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A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression
Khalifa University, ARE; Technische Universität Dresden, DEU.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Univ Chester, GBR.ORCID iD: 0000-0002-9743-8636
Luiss University, ITA.
2021 (English)In: Mathematics, E-ISSN 2227-7390, Vol. 9, no 20, article id 2530Article in journal (Refereed) Published
Abstract [en]

Typically stochastic differential equations (SDEs) involve an additive or multiplicative noise term. Here, we are interested in stochastic differential equations for which the white noise is nonlinearly integrated into the corresponding evolution term, typically termed as random ordinary differential equations (RODEs). The classical averaging methods fail to treat such RODEs. Therefore, we introduce a novel averaging method appropriate to be applied to a specific class of RODEs. To exemplify the importance of our method, we apply it to an important biomedical problem, in particular, we implement the method to the assessment of intratumoral heterogeneity impact on tumor dynamics. Precisely, we model gliomas according to a well-known Go or Grow (GoG) model, and tumor heterogeneity is modeled as a stochastic process. It has been shown that the corresponding deterministic GoG model exhibits an emerging Allee effect (bistability). In contrast, we analytically and computationally show that the introduction of white noise, as a model of intratumoral heterogeneity, leads to monostable tumor growth. This monostability behavior is also derived even when spatial cell diffusion is taken into account.

Place, publisher, year, edition, pages
MDPI, 2021. Vol. 9, no 20, article id 2530
Keywords [en]
averaging, white noise, intrinsic heterogeneity, phenotypic switching, tumor growth
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-87316DOI: 10.3390/math9202530ISI: 000711662500001Scopus ID: 2-s2.0-85117285281OAI: oai:DiVA.org:kau-87316DiVA, id: diva2:1613369
Available from: 2021-11-22 Created: 2021-11-22 Last updated: 2022-11-21Bibliographically approved

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Kavallaris, Nikos I.

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