scholarly journals Towards a mathematical theory of behavioral human crowds

2022 ◽  
pp. 1-38
Author(s):  
Nicola Bellomo ◽  
Livio Gibelli ◽  
Annalisa Quaini ◽  
Alessandro Reali
Keyword(s):  
Critical Analysis ◽  
Mathematical Theory ◽  
Social Dynamics ◽  
Living Systems ◽  
General Survey ◽  
Multiscale Problems ◽  
Modeling Approach ◽  
Research Perspectives

The first part of our paper presents a general survey on the modeling, analytic problems, and applications of the dynamics of human crowds, where the specific features of living systems are taken into account in the modeling approach. This critical analysis leads to the second part which is devoted to research perspectives on modeling, analytic problems, multiscale topics which are followed by hints towards possible achievements. Perspectives include the modeling of social dynamics, multiscale problems and a detailed study of the link between crowds and swarms modeling.

Modeling virus pandemics in a globally connected world a challenge towards a mathematics for living systems

2021 ◽  
pp. 1-7
Author(s):  
N. Bellomo ◽  
F. Brezzi ◽  
M. A. J. Chaplain
Keyword(s):  
Complex System ◽  
Population Dynamics ◽  
Mathematical Models ◽  
Modeling And Simulation ◽  
Critical Analysis ◽  
Living Systems ◽  
Special Issue ◽  
Research Perspectives ◽  
Heterogeneous Features

This editorial paper presents the papers published in a special issue devoted to the modeling and simulation of mutating virus pandemics in a globally connected world. The presentation is proposed in three parts. First, motivations and objectives are presented according to the idea that mathematical models should go beyond deterministic population dynamics by considering the multiscale, heterogeneous features of the complex system under consideration. Subsequently, the contents of the papers in this issue are presented referring to the aforementioned complexity features. Finally, a critical analysis of the overall contents of the issue is proposed, with the aim of providing a forward look to research perspectives.

Collective dynamics in science and society

2021 ◽  
pp. 1-6
Author(s):  
N. Bellomo ◽  
F. Brezzi
Keyword(s):  
Critical Analysis ◽  
Large Scale ◽  
Particle Methods ◽  
Science And Society ◽  
Special Issue ◽  
Collective Dynamics ◽  
Multiscale Problems ◽  
Research Perspectives ◽  
Active Particles ◽  
Large Systems

This editorial paper presents the articles published in a special issue devoted to active particle methods applied to modeling, qualitative analysis, and simulation of the collective dynamics of large systems of interacting living entities in science and society. The modeling approach refers to the mathematical tools of behavioral swarms theory and to the kinetic theory of active particles. Applications focus on classical problems of swarms theory, on crowd dynamics related to virus contagion problems, and to multiscale problems related to the derivation of models at a large scale from the mathematical description at the microscopic scale. A critical analysis of the overall contents of the issue is proposed, with the aim to provide a forward look to research perspectives.

MATHEMATICAL TOPICS ON THE MODELLING COMPLEX MULTICELLULAR SYSTEMS AND TUMOR IMMUNE CELLS COMPETITION

2004 ◽  
Vol 14 (11) ◽  
pp. 1683-1733 ◽  
Author(s):  
N. BELLOMO ◽  
A. BELLOUQUID ◽  
M. DELITALA
Keyword(s):  
Immune Cells ◽  
Critical Analysis ◽  
Mathematical Theory ◽  
Cellular Level ◽  
Mathematical Framework ◽  
Mathematical Methods ◽  
Microscopic Description ◽  
Macroscopic Equation ◽  
Research Perspectives ◽  
Mathematical Literature

This paper deals with a critical analysis and some developments related to the mathematical literature on multiscale modelling of multicellular systems involving tumor immune cells competition at the cellular level. The analysis is focused on the development of mathematical methods of the classical kinetic theory to model the above physical system and to recover macroscopic equation from the microscopic description. Various hints are given toward research perspectives, with special attention on the modelling of the interplay of microscopic (at the cellular level) biological and mechanical variables on the overall evolution of the system. Indeed the final aim of this paper consists of organizing the various contributions available in the literature into a mathematical framework suitable to generate a mathematical theory for complex biological systems.

LOOKING FOR NEW PARADIGMS TOWARDS A BIOLOGICAL-MATHEMATICAL THEORY OF COMPLEX MULTICELLULAR SYSTEMS

2006 ◽  
Vol 16 (07) ◽  
pp. 1001-1029 ◽  
Author(s):  
NICOLA BELLOMO ◽  
GUIDO FORNI
Keyword(s):  
Kinetic Theory ◽  
Complex Systems ◽  
Critical Analysis ◽  
Mathematical Theory ◽  
Classical Mechanics ◽  
Biological Functions ◽  
Living Matter ◽  
Research Perspectives ◽  
Active Particles ◽  
Large Systems

This paper deals with the development of new paradigms based on the methods of the mathematical kinetic theory for active particles to model the dynamics of large systems of interacting cells. Interactions are ruled, not only by laws of classical mechanics, but also by a few biological functions which are able to modify the above laws. The paper technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in biology. The last part of the paper deals with a critical analysis and with the indication of research perspectives concerning the challenging target of developing a biological-mathematical theory for the living matter.

Active particles methods and challenges in behavioral systems

2020 ◽  
Vol 30 (04) ◽  
pp. 653-658 ◽  
Author(s):  
N. Bellomo ◽  
F. Brezzi ◽  
J. Soler
Keyword(s):  
Qualitative Analysis ◽  
Critical Analysis ◽  
Mathematical Approach ◽  
Special Issue ◽  
Behavioral Systems ◽  
Research Perspectives ◽  
Active Particles ◽  
Challenging Research ◽  
Large Systems

This paper first provides an introduction to the mathematical approach to the modeling, qualitative analysis, and simulation of large systems of living entities, specifically self-propelled particles. Subsequently, a presentation of the papers published in this special issue follows. Finally, a critical analysis of the overall contents of the issue is proposed, thus leading to define some challenging research perspectives.

Cross-diffusion models: Analytic and multiscale problems

2018 ◽  
Vol 28 (11) ◽  
pp. 2097-2102 ◽  
Author(s):  
N. Bellomo ◽  
Y. Tao ◽  
M. Winkler
Keyword(s):  
Diffusion Models ◽  
Special Issue ◽  
Multiscale Problems ◽  
Cross Diffusion ◽  
Research Perspectives ◽  
Concise Description

A presentation of a special issue on the derivation of cross-diffusion models and on the related analytical problems is proposed in this note. A brief introduction to motivations and recently published literature is presented in the first part. Subsequently, a concise description of the contents of the papers published in the issue follows. Finally, some ideas on possible research perspectives are proposed.

On coupled dynamics and regime shifts in coupled human-water systems

2020 ◽  
Author(s):  
Rachata Muneepeerakul ◽  
Mehran Homayounfar
Keyword(s):  
Social Dynamics ◽  
Water System ◽  
Water Systems ◽  
Regime Shifts ◽  
Adaptation Strategies ◽  
Coupled Dynamics ◽  
Modeling Approach ◽  
Floods And Droughts

<p>To clarify the nonlinear and intertwined dynamics in coupled human-water systems, we developed a stylized model that combines simple hydrological and social dynamics. In this model, neither too much nor too little water is good (think floods and droughts, respectively; this is a feature absent in previous models) and the population self-organizes to respond to relative benefits they derive from the water system and outside opportunities. Despite its simplicity, the model richly yields 6 different regimes. A closer look at the conditions giving rise to these different regimes sheds light on the design of policies and adaptation strategies for the coupled human-water system under different social-hydrological settings. Advantages and limitations of this modeling approach will also be discussed.</p>

Mathematics, complexity and multiscale features of large systems of self-propelled particles

2015 ◽  
Vol 26 (02) ◽  
pp. 207-214 ◽  
Author(s):  
N. Bellomo ◽  
F. Brezzi
Keyword(s):  
Complex Systems ◽  
Mathematical Theory ◽  
Life Sciences ◽  
Living Systems ◽  
Future Research ◽  
Large Systems

This issue is devoted to complex systems in life sciences. Some perspective ideas on possible objectives of future research are extracted from the contents of this issue and brought to the reader’s attention. The final ambitious aim is the development of a mathematical theory for complex living systems.

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