This paper presents a review and critical analysis on the modeling of the dynamics of
vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It …

Opinion dynamics have attracted the interest of researchers from different fields. Local
interactions among individuals create interesting dynamics for the system as a whole. Such …

Solving inverse problems without the use of derivatives or adjoints of the forward model is
highly desirable in many applications arising in science and engineering. In this paper we …

This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an
aggressive virus, specifically the so-called SARS–CoV–2 Severe Acute Respiratory …

In this survey we consider the development and mathematical analysis of numerical
methods for kinetic partial differential equations. Kinetic equations represent a way of …

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 …

The modeling of living systems composed of many interacting entities is treated in this paper
with the aim of describing their collective behaviors. The mathematical approach is …

We introduce a novel first-order stochastic swarm intelligence (SI) model in the spirit of
consensus formation models, namely a consensus-based optimization (CBO) algorithm …

This paper presents a survey and critical analysis of the mathematical literature on modeling
and simulation of human crowds taking into account behavioral dynamics. The main focus is …

Abstract We study the McKean–Vlasov equation ∂ _t ϱ= β^-1 Δ ϱ+ κ\, ∇ ⋅\,(ϱ ∇ (W ⋆
ϱ)),∂ t ϱ= β-1 Δ ϱ+ κ∇·(ϱ∇(W⋆ ϱ)), with periodic boundary conditions on the torus. We …