Related papers: Turing pattern induced by cross-diffusion in cance…
This study proposes an effective positive control design strategy for cancer treatment by resorting to the combination of immunotherapy and chemotherapy. The treatment objective is to transfer the initial number of tumor cells and…
We consider a time-continuous Markov branching process of proliferating cells with a countable collection of types. Among-type transitions are inspired by the Tug-of-War process introduced in McFarland et al. as a mathematical model for…
Using a novel modeling approach based on the so-called environmental stress level (ESL), we develop a mathematical model to describe systematically the collective influence of oxygen concentration and stiffness of the extracellular matrix…
Tumor growth beyond a critical size relies on the development of a functional vascular network, which ensures adequate oxygen and nutrient supply. In this work, we present a modeling framework based on an optimization-based 3D-1D coupling…
Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…
We consider the problem of the long time dynamics for a diffuse interface model for tumor growth. The model describes the growth of a tumor surrounded by host tissues in the presence of a nutrient and consists in a Cahn-Hilliard-type…
In this letter we propose a Turing model of the formation of patterns of visible light emission intensity in atmospheric pressure gas discharges. The electron density and the electron temperature take the roles of activator and inhibitor…
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…
Cancer invasion of the surrounding tissue is a multiscale process that involves not only tumour cells but also other immune cells in the environment, such as the tumour-associated macrophages (TAMs). The heterogeneity of these immune cells,…
Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…
Adaptive therapy (AT) is designed to postpone the emergence of drug resistance by exploiting evolutionary competition among tumor subclones. Most mathematical models of AT assume a binary population structure of drug-sensitive and…
We present a problem-suited numerical method for a particularly challenging cancer invasion model. This model is a multiscale haptotaxis advection-reaction-diffusion system that describes the macroscopic dynamics of two types of cancer…
In this paper, we present a probabilistic analysis of a dynamical particle model for the self-adaptive immune response to cancer, as proposed by the first author in a previous work. The model is motivated by the interplay between immune…
An understanding of the disease spreading phenomenon based on a mathematical model is extremely needed for the implication of the correct policy measures to contain the disease propagation. Here, we report a new model namely the Ising-SIR…
This paper deals with the estimation of regions of attraction (RoAs) under parametric uncertainties for a cancer growth model with combined therapies. We propose a framework of probabilistic certification, based on the randomized methods,…
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…
We consider a phenotype-structured reaction-diffusion model of avascular glioma growth. The model describes the interaction dynamics between tumour cells and oxygen, and takes into account anisotropic cell movement and oxygen diffusion…
This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…
High-throughput screening technology has facilitated the generation of large-scale drug responses across hundreds of cancer cell lines. However, there exists significant discrepancy between in vitro cell lines and actual tumors in vivo in…
The growth of many solid tumors has been found to be driven by chemo- and radiotherapy-resistant cancer stem cells (CSCs). A suitable therapeutic avenue in these cases may involve the use of a differentiating agent (DA) to force the…