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We consider a cell population structured by a positive real number, describing the number of P-glycoproteins carried by the cell. We are interested in the effect of those proteins on the growth of the population: those proteins are indeed…

Analysis of PDEs · Mathematics 2015-11-10 Pierre Magal , Gaël Raoul

A simple kinematical argument suggests that the classical approximation may be inadequate to describe the evolution of a system with an anisotropic particle distribution. In order to verify this quantitatively, we study the Boltzmann…

High Energy Physics - Phenomenology · Physics 2015-10-28 Thomas Epelbaum , Francois Gelis , Sangyong Jeon , Guy Moore , Bin Wu

The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic…

Statistical Mechanics · Physics 2020-04-22 J. Javier Brey , P. Maynar , M. I. García de Soria

Unlike the classical kinetic theory of rarefied gases, where microscopic interactions among gas molecules are described as binary collisions, the modelling of socio-economic phenomena in a multi-agent system naturally requires to consider,…

Physics and Society · Physics 2020-09-15 Giuseppe Toscani , Andrea Tosin , Mattia Zanella

Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the derivation of these…

We propose a minimal model for the collective dynamics of opinion formation in the society, by modifying kinetic exchange dynamics studied in the context of income, money or wealth distributions in a society. This model has an intriguing…

Physics and Society · Physics 2010-10-27 Mehdi Lallouache , Anirban Chakraborti , Bikas K. Chakrabarti

We introduce a kinetic framework for modeling the time evolution of the statistical distributions of the population densities in the three compartments of susceptible, infectious, and recovered individuals, under epidemic spreading driven…

Analysis of PDEs · Mathematics 2025-12-16 Giorgio Martalò , Giuseppe Toscani , Mattia Zanella

In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…

Probability · Mathematics 2015-01-13 Federico Bassetti , Giuseppe Toscani

We consider systems of agents interacting through topological interactions. These have been shown to play an important part in animal andhuman behavior. Precisely, the system consists of a finite number of particles characterized by their…

Mathematical Physics · Physics 2017-11-22 Adrien Blanchet , Pierre Degond

In this work we define a kinetic model for understanding the impact of heterogeneous opinion formation dynamics on epidemics. The considered many-agent system is characterized by nonsymmetric interactions which define a coupled system of…

Physics and Society · Physics 2024-03-13 Sabrina Bonandin , Mattia Zanella

Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the…

Machine Learning · Statistics 2016-11-08 Zhen Xu , Wen Dong , Sargur Srihari

We study the dynamics of individual agents in some kinetic models of wealth exchange, particularly, the models with savings. For the model with uniform savings, agents perform simple random walks in the "wealth space". On the other hand, we…

Physics and Society · Physics 2011-01-04 Arnab Chatterjee , Parongama Sen

We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the influence of knowledge in the evolution of wealth in a system of agents which interact through the binary trades introduced in Cordier, Pareschi,…

General Finance · Quantitative Finance 2015-06-18 Lorenzo Pareschi , Giuseppe Toscani

We discuss several models of the dynamics of interacting populations. The models are constructed by nonlinear differential equations and have two sets of parameters: growth rates and coefficients of interaction between populations. We…

Adaptation and Self-Organizing Systems · Physics 2013-07-29 Nikolay K. Vitanov , Zlatinka I. Dimitrova

Owing to the analogies between the problem of wealth redistribution with taxation in a multi-agent society, we introduce and discuss a kinetic model describing the statistical distributions in time of the sizes of groups of biological…

Populations and Evolution · Quantitative Biology 2023-11-15 Giuseppe Toscani , Mattia Zanella

Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a…

Populations and Evolution · Quantitative Biology 2022-01-19 K. Bodova , E. Szep , N. H. Barton

It is shown, that the Boltzmann-like equations allow the formulation of a very general model for behavioral changes. This model takes into account spontaneous (or externally induced) behavioral changes and behavioral changes by pair…

Statistical Mechanics · Physics 2009-10-31 Dirk Helbing

In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme…

Statistical Mechanics · Physics 2015-07-15 Umberto Marini Bettolo Marconi , Simone Melchionna

Multi-agent systems can be successfully described by kinetic models, which allow one to explore the large scale aggregate trends resulting from elementary microscopic interactions. The latter may be formalised as collision-like rules, in…

Statistical Mechanics · Physics 2020-11-06 Nadia Loy , Andrea Tosin

In the present paper the macroscopic limits of the kinetic model for inter-acting entities (individuals, organisms, cells) are studied. The kinetic model is one-dimensional and entities are characterized by their position and orientation…

Analysis of PDEs · Mathematics 2012-07-12 Jacek Banasiak , Miroslaw Lachowicz