Mathematical modelling of chemotaxis (the movement of biological cells or organisms in
response to chemical gradients) has developed into a large and diverse discipline, whose …

This paper proposes a survey and critical analysis focused on a variety of chemotaxis
models in biology, namely the classical Keller–Segel model and its subsequent …

This paper proposes a review and critical analysis of the asymptotic limit methods focused
on the derivation of macroscopic equations for a class of equations modeling complex …

This work deals with a parabolic chemotaxis model with nonlinear diffusion and nonlocal
reaction source. The problem is formulated on the whole space and, depending on a …

This book presents models written as partial differential equations and originating from
various questions in population biology, such as physiologically structured equations …

The Keller-Segel system describes the collective motion of cells which are attracted by a
chemical substance and are able to emit it. In its simplest form it is a conservative drift …

Motivated by empirical observations of spatio-temporal clusters of crime across a wide
variety of urban settings, we present a model to study the emergence, dynamics, and steady …

We study a system arising in the modelling of the motion of swimming bacteria under the
effect of diffusion, oxygen-taxis and transport through an incompressible fluid. The novelty …

We study global solutions of a class of chemotaxis systems generalizing the prototype
{ut=∇⋅((u+ 1) m− 1∇ u)− χ∇⋅(u (u+ 1) q− 1∇ v)+ au− bur, x∈ Ω, t> 0, 0= Δ v− v+ u, x∈ Ω …

We present a weakly nonlinear analysis of our recently developed model for the formation of
crime patterns. Using a perturbative approach, we find amplitude equations that govern the …