Influence of diffusion on interactions between malignant gliomas and immune system

• Autorzy: Urszula Foryś
• Języki publikacji: EN

Abstrakty

EN

We analyse the influence of diffusion and space distribution of cells in a simple model of interactions between an activated immune system and malignant gliomas, among which the most aggressive one is GBM Glioblastoma Multiforme. It turns out that diffusion cannot affect stability of spatially homogeneous steady states. This suggests that there are two possible outcomes-the solution is either attracted by the positive steady state or by the semitrivial one. The semitrivial steady state describes the healthy state, while the positive one reflects the chronic disease and typically the level of tumour cells in this state is very high, exceeding the threshold of lethal outcome. Results of numerical simulation show that the initial tumour cells distribution has an essential impact on the dynamics of the system. If the positive steady state exists, then we observe bistability and the initial distribution decides to which steady state the solution tends.

Kategorie tematyczne

• 35K57: Reaction-diffusion equations
• 35B35: Stability
• 35B30: Dependence of solutions on initial and boundary data, parameters
• 35B09: Positive solutions
• 92D25: Population dynamics (general)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2010
• Tom: 37
• Numer: 1
• Strony: 53-67

Daty

wydano

2010

Twórcy

autor

Urszula Foryś

• Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/am37-1-4