A convergent numerical scheme for integrodifferential kinetic models of angiogenesis

We study a robust finite difference scheme for integrodifferential kinetic systems of Fokker-Planck type modeling tumor driven blood vessel growth. The scheme is of order one and enjoys positivity features. We analyze stability and convergence properties, and show that soliton-like asymptotic solutions are correctly captured. We also find good agreement with the solution of the original stochastic model from which the deterministic kinetic equations are derived working with ensemble averages. A numerical study clarifies the influence of velocity cut-offs on the solutions for exponentially decaying data

On the numerical solution to a parabolic-elliptic system with chemotactic and periodic terms using Generalized Finite Differences

In the present paper we propose the Generalized Finite Difference Method (GFDM) for numerical solution of a cross-diffusion system with chemotactic terms. We derive the discretization of the system using a GFD scheme in order to prove and illustrate that the uniform stability behavior/ convergence of the continuous model is also preserved for the discrete model. We prove the convergence of the explicit method and give the conditions of convergence. Extensive numerical experiments are presented to illustrate the accuracy, efficiency and robustness of the GFDM

Solving a fully parabolic chemotaxis system with periodic asymptotic behavior using Generalized Finite Difference Method

This work studies a parabolic-parabolic chemotactic PDE's system which describes the evolution of a biological population “U” and a chemical substance “V”, using a Generalized Finite Difference Method, in a two dimensional bounded domain with regular boundary. In a previous paper [12], the authors asserted global classical solvability and periodic asymptotic behavior for the continuous system in 2D. In this continuous work, a rigorous proof of the global classical solvability to the discretization of the model proposed in [12] is presented in two dimensional space. Numerical experiments concerning the convergence in space and in time, and long-time simulations are presented in order to illustrate the accuracy, efficiency and robustness of the developed numerical algorithms

Solving a reaction-diffusion system with chemotaxis and non-local terms using Generalized Finite Difference Method. Study of the convergence

In this paper a parabolic-parabolic chemotaxis system of PDEs that describes the evolution of a population with non-local terms is studied. We derive the discretization of the system using the meshless method called Generalized Finite Difference Method. We prove the conditional convergence of the solution obtained from the numerical method to the analytical solution in the two dimensional case. Several examples of the application are given to illustrate the accuracy and efficiency of the numerical method. We also present two examples of a parabolic-elliptic model, as generalized by the parabolic-parabolic system addressed in this paper, to show the validity of the discretization of the non-local terms

On the convergence of the Generalized Finite Difference Method for solving a chemotaxis system with no chemical diffusion

This paper focuses on the numerical analysis of a discrete version of a nonlinear reaction–diffusion system consisting of an ordinary equation coupled to a quasilinear parabolic PDE with a chemotactic term. The parabolic equation of the system describes the behavior of a biological species, while the ordinary equation defines the concentration of a chemical substance. The system also includes a logistic-like source, which limits the growth of the biological species and presents a time-periodic asymptotic behavior. We study the convergence of the explicit discrete scheme obtained by means of the generalized finite difference method and prove that the nonnegative numerical solutions in two-dimensional space preserve the asymptotic behavior of the continuous ones. Using different functions and long-time simulations, we illustrate the efficiency of the developed numerical algorithms in the sense of the convergence in space and in time

Tackling antibiotic resistance: the environmental framework

Antibiotic resistance is a threat to human and animal health worldwide, and key measures are required to reduce the risks posed by antibiotic resistance genes that occur in the environment. These measures include the identification of critical points of control, the development of reliable surveillance and risk assessment procedures, and the implementation of technological solutions that can prevent environmental contamination with antibiotic resistant bacteria and genes. In this Opinion article, we discuss the main knowledge gaps, the future research needs and the policy and management options that should be prioritized to tackle antibiotic resistance in the environment

Primary oesophageal motility disorders (excluding achalasia)

Les troubles moteurs primitifs de l'oesophage regroupent des troubles moteurs d'étiologie indéterminée affectant le corps de l'oesophage et/ou le sphincter inférieur de l'oesophage. Les symptômes habituels sont dominés par la dysphagie et les douleurs pseudo angineuses. Le diagnostic repose encore aujourd'hui sur les anomalies manométriques. Mais les signes manométriques sont souvent inconstants et les définitions manométriques non consensuelles. Grâce aux progrès sur la connaissance de la pathogénie, d'autres explorations peuvent aider au diagnostic telles que la manométrie holter ou l'écho endoscopie. La maladie des spasmes diffus, l'oesophage casse-noisettes (péristaltisme douloureux), l'hypertonie du sphincter inférieur de l'oesophage et la motricité inefficace oesophagienne sont présentés dans cette revue des troubles moteurs primitifs de l'oesophage. Un chapitre est particulièrement consacré à la pathogénie des douleurs oesophagiennes en abordant les avancées récentes dans la connaissance de la pathogénie, du diagnostic et des traitements. L'efficacité des traitements médicamenteux est souvent décevante avec des problèmes de tolérance. La prise en charge d'un reflux gastro-oesophagien ou des troubles psychiatriques associés peut améliorer les résultats, notamment en cas de troubles moteurs non spécifiques. Les résultats des traitements endoscopiques (bougienage, dilatation pneumatique, toxine botulique) sont présentés, ainsi que ceux de la myotomie chirurgicale qui doit être réservée aux troubles les plus sévères