Research article Special Issues

Is the Allee effect relevant in cancer evolution and therapy?

  • Received: 31 August 2020 Accepted: 08 September 2020 Published: 25 September 2020
  • MSC : 92B05, 92D25

  • Most models of cancer assume that tumor cells populations, at low densities, grow exponentially to be eventually limited by the available amount of resources such as space and nutrients. However, recent pre-clinical and clinical data of cancer onset or recurrence indicate the presence of a population dynamics in which growth rates increase with cell numbers. Such effect is analogous to the cooperative behavior in an ecosystem described by the so called Allee effect. In this work, we study the consequences of the Allee effect on cancer growth via the properties of dynamical models incorporating the Allee effect, and the implications that the occurrence of such effect has for the choice of the more appropriate therapy. Some simulations will be presented in which the model is used to fit data from in vitro experiments and clinical trials.

    Citation: Marcello Delitala, Mario Ferraro. Is the Allee effect relevant in cancer evolution and therapy?[J]. AIMS Mathematics, 2020, 5(6): 7649-7660. doi: 10.3934/math.2020489

    Related Papers:

  • Most models of cancer assume that tumor cells populations, at low densities, grow exponentially to be eventually limited by the available amount of resources such as space and nutrients. However, recent pre-clinical and clinical data of cancer onset or recurrence indicate the presence of a population dynamics in which growth rates increase with cell numbers. Such effect is analogous to the cooperative behavior in an ecosystem described by the so called Allee effect. In this work, we study the consequences of the Allee effect on cancer growth via the properties of dynamical models incorporating the Allee effect, and the implications that the occurrence of such effect has for the choice of the more appropriate therapy. Some simulations will be presented in which the model is used to fit data from in vitro experiments and clinical trials.


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    [1] M. Al-Tameemi, M. Chaplain, A. d'Onofrio, Evasion of tumours from the control of the immune system: consequences of brief encounters, Biol. direct, 7 (2012), 31.
    [2] N. Bellomo, N. K. Li, Ph K. Maini, On the foundations of cancer modelling: selected topics, speculations, and perspectives, Math. Mod. Meth. Appl. Sci., 18 (2008), 593-646.
    [3] S. Benzekry, C. Lamont, A. Beheshti, et al., Classical mathematical models for description and prediction of experimental tumor growth, PLoS Comput. Biol., 10 (2014), e1003800.
    [4] K. Böttger, H. Hatzikirou, A. Voss-Böhme, et al., An emerging allee effect is critical for tumor initiation and persistence, PLoS Comput. Biol., 11 (2015), e1004366.
    [5] D. S. Boukal, M. W. Sabelis, L. Berec, How predator functional responses and allee effects in prey affect the paradox of enrichment and population collapses, Theor. Popul. Biol., 72 (2007), 136-147.
    [6] R. Brady and H. Enderling, Mathematical models of cancer: when to predict novel therapies, and when not to, B. Math. Biol., 81 (2019), 3722-3731.
    [7] F. Courchamp, L. Berec, J. Gascoigne, Allee effects in ecology and conservation, Oxford University Press, 2008.
    [8] L. G. De Pillis, A. Eladdadi, A. E. Radunskaya, Modeling cancer-immune responses to therapy, J. Pharmacokinet. Phar., 41 (2014), 461-478.
    [9] L. G. De Pillis, W. Gu, A. E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations, J. Theor. Biol., 238 (2006), 841-862.
    [10] V. DeVita and P. S. Schein, The use of drugs in combination for the treatment of cancer: rationale and results, New Engl. J. Med., 288 (1973), 998-1006.
    [11] R. Eftimie, J. L. Bramson, D. J. D. Earn, Interactions between the immune system and cancer: a brief review of non-spatial mathematical models, B. Math. Biol., 73 (2011), 2-32.
    [12] P. Feng, Z. Dai, D. Wallace, On a 2d model of avascular tumor with weak allee effect, J. Appl. Math., 2019 (2019).
    [13] F. Frascoli, P. S. Kim, B. D. Hughes, et al., A dynamical model of tumour immunotherapy, Math. Biosci., 253 (2014), 50-62.
    [14] R. A. Gatenby, J. Brown, T. Vincent, Lessons from applied ecology: cancer control using an evolutionary double bind, Cancer Res., 69 (2009), 7499-7502.
    [15] R. A. Gatenby, A. S. Silva, R. J. Gillies, et al., Adaptive therapy, Cancer Res., 69 (2009), 4894-4903.
    [16] M. Gerlinger and C. Swanton, How darwinian models inform therapeutic failure initiated by clonal heterogeneity in cancer medicine, Brit. J. Cancer, 103 (2010), 1139-1143.
    [17] D. Hanahan and R. A. Weinberg, Hallmarks of cancer: the next generation, cell, 144 (2011), 646-674.
    [18] L. G. De Pillis and A. Radunskaya, A mathematical tumor model with immune resistance and drug therapy: an optimal control approach, Comput. Math. Method. M., 3 (2001), 79-100.
    [19] T. Hillen and M. A. Lewis, Mathematical ecology of cancer, Managing Complexity, Reducing Perplexity, (2014), 1-13. Springer.
    [20] K. E. Johnson, G. Howard, W. Mo, et al., Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an allee effect, PLoS biology, 17 (2019), e3000399.
    [21] A. Konstorum, T. Hillen, J. Lowengrub, Feedback regulation in a cancer stem cell model can cause an allee effect, B. Math. Biol., 78 (2016), 754-785.
    [22] K. S. Korolev, J. B. Xavier, J. Gore, Turning ecology and evolution against cancer, Nat. Rev. Cancer, 14 (2014), 371-380.
    [23] A. Marusyk, V. Almendro, K. Polyak, Intra-tumour heterogeneity: a looking glass for cancer? Nat. Rev. Cancer, 12 (2012), 323-334.
    [24] S. Misale, I. Bozic, J. Tong, et al., Vertical suppression of the egfr pathway prevents onset of resistance in colorectal cancers, Nat. Commun., 6 (2015), 1-9.
    [25] J. D. Murray, Mathematical Biology, Springer-Verlag, 2002.
    [26] Z. Neufeld, W. von Witt, D. Lakatos, et al., The role of allee effect in modelling post resection recurrence of glioblastoma, PLoS Comput. Biol., 13 (2017), e1005818.
    [27] J. M. Pacheco, F. C. Santos, D. Dingli, The ecology of cancer from an evolutionary game theory perspective, Interface focus, 4 (2014), 20140019.
    [28] E. Piretto, M. Delitala, M. Ferraro, Combination therapies and intra-tumoral competition: insights from mathematical modelling J. Theor. Biol., 446 (2018), 149-159.
    [29] N. Saunders, F. Simpson, E. Thompson, et al., Role of intratumoural heterogeneity in cancer drug resistance: molecular and clinical perspectives, EMBO Mol. Med., 4 (2012), 675-684.
    [30] L. Sewalt, K. Harley, P. van Heijster, et al., Influences of allee effects in the spreading of malignant tumours, J. Theor. Biol., 394 (2016), 77-92.
    [31] G. Wang, X.-G. Liang, F.-Z. Wang, The competitive dynamics of populations subject to an allee effect, Ecol. Model., 124 (1999), 183-192.
    [32] K. P. Wilkie, A review of mathematical models of cancer-immune interactions in the context of tumor dormancy, Systems Biology of Tumor Dormancy, (2013), 201-234. Springer.
    [33] S. Wilson and D. Levy, A mathematical model of the enhancement of tumor vaccine efficacy by immunotherapy, B. Math. Biol., 74 (2012), 1485-1500.
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