This paper deals with the modeling of the early stage of cancer phenomena, namely mutations, onset, progression of cancer cells, and their competition with the immune system. The mathematical approach is based on the kinetic theory of active particles developed to describe the dynamics of large systems of interacting cells, called active particles. Their microscopic state is modeled by a scalar variable which expresses the main biological function. The modeling focuses on an interpretation of the immune-hallmarks of cancer.

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