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The worldwide spread of COVID-19 has called for fast advancement of new modelling strategies to estimate its unprecedented spread. Here, we introduce a model based on the fundamental SIR equations with a stochastic disorder by a random…
The endogenous adaptation of agents, that may adjust their local contact network in response to the risk of being infected, can have the perverse effect of increasing the overall systemic infectiveness of a disease. We study a dynamical…
Many complex adaptive systems contain a large diversity of specialized components. The specialization at the level of the microscopic degrees of freedom, and diversity at the level of the system as a whole are phenomena that appear during…
Agent-based models provide a constructive approach to studying emergent dynamics in life-like systems composed of interacting, adaptive agents. Financial markets serve as a canonical example of such systems, where collective price dynamics…
We present an agent-based model of microscopic wealth exchange in a dynamic network to study the topological features associated with economic inequality. The model evolves through two alternating processes, the conservative exchange of…
The kinetic exchange model has gained popularity in the field of statistical mechanics for investigating wealth interaction. Traditionally, kinetic exchange models have been studied without considering preferential interactions. However, in…
In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We…
Agent-based models describing social interactions among individuals can help to better understand emerging macroscopic patterns in societies. One of the topics which is worth tackling is the formation of different kinds of hierarchies that…
A deterministic system of coupled maps is proposed as a model for economic activity among interacting agents. The values of the maps represent the wealth of the agents. The dynamics of the system is controlled by two parameters. One…
We introduce an agent-based model of interaction, drawing on the contingency approach from Luhmann's theory of social systems. The agent interactions are defined by the exchange of distinct messages. Message selection is based on the…
We suggest a novel approach to treating symbiotic relations between biological species or social entities. The main idea is the characterisation of symbiotic relations of coexisting species through their mutual influence on their respective…
A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into…
Exploiting the mathematical curiosity of intransitive dice, we present a simple theoretical model for co-evolution that captures scales ranging from the genome of the individual to the system-wide emergence of species diversity. We study a…
This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution.…
We develop an agent-based model on a lattice to investigate territorial development motivated by markings such as graffiti, generalizing a previously-published model to account for $K$ groups instead of two groups. We then analyze this…
We propose an epidemic model for the spread of vector-borne diseases. The model, which is built extending the classical susceptible-infected-susceptible model, accounts for two populations -- humans and vectors -- and for cross-contagion…
Classical swarm models, exemplified by the Cucker--Smale framework, provide foundational insights into collective alignment but exhibit fundamental limitations in capturing the adaptive, heterogeneous behaviours intrinsic to living systems.…
Cognitive modeling, which explores the essence of cognition, including motivation, emotion, and perception, has been widely applied in the artificial intelligence (AI) agent domains, such as robotics. From the computational perspective,…
The statistical mechanics approach to wealth distribution is based on the conservative kinetic multi-agent model for money exchange, where the local interaction rule between the agents is analogous to the elastic particle scattering…
Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a…