Influence of diffusion on interactions between malignant gliomas and immune system

Tom 37 / 2010

Urszula Foryś Applicationes Mathematicae 37 (2010), 53-67 MSC: 35K57, 35B09, 35B30, 35B35, 92D25. DOI: 10.4064/am37-1-4


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.


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

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