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
[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. |