Related papers: A reaction-diffusion model for relapsing-remitting…
We present a mathematical study for the development of Multiple Sclerosis in which a spatio-temporal kinetic { theory} model describes, at the mesoscopic level, the dynamics of a high number of interacting agents. We consider both…
Multiple Sclerosis is a chronic autoimmune disorder characterized by the degradation of the myelin sheath in the central nervous system, leading to neurological impairments. In this work, we analyze a reaction-diffusion model derived from…
In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic…
In this paper, we investigate a mathematical model describing the interactions between effector cells (E), cancer cells (T), and the IL-2 compound (IL). The model considered here is a generalization, taking into account some cross-diffusion…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
In this paper, we study a modification of the mathematical model describing inflammation and demyelination patterns in the brain caused by Multiple Sclerosis proposed in [Lombardo et al. (2017), Journal of Mathematical Biology, 75,…
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with…
The temporal and spatial development of Parkinson's disease has been characterised as the progressive formation of {\alpha}-synuclein aggregations through susceptible neuronal pathways. This article describes a new model for this…
Multiple Sclerosis is a degenerative condition of the central nervous system that affects nearly 2.5 million of individuals in terms of their physical, cognitive, psychological and social capabilities. Researchers are currently…
The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…
To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in…
Image-based personalized medicine has the potential to transform healthcare, particularly for diseases that exhibit heterogeneous progression such as Multiple Sclerosis (MS). In this work, we introduce the first treatment-aware…
We present spatio-temporal characteristics of spreading depolarizations (SD) in two experimental systems: retracting SD wave segments observed with intrinsic optical signals in chicken retina, and spontaneously occurring re-entrant SD waves…
In this paper we study a mathematical model for an infectious disease such as Cholera without life-time immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are…
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…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
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…
The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state…
We investigate a recently proposed cross-diffusion system modelling the growth of gliobastoma taking into account size exclusion both in the migration and proliferation process. In addition to degenerate nonlinear cross-diffusion the model…
The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand are…