A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression

Haralampos Hatzikirou, Nikos I. Kavallaris and Marta Leocata
Additional contact information
Haralampos Hatzikirou: Mathematics Department, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates
Nikos I. Kavallaris: Department of Mathematical and Physical Sciences, University of Chester, Thornton Science Park Pool Lane, Ince, Chester CH2 4NU, UK
Marta Leocata: Department of Economics and Finance, Luiss University, Viale Romania, 32, 00197 Roma, Italy

Mathematics, 2021, vol. 9, issue 20, 1-27

Abstract: 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.

Keywords: averaging; white noise; intrinsic heterogeneity; phenotypic switching; tumor growth (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/20/2530/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/20/2530/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:20:p:2530-:d:652123

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().