相关论文: A chemotaxis reaction-diffusion model for Multiple…
Computational models of neurodegeneration aim to emulate the evolving pattern of pathology in the brain during neurodegenerative disease, such as Alzheimer's disease. Previous studies have made specific choices on the mechanisms of…
We study a stochastic epidemic model consisting of elements (organisms in a community or cells in tissue) with fixed positions, in which damage or disease is transmitted by diffusing agents ("signals") emitted by infected individuals. The…
Turing's reaction-diffusion theory of morphogenesis has been very successful in understanding macroscopic patterns within complex objects ranging from biological systems to sand dunes. However, this mechanism was never tested against…
We focus on the spreading properties of solutions of monostable equations with non-linear diffusion. We consider both the porous medium diffusion and the fast diffusion regimes. Initial data may have heavy tails, which tends to accelerate…
An extensive rewiring of cell metabolism supports enhanced proliferation in cancer cells. We propose a systems level approach to describe this phenomenon based on Flux Balance Analysis (FBA). The approach does not explicit a cell biomass…
Multiple Sclerosis (MS) is a chronic autoimmune disease that can significantly reduce the quality of life of a patient. Existing treatment options can only help slow down the progression of the disease. Therefore, early detection and…
Acute lymphoblastic leukemia is the most common malignancy in childhood. Successful treatment requires initial high-intensity chemotherapy, followed by low-intensity oral maintenance therapy with oral 6-mercaptopurine (6MP) and methotrexate…
We introduce conversion to the stochastic process known as chase-escape in an effort to model aspects of inflammatory damage from multiple sclerosis. We prove monotonicity results for aggregate damage for the model on the positive integers,…
Nonlinear mixed effects models have received a great deal of attention in the statistical literature in recent years because of their flexibility in handling longitudinal studies, including human immunodeficiency virus viral dynamics,…
The Allee effect is an important phenomenon in population biology characterized by positive density dependence, that is a positive correlation between population density and individual fitness. However, the effect is not well studied in…
In this paper, we propose a new workflow to analyze macrophage motion during wound healing. These immune cells are attracted to the wound after an injury and they move showing both directional and random motion. Thus, first, we smooth the…
Recent advances in multiplex imaging have enabled researchers to locate different types of cells within a tissue sample. This is especially relevant for tumor immunology, as clinical regimes corresponding to different stages of disease or…
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…
The aim of this paper is to introduce, analyse and test in practice a new mathematical model describing the interplay between biological tissue atrophy driven by pathogen diffusion, with applications to neurodegenerative disorders. This…
Machine learning has been increasingly used to obtain individualized neuroimaging signatures for disease diagnosis, prognosis, and response to treatment in neuropsychiatric and neurodegenerative disorders. Therefore, it has contributed to a…
In this work we propose and investigate a family of models, which admits as particular cases some well known mathematical models of tumor-immune system interaction, with the additional assumption that the influx of immune system cells may…
Inflammation of brain tissue is a complex response of the immune system to the presence of toxic compounds or to cell injury, leading to a cascade of pathological processes that include glial cell activation. Noninvasive magnetic resonance…
We investigate possible effects of high order nonlinearities on the shapes of infection refugia of the Hantavirus epidemic. We replace Fisher-like equations that have been recently used to describe Hantavirus spread in mouse populations by…
Clustering of gene expression time series gives insight into which genes may be coregulated, allowing us to discern the activity of pathways in a given microarray experiment. Of particular interest is how a given group of genes varies with…
We propose a simple dynamic model of cancer development that captures carcinogenesis and subsequent cancer progression. A central idea of the model is to include the immune system as an extinction threshold, similar to the strong Allee…