Cross diffusion models in complex frameworks From microscopic to macroscopic

D Burini, N Chouhad - arXiv preprint arXiv:2303.11210, 2023 - arxiv.org
This paper deals with the micro-macro derivation of models from the underlying description
provided by methods of the kinetic theory for active particles. We consider the so-called …

From a multiscale derivation of nonlinear cross-diffusion models to Keller–Segel models in a Navier–Stokes fluid

N Bellomo, A Bellouquid, N Chouhad - Mathematical Models and …, 2016 - World Scientific
This paper deals with a micro–macro derivation of a variety of cross-diffusion models for a
large system of active particles. Some of the models at the macroscopic scale can be viewed …

Virus models in complex frameworks: Towards modeling space patterns of SARS-CoV-2 epidemics

D Burini, N Chouhad - … Models and Methods in Applied Sciences, 2022 - World Scientific
This paper deals with the micro–macro-derivation of virus models coupled with a reaction–
diffusion system that generates the dynamics in space of the virus particles. The first part of …

Keller-Segel-type models and kinetic equations for interacting particles: long-time asymptotic analysis

FKO Hoffmann - 2017 - repository.cam.ac.uk
Keller-Segel-Type Models and Kinetic Equations for Interacting Particles: Long-Time Asymptotic
Analysis Page 1 Keller-Segel-Type Models and Kinetic Equations for Interacting Particles …

Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision

N Bellomo, N Outada, J Soler, Y Tao… - … Models and Methods in …, 2022 - World Scientific
This paper proposes a review focused on exotic chemotaxis and cross-diffusion models in
complex environments. The term exotic is used to denote the dynamics of models interacting …

Pandemics of mutating virus and society: a multi-scale active particles approach

N Bellomo, D Burini, N Outada - … Transactions of the …, 2022 - royalsocietypublishing.org
This article presents, within a multiscale framework, a search for a unified approach towards
modelling the COVID-19 pandemic, from contagion to within-host dynamics. The modelling …

Network structured kinetic models of social interactions

M Burger - Vietnam Journal of Mathematics, 2021 - Springer
The aim of this paper is to study the derivation of appropriate meso-and macroscopic models
for interactions as appearing in social processes. There are two main characteristics the …

Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods

G Bertaglia, L Pareschi - ESAIM: Mathematical Modelling and …, 2021 - esaim-m2an.org
We consider the development of hyperbolic transport models for the propagation in space of
an epidemic phenomenon described by a classical compartmental dynamics. The model is …

On a probabilistic interpretation of the Keller-Segel parabolic-parabolic equations

M Tomasevic - 2018 - theses.hal.science
The standard d-dimensional parabolic--parabolic Keller--Segel model for chemotaxis
describes the time evolution of the density of a cell population and of the concentration of a …

Generalized solution and eventual smoothness in a logarithmic Keller–Segel system for criminal activities

B Li, L Xie - Mathematical Models and Methods in Applied …, 2023 - World Scientific
This paper focuses on a simplified variant of the Short et al. model, which is originally
introduced by Rodríguez, and consists of a system of two coupled reaction–diffusion-like …