Transient behavior of a chemotaxis system modelling certain types of tissue inflammation
type: Item
instance of: scholarly article
title: Transient behavior of a chemotaxis system modelling certain types of tissue inflammation
zbMATH Open document ID: 0609.92020
DOI: 10.1007/BF00275511
author: Wolfgang Alt
author: Douglas A. Lauffenburger
published in: Journal of Mathematical Biology
publication date: 1987-01-01T00:00:00Z
review text: A spatially-distributed mathematical model for the inflammatory response to bacterial invasion of tissue is proposed which includes leukocyte motility and chemotaxis behavior and chemical mediator properties explicitly. This system involves three coupled nonlinear partial differential equations and so is not amenable to analysis. Using scaling arguments and singular perturbation techniques, an approximating system of two coupled nonlinear ordinary differential equations is developed. This system is analyzed by phase plane methods. Using the approximating model, the dependence of the dynamic behaviour of the inflammatory response upon key process parameters, including leukocyte chemotaxis, is studied. Consistency of the model predictions with experimental observations are discussed.
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 3987098
zbMATH Keywords: steady state properties
zbMATH Keywords: spatially-distributed mathematical model
zbMATH Keywords: inflammatory response to bacterial invasion of tissue
zbMATH Keywords: leukocyte motility
zbMATH Keywords: chemotaxis
zbMATH Keywords: chemical mediator properties
zbMATH Keywords: scaling arguments
zbMATH Keywords: approximating system
zbMATH Keywords: phase plane methods
Wikidata QID: Q52612005
MaRDI profile type: Publication
cites work: Biased random walk models for chemotaxis and related diffusion approximations
cites work: Q4836474
cites work: Q5586677
cites work: Q5630031
cites work: Qualitative analyses of communicable disease models
cites work: Properties of solutions of ordinary differential equations with small parameters
cites work: Model for chemotaxis
cites work: Measurement of leukocyte motility and chemotaxis parameters using a quantitative analysis of the under-agarose migration assay
cites work: Analysis of a lumped model for tissue inflammation dynamics
cites work: Localized bacterial infection in a distributed model for tissue inflammation
full work available at URL: https://doi.org/10.1007/bf00275511
OpenAlex ID: W1982935914
description: scientific article; zbMATH DE number 3987098