V. Giunta

• Lecturer at Swansea University

Background Models of utilization distribution in the form of partial differential equations have long contributed to our understanding of organismal space use patterns. In studies of infectious diseases, they are also being increasingly adopted in support of epidemic forecasting and scenario planning. However, as movement research shifts its focus...

In a chase-and-run dynamic, the interaction between two individuals is such that one moves towards the other (the chaser), while the other moves away (the runner). Examples can be found in both interacting cells and animals. Here, we investigate the behaviours that can emerge at a population level, for a heterogeneous group that contains subpopulat...

In a chase-and-run dynamic, the interaction between two individuals is such that one moves towards the other (the chaser), while the other moves away (the runner). Examples can be found in both interacting cells and interacting animals. Here we investigate the behaviours that can emerge at a population level, for a heterogeneous group that contains...

Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection-diffusion model with nonlocal advection terms describing the species movements generated by inter-species interactions. We use linear analysis to assess the stability of...

Pattern formation, Bifurcation Analysis, Nonlinear Diffusion, Three Species Lotka-Volterra

Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations, these emergent patterns sometimes appear as local minimisers of a corresponding energy functional. Here we give methods for determining the qualitative structure of local minimum energy states o...

Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a corresponding energy functional. Here we give methods for determining the qualitative structure of local minimum energy s...

A principal concern of ecological research is to unveil the causes behind observed spatio–temporal distributions of species. A key tactic is to correlate observed locations with environmental features, in the form of resource selection functions or other correlative species distribution models. In reality, however, the distribution of any populatio...

We investigate the formation of stationary patterns in the FitzHugh-Nagumo reaction-diffusion system with linear cross-diffusion terms. We focus our analysis on the effects of cross-diffusion on the Turing mechanism. Linear stability analysis indicates that positive values of the inhibitor cross-diffusion enlarge the region in the parameter space w...

A principal concern of ecological research is to unveil the causes behind observed spatio-temporal distributions of species. A key tactic is to correlate observed locations with environmental features, in the form of resource selection functions or other correlative species distribution models. In reality, however, the distribution of any populatio...

Non-local advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modelling non-local advection mathematically. These often take the form of partial differential equations, with integral terms modelling the no...

We consider a system of reaction–diffusion equations including chemotaxis terms and coming out of the modelling of multiple sclerosis. The global existence of strong solutions to this system in any dimension is proved, and it is also shown that the solution is bounded uniformly in time. Finally, a nonlinear stability result is obtained when the che...

Non-local advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modelling non-local advection mathematically. These often take the form of partial differential equations, with integral terms modelling the no...

We consider a system of reaction-diffusion equations including chemotaxis terms and coming out of the modeling of multiple sclerosis. The global existence of strong solutions to this system in any dimension is proved, and it is also shown that the solution is bounded uniformly in time. Finally, a nonlinear stability result is obtained when the chem...

We study in this work the global existence of solutions to a system of reaction cross diffusion equations appearing in the modeling of multiple sclerosis, in the one-dimensional case. Weak solutions are obtained for general initial data, and existence, uniqueness, stability and smoothness are proven when initial data are smooth.

In this paper we study radially symmetric solutions for our recently proposed reaction–diffusion–chemotaxis model of Multiple Sclerosis. Through a weakly nonlinear expansion we classify the bifurcation at the onset and derive the amplitude equations ruling the formation of concentric demyelinating patterns which reproduce the concentric layers obse...