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Aspects of Social Dynamics: Models and Concepts

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: 20 September 2025 | Viewed by 2120

Special Issue Editor


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Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria
Interests: nonlinear dynamics; nonlinear time series analysis; fluid mechanics; nonlinear partial differential equations; application of the methods of statistics and probability theory to natural; social and economic systems
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Special Issue Information

Dear Colleagues,

One of the most important tasks for researchers of human and animal societies is to understand the dynamics of these societies. In order to do this, researchers often use models and concepts from different areas of mathematics and natural sciences. This Special Issue aims to contribute to the development of Mathematical Social Dynamics by presenting a discussion of various models of structures and processes in animal and human societies. We have listed several sources of concepts and models such as Statistical Physics and Thermodynamics, Mathematical Biology and Mathematical Sociology, Nonlinear Dynamics, Game Theory, Time Series Analysis, and Theory of Networks. However, concepts and mathematical models of society dynamics from other areas of natural and social sciences are also warmly welcomed. Another goal of the Special Issue is to provide a platform for those researchers who study the dynamics of these societies using mathematical models. We also hope to attract the interest of young researchers to the huge and promising area of mathematical studies of social systems.

Prof. Dr. Nikolay K. Vitanov
Guest Editor

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Keywords

  • mathematical models
  • social systems
  • statistical physics
  • thermodynamics
  • mathematical biology
  • mathematical sociology
  • nonlinear dynamics
  • game theory
  • time series analysis
  • theory of networks
  • social sciences
  • animal societies
  • human societies

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Published Papers (1 paper)

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Research

25 pages, 3049 KiB  
Article
Sic Transit Gloria Mundi: A Mathematical Theory of Popularity Waves Based on a SIIRR Model of Epidemic Spread
by Nikolay K. Vitanov and Zlatinka I. Dimitrova
Entropy 2025, 27(6), 611; https://doi.org/10.3390/e27060611 - 9 Jun 2025
Viewed by 1598
Abstract
We discuss the spread of epidemics caused by two viruses which cannot infect the same individual at the same time. The mathematical modeling of this epidemic leads to a kind of SIIRR model with two groups of infected individuals and two groups of [...] Read more.
We discuss the spread of epidemics caused by two viruses which cannot infect the same individual at the same time. The mathematical modeling of this epidemic leads to a kind of SIIRR model with two groups of infected individuals and two groups of recovered individuals. An additional assumption is that after recovering from one of the viruses, the individual cannot be infected by the other virus. The mathematical model consists of five equations which can be reduced to a system of three differential equations for the susceptible and for the recovered individuals. This system has analytical solutions for the case when one of the viruses infects many more individuals than the other virus. Cases which are more complicated than this one can be studied numerically. The theory is applied to the study of waves of popularity of an individual/groups of individuals or of an idea/group of ideas in the case of the presence of two opposite opinions about the popularity of the corresponding individual/group of individuals or idea/group of ideas. We consider two cases for the initial values of the infected individuals: (a) the initial value of the individuals infected with one of the viruses is much larger than the initial values of the individuals infected by the second virus, and (b) the two initial values of the infected individuals are the same. The following effects connected to the evolution of the numbers of infected individuals are observed: 1. arising of bell-shaped profiles of the numbers of infected individuals; 2. suppression of popularity; 3. faster increase–faster decrease effect for the peaks of the bell-shaped profiles; 4. peak shift in the time; 5. effect of forgetting; 6. window of dominance; 7. short-term win–long-term loss effect; 8. effect of the single peak. The proposed SIIRR model is used to build a mathematical theory of popularity waves where a person or idea can have positive and negative popularity at the same time and these popularities evolve with time. Full article
(This article belongs to the Special Issue Aspects of Social Dynamics: Models and Concepts)
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