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

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  • Haralampos Hatzikirou

    (Mathematics Department, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates
    Centre for Information Services and High Performance Computing, Technische Universität Dresden, Nöthnitzer Straße 46, 01062 Dresden, Germany
    These authors contributed equally to this work.)

  • Nikos I. Kavallaris

    (Department of Mathematical and Physical Sciences, University of Chester, Thornton Science Park Pool Lane, Ince, Chester CH2 4NU, UK
    Department of Mathematics and Computer Science, Faculty of Health, Science and Technology, Karlstad University, SE-651 88 Karlstad, Sweden
    These authors contributed equally to this work.)

  • Marta Leocata

    (Department of Economics and Finance, Luiss University, Viale Romania, 32, 00197 Roma, Italy
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Haralampos Hatzikirou & Nikos I. Kavallaris & Marta Leocata, 2021. "A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression," Mathematics, MDPI, vol. 9(20), pages 1-27, October.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2530-:d:652123
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    References listed on IDEAS

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    1. Corbin E. Meacham & Sean J. Morrison, 2013. "Tumour heterogeneity and cancer cell plasticity," Nature, Nature, vol. 501(7467), pages 328-337, September.
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