Abstract
In this paper, we suggest a discrete variant space model of cancer evolution. The model is reasonably simple, deterministic, and is formulated as a system of ordinary differential equations. The model is based on the concept of “multi-strain modeling” (or quasi-species), which is successfully applied in modeling of the infectious disease dynamics and viral dynamics. The model constructed in this paper is mechanistic; that is, it is based upon a set of explicitly stated assumptions and hypothesis (“the first principles”). This implies that model’s parameters, as well as results obtained, can be immediately interpreted, and that a further model development, e.g., incorporation into the model factors such as anticancer therapies, immune response, etc., is a reasonably straightforward procedure. To illustrate this model applicability, results of numerical simulations, as well as their biological interpretations, are provided.
A. Korobeinikov is supported by Ministerio de Economía y Competitividad of Spain via grant MTM2015-71509-C2-1-R.
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References
A.A. Archibasov, A. Korobeinikov, V.A. Sobolev, Asymptotic expansions of solutions for a singularly perturbed model of viral evolution. Comput. Math. Math. Phys. 55(2), 240–250 (2015)
A.A. Archibasov, A. Korobeinikov, V.A. Sobolev, Passage to the limits in a singularly perturbed partial integro-differential system. Differ. Equ. 52(9), 1115–1122 (2016)
Y.A. Fouad, C. Aanei, Revisiting the hallmarks of cancer. Am. J. Cancer Res. 7(5), 1016–1036 (2017)
D. Hanahan, R.A. Weinberg, The hallmarks of cancer. Cell 100(1), 57–70 (2000)
D. Hanahan, R.A. Weinberg, Hallmarks of cancer: the next generation. Cell 144(5), 646–674 (2011)
A. Korobeinikov, Immune response and within-host viral evolution: immune response can accelerate evolution. J. Theor. Biol. 456, 74–83 (2018)
A. Korobeinikov, A. Archibasov, V. Sobolev, Order reduction for an RNA virus evolution model. Math. Biosci. Eng. 12(5), 1007–1016 (2015)
A. Korobeinikov, A. Archibasov, V. Sobolev, Multi-scale problem in the model of RNA virus evolution. J. Phys. Conf. Ser. 727, 012007 (2016)
A. Korobeinikov, K.E. Starkov, P.A. Valle, Modeling cancer evolution. J. Phys. Conf. Ser. 811, 012004 (2017)
D. Masip, A. Korobeinikov, A continuous phenotype space model of cancer evolution. J. Phys. Conf. Ser. 811, 012005 (2017)
D. Moreno-Martos, A. Korobeinikov, A mathematical model of cancer evolution. Trends Math. Res. Perspect. CRM Barcelona 11, Summer 2018, Birkhäuser, Basel (2018)
J.D. Murray, Mathematical Biology I, An Introduction, 3rd edn. (Springer, New York, 2002)
S. Pagliarini, A. Korobeinikov, A mathematical model of marine bacteriophage evolution. R. Soc. Open Sci. 5, 171661 (2018)
J. Sardanyés, R. Martínez, C. Simó, R.V. Solé, Abrupt transitions to tumor extinction: a phenotypic quasispecies model. J. Math. Biol. 74, 1589–1609 (2017)
R.V. Solé, S. Valverde, C. Rodríguez-Caso, J. Sardanyés, Can a minimal replicating construct be identified as the embodiment of cancer? Bioessays 36, 503–512 (2014)
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Korobeinikov, A., Pedarra, S. (2019). A Discrete Variant Space Model of Cancer Evolution. In: Korobeinikov, A., Caubergh, M., Lázaro, T., Sardanyés, J. (eds) Extended Abstracts Spring 2018. Trends in Mathematics(), vol 11. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-25261-8_4
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DOI: https://doi.org/10.1007/978-3-030-25261-8_4
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