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Adenis, L., Plaszczynski, S., Grammaticos, B., Pallud, J. and Badoual, M. (2021). The effect of radiotherapy on diffuse low-grade gliomas evolution: Confronting theory with clinical data, Journal of Personalized Medicine 11(8): 818.Search in Google Scholar

Belmonte-Beitia, J. (2016). Existence of travelling wave solutions for a Fisher–Kolmogorov system with biomedical applications, Communications in Nonlinear Science and Numerical Simulation 36: 14–20, DOI:10.1016/j.cnsns.2015.11.016.Search in Google Scholar

Bodnar, M., Bogdańska, M.U. and Piotrowska, M. (2019). Mathematical analysis of a generalised model of chemotherapy for low grade gliomas, Discrete and Continuous Dynamical Systems B 24(5): 2149–2167, DOI: 10.3934/dcdsb.2019088.Search in Google Scholar

Bodnar, M. and Vela Pérez, M. (2019). Mathematical and numerical analysis of low-grade gliomas model and the effects of chemotherapy, Communications in Nonlinear Science and Numerical Simulation 72: 552–564, DOI: D0I:10.1016/j.cnsns.2019.01.015.Search in Google Scholar

Bogdańska, M.U., Bodnar, M., Belmonte-Beitia, J., Murek, M., Schucht, P., Beck, J. and Pérez-García, V.M. (2017). A mathematical model of low grade gliomas treated with temozolomide and its therapeutical implications, Mathematical Biosciences 288: 1–13, DOI: 10.1016/j.mbs.2017.02.003.Search in Google Scholar

Bogdańska, M.U., Bodnar, M., Piotrowska, M.J., Murek, M., Schucht, P., Beck, J., Martínez-González, A. and Pérez-García, V.M. (2017). A mathematical model describes the malignant transformation of low grade gliomas: Prognostic implications, PLOS ONE 12(8): 1–24, DOI: 10.1371/journal.pone.0179999.Search in Google Scholar

Bressloff, P.C. (2013). Waves in Neural Media: From Single Neurons to Neural Fields, Springer, New York.Search in Google Scholar

Fenichel, N. (1979). Geometric singular perturbations theory for ordinary differential equations, Journal of Differential Equations 31: 53–98, DOI: 10.1016/0022-0396(79)90152-9.Search in Google Scholar

Fife, P.C. (1979). Mathematical Aspects of Reacting and Diffusing Systems, Springer, Berlin.Search in Google Scholar

Gourley, S.A. and Bartuccelli, M.V. (2000). Existence and construction of travelling wavefront solutions of Fisher equations with fourth-order perturbations, Dynamics and Stability of Systems 15(3): 253–262, DOI: 10.1080/026811100418710.Search in Google Scholar

Gugat, M. and Wintergerst, D. (2018). Transient flow in gas networks: Traveling waves, International Journal of Applied Mathematics and Computer Science 28(2): 341–348, DOI: 10.2478/amcs-2018-0025.Search in Google Scholar

Henry, D. (1981). Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag, Berlin/Heidelberg.Search in Google Scholar

Joiner, M.C. and van der Kogel, A. (2019). Basic Clinical Radiobiology, CRC Press, Boca Raton.Search in Google Scholar

Jones, C.K.R.T. (1995). Geometric singular perturbation theory, in R. Jonson (Ed), Dynamical Systems, Lecture Notes in Mathematics, Vol. 1609, Springer, Berlin/Heidelberg, pp. 44–118, DOI:10.1007/BFb0095239.Search in Google Scholar

Keles, G.E., Lamborn, K.R. and S.Berger, M. (2011). Low-grade hemispheric gliomas in adults: A critical review of extent of resection as a factor influencing outcome, Journal of Neurosurgery 95(5): 735–45, D0I:10.3171/jns.2001.95.5.0735.Search in Google Scholar

Kowal, M., Skobel, M., Gramacki, A. and Korbicz, J. (2021). Breast cancer nuclei segmentation and classification based on a deep learning approach, International Journal of Applied Mathematics and Computer Science 31(1): 85–106, D0I:10.34768/amcs-2021-0007.Search in Google Scholar

Murray, J.D. (1989). Mathematical Biology, Springer, Berlin.Search in Google Scholar

Pallud, J., Blonski, M., Mandonnet, E., Audureau, E., Fontaine, D., Sanai, N., Bauchet, L., Peruzzi, P., Frénay, M., Colin, P., Guillevin, R., Bernier, V., Baron, M.-H., Guyotat, J., Duffau, H., Taillandier, L. and Capelle, L. (2013). Velocity of tumor spontaneous expansion predicts long-term outcomes for diffuse low-grade gliomas, Neuro-Oncology 15(5): 595–606.Search in Google Scholar

Pallud, J., Capelle, L., Taillandier, L., Badoual, M., Duffau, H. and Mandonnet, E. (2013). The silent phase of diffuse low-grade gliomas. Is it when we missed the action?, Acta Neurochirurgica 155(12): 2237–2242.Search in Google Scholar

Pallud, J., Taillandier, L., Capelle, L., Fontaine, D., Peyre, M., Ducray, F., Duffau, H. and Mandonnet, E. (2012). Quantitative morphological magnetic resonance imaging follow-up of low-grade glioma, Neurosurgery 71(3): 729–740.Search in Google Scholar

Pouratian, N. and Schiff, D. (2010). Management of low-grade glioma, Current Neurology and Neuroscience Reports 10(3): 224–31.Search in Google Scholar

Pérez-García, V.M., Bogdanska, M., Martínez-González, A., Belmonte-Beitia, J., Schucht, P. and Pérez-Romasanta, L.A. (2014). Delay effects in the response of low-grade gliomas to radiotherapy: A mathematical model and its therapeutical implications, Mathematical Medicine and Biology: A Journal of the IMA 32(3): 307–329.Search in Google Scholar

Sakarunchai, I., Sangthong, R., Phuenpathom, N. and Phukaoloun, M. (2013). Free survival time of recurrence and malignant transformation and associated factors in patients with supratentorial low-grade gliomas, Journal of the Medical Association of Thailand 96(12): 1542–9.Search in Google Scholar

Swanson, K., Rostomily, R. and Alvord, E. (2008). A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: A proof of principle, British Journal of Cancer 98(1): 113–119, DOI: 10.1038/sj.bjc.6604125.Search in Google Scholar

Wang, C.H., Rockhill, J.K., Mrugala, M., Peacock, D.L., Lai, A., Jusenius, K., Wardlaw, J.M., Cloughesy, T., Spence, A.M., Rockne, R., Alvord Jr, E.C. and Swanson, K.R. (2009). Prognostic significance of growth kinetics in newly diagnosed glioblastomas revealed by combining serial imaging with a novel biomathematical model, Cancer Research 69(23): 9133–9140, DOI:10.1158/0008-5472.CAN-08-3863.Search in Google Scholar

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