Related papers: Biological Modelling with Nonlocal Advection Diffu…
In this paper, we examine the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators.The spreading front of the disease is represented by the free…
The vertex model is widely used to describe the dynamics of epithelial tissues, because of its simplicity and versatility and the direct inclusion of biophysical parameters. Here, it is shown that quite generally, when cells modify their…
Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical…
Wild animals are commonly fitted with trackers that record their position through time, and statistical models for tracking data broadly fall into two categories: models focused on small-scale movement decisions, and models for large-scale…
We investigate the nonlocal behavior of passive tracer dispersion with random stopping at various sites in fluids. This kind of dispersion processes is modeled by an integral partial differential equation, i.e., an advection-diffusion…
Age-structured models capture the dynamic behavior of populations over time and result in nonlinear integro-partial differential equations (IPDEs). These processes arise in various fields such as biotechnology, economics, or demography.…
Adhesion-independent migration is a prominent mode of cell motility in confined environments, yet the physical principles that guide such movement remain incompletely understood. We present a phase-field model for simulating the motility of…
The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
Inspired by motile cells in tissue formation, we find that active systems of self-aligning adhesive particles undergo ballistic aggregation through a flocking transition. This kinetic regime emerges when the cluster persistence length grows…
In this work a physical modelling framework is presented, describing the intelligent, non-local, and anisotropic behaviour of pedestrians. Its phenomenological basics and constitutive elements are detailed, and a qualitative analysis is…
The question addressed here is the long time evolution of the solutions to a class of one-dimensional reaction-diffusion equations, in which the diffusion is given by an integral operator. The underlying motivation, discussed in the first…
In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with a nonlocal mass transfer admits the local existence of classical solutions. The equation was developed to…
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with…
Collective motion is a phenomenon observed across length scales in nature, from bacterial swarming and tissue migration to the flocking of animals. The mechanisms underlying this behavior vary significantly depending on the biological…
Collective cell migration underlies important biological processes, such as embryonic development, wound healing and cancer invasion. While many aspects of single cell movements are now well established, the mechanisms leading to…
We study an elliptic-parabolic system of partial differential equations describing formation of biological network structures. The model takes into consideration the evolution of the permeability tensor under the influence of a diffusion…
The immune response to a pathogen has two basic features. The first is the expansion of a few pathogen-specific cells to form a population large enough to control the pathogen. The second is the process of differentiation of cells from an…
Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated…
In both biological and artificial systems, concentration gradients can serve as a convenient mechanism for manipulating particles and generating motility. Particles that interact with a solute will move along its gradient; if they…