Home
Deutsch
Advanced Search
Browse by ...
Publication overview
Contact persons
Help
 |
|
as soon as is submitted to ZB.
Analysis and simulation of a meso-scale model of diffusive restistance of bacterial biofilms to penetration of antibiotics.
Adv. Math. Sci. Appl. 18, 269-304 (2008)
Most bacteria live in biofilm communities, which offer protection against harmful external impacts. This makes treatment of biofilm borne bacterial infections with antibiotics difficult. We discuss a dynamic mathematical model that focuses on the diffusive resistance that a growing biofilm exerts against penetration of antibiotics. This allows bacteria in the protected inner layers to grow while those in the outer rim are inactivated. The model consists of four parabolic partial differential equations for the dependent variables antibiotic concentration, oxygen concentration, active biomass fraction and inert biomass fraction. The equations for the last two variables show power law degeneracy (like the porous medium equation) as the dependent variable vanishes, and a power law singularity (like the fast diffusion equation) as the dependent variable approaches ist a priori known maximum value, and thus are highly non-linear. We show the existence of solutions to this model. This proof uses a positivity criterion, which is formulated and proved as a Lemma for more general nonlinear parabolic systems. Furthermore, a number of computer simulations are carried out to illustrate the behavior of the antibiotic isinfection model in dependence of the antibiotics added to the system.
Additional Metrics?
Edit extra informations
Login
Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Reaction-diffusion equations; Dynamical systems in biology; Biofilm Modelling
ISSN (print) / ISBN
1343-4373
Quellenangaben
Volume: 18,
Issue: 1,
Pages: 269-304
Publisher
Gakkōtosho
Publishing Place
Tokyo
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)