T. Alarcon, H. M. Byrne, and P. K. Maini, A cellular automaton model for tumour growth in inhomogeneous environment, Journal of Theoretical Biology, vol.225, issue.2, pp.257-274, 2003.
DOI : 10.1016/S0022-5193(03)00244-3

P. M. Altrock, L. L. Liu, and F. Michor, The mathematics of cancer: integrating quantitative models, Nature Reviews Cancer, vol.28, issue.12, pp.730-745, 2015.
DOI : 10.1126/scitranslmed.3002356

A. R. Anderson, A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion, Mathematical Medicine and Biology: A Journal of the IMA, vol.22, issue.2, pp.163-186, 2005.
DOI : 10.1093/imammb/dqi005

M. J. Bissel and W. C. Hines, Why don't we get more cancer? A proposed role of the microenvironment in restraining cancer progression, Nature Medicine, vol.23, issue.3, pp.320-329, 2011.
DOI : 10.1200/JCO.2005.11.030

J. R. Brahmer, Safety and activity of anti-PD-1-L1 antibody in patients with advanced cancer. New Engl, J. Med, vol.366, issue.26, pp.2455-2465, 2012.

S. Bunimovich-mendrazitsky, J. Gluckman, and J. Chaskalovic, A mathematical model of combined bacillus Calmette-Guerin (BCG) and interleukin (IL)-2 immunotherapy of superficial bladder cancer, Journal of Theoretical Biology, vol.277, issue.1, pp.27-40, 2011.
DOI : 10.1016/j.jtbi.2011.02.008

F. Castiglione and B. Piccoli, Optimal Control in a Model of Dendritic Cell Transfection Cancer Immunotherapy, Bulletin of Mathematical Biology, vol.39, issue.4, pp.255-274, 2006.
DOI : 10.1007/s11538-005-9014-3

F. Castiglione and B. Piccoli, Cancer immunotherapy, mathematical modeling and optimal control, Journal of Theoretical Biology, vol.247, issue.4, pp.723-732, 2007.
DOI : 10.1016/j.jtbi.2007.04.003

M. A. Chaplain, S. R. Mcdougall, and A. R. Anderson, MATHEMATICAL MODELING OF TUMOR-INDUCED ANGIOGENESIS, Annual Review of Biomedical Engineering, vol.8, issue.1, pp.233-257, 2006.
DOI : 10.1146/annurev.bioeng.8.061505.095807

D. Angelis, E. Preziosi, and L. , AND RELATED FREE BOUNDARY PROBLEM, Mathematical Models and Methods in Applied Sciences, vol.16, issue.03, pp.379-407, 2000.
DOI : 10.1093/imammb/15.1.1

D. Pillis, L. G. Radunskaya, and A. , A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach, Journal of Theoretical Medicine, vol.3, issue.2, pp.79-100, 2001.
DOI : 10.1080/10273660108833067

D. Pillis, L. G. Radunskaya, and A. , The dynamics of an optimally controlled tumor model: A case study, Mathematical and Computer Modelling, vol.37, issue.11, pp.1221-1244, 2003.
DOI : 10.1016/S0895-7177(03)00133-X

D. Pillis, L. G. Gu, W. Radunskaya, and A. , Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations, Journal of Theoretical Biology, vol.238, issue.4, pp.841-862, 2006.
DOI : 10.1016/j.jtbi.2005.06.037

B. F. Dibrov, A. M. Zhabotinsky, Y. A. Nayfaleh, M. P. Orlova, and L. I. Churikova, Mathematical model of cancer chemotherapy. periodic schedules of phase-specific cytotoxic-agent administration increasing the selectivity of therapy, Math. Bioscences, vol.73, issue.1, pp.1-31, 1985.

R. Eftimie and J. L. Bramson, Interactions Between the Immune System and Cancer: A??Brief Review of??Non-spatial Mathematical Models, Bulletin of Mathematical Biology, vol.39, issue.5, pp.2-32, 2011.
DOI : 10.1002/eji.200839152

R. Eftimie, J. L. Bramson, and D. J. Earn, Modeling anti-tumor Th1 and Th2 immunity in the rejection of melanoma, Journal of Theoretical Biology, vol.265, issue.3, pp.467-480, 2010.
DOI : 10.1016/j.jtbi.2010.04.030

S. Eikenberry, C. Thalhauser, and Y. Kuang, Tumor-Immune Interaction, Surgical Treatment, and Cancer Recurrence in a Mathematical Model of Melanoma, PLoS Computational Biology, vol.52, issue.4, p.1000362, 2009.
DOI : 10.1371/journal.pcbi.1000362.t002

M. Eisen, Mathematical Models in Cell Biology and Cancer Chemotherapy, 1979.
DOI : 10.1007/978-3-642-93126-0

O. J. Finn, Immuno-oncology: understanding the function and dysfunction of the immune system in cancer, Annals of Oncology, vol.6, issue.3, pp.5-9, 2012.
DOI : 10.1038/nrc1815

K. Groebe and W. Mueller-klieser, On the relation between size of necrosis and L. Viger et al, Journal of Theoretical Biology, vol.416, pp.99-112, 1996.

J. B. Haanen, Immunotherapy of melanoma, European Journal of Cancer Supplements, vol.11, issue.2, pp.97-105, 2013.
DOI : 10.1016/j.ejcsup.2013.07.013

M. Itik and S. P. Banks, CHAOS IN A THREE-DIMENSIONAL CANCER MODEL, International Journal of Bifurcation and Chaos, vol.20, issue.01, pp.71-79, 2010.
DOI : 10.1088/0951-7715/19/10/006

R. P. Jiménez and E. O. Hernandez, Tumour???host dynamics under radiotherapy, Chaos, Solitons & Fractals, vol.44, issue.9, pp.685-692, 2011.
DOI : 10.1016/j.chaos.2011.06.001

A. R. Kansal, S. Torquato, G. R. Harsh-iva, E. A. Chiocca, and T. S. Deisboeck, Simulated Brain Tumor Growth Dynamics Using a Three-Dimensional Cellular Automaton, Journal of Theoretical Biology, vol.203, issue.4, pp.367-382, 2000.
DOI : 10.1006/jtbi.2000.2000

H. Knolle, Cell Kinetic Modelling and the Chemotherapy of Cancer, 1988.
DOI : 10.1007/978-3-642-45651-0

C. Letellier, F. Denis, and L. Aguirre, What can be learned from a chaotic cancer model?, Journal of Theoretical Biology, vol.322, pp.7-16, 2013.
DOI : 10.1016/j.jtbi.2013.01.003

J. D. Naguy and D. Armbruster, Evolution of uncontrolled proliferation and the angiogenic switch in cancer, Mathematical Biosciences and Engineering, vol.9, issue.4, pp.843-876, 2012.
DOI : 10.3934/mbe.2012.9.843

M. R. Owen and J. A. Sherrat, Modelling the macrophage invasion of tumours: Effects on growth and composition, Mathematical Medicine and Biology, vol.15, issue.2, pp.165-185, 1998.
DOI : 10.1093/imammb/15.2.165

A. H. Panaretos, J. T. Aberle, and R. E. Diaz, The effect of the 2-D Laplacian operator approximation on the performance of finite-difference time-domain schemes for Maxwell???s equations, Journal of Computational Physics, vol.227, issue.1, pp.513-536, 2007.
DOI : 10.1016/j.jcp.2007.08.019

M. Patra and M. Karttunen, Stencils with isotropic discretization error for differential operators, Numerical Methods for Partial Differential Equations, vol.29, issue.4, pp.936-953, 2006.
DOI : 10.1145/321033.321040

G. K. Philips and M. Atkins, Therapeutic uses of anti-PD-1 and anti-PD-L1 antibodies, International Immunology, vol.32, issue.4, pp.39-46, 2015.
DOI : 10.1200/JCO.2013.49.4757

K. A. Rejniak and A. R. Anderson, Hybrid models of tumor growth, Wiley Interdisciplinary Reviews: Systems Biology and Medicine, vol.5, issue.1, pp.115-125, 2011.
DOI : 10.1098/rsif.2007.1054

A. Ribas, Tumor immunotherapy directed at PD-1. New Engl, J. Med, vol.366, issue.26, pp.2517-2519, 2012.
DOI : 10.1056/nejme1205943

R. R. Sarkar and S. Banerjee, Cancer self remission and tumor stability ??? a stochastic approach, Mathematical Biosciences, vol.196, issue.1, pp.65-81, 2005.
DOI : 10.1016/j.mbs.2005.04.001

R. D. Schreiber, L. J. Old, and M. J. Smyth, Cancer Immunoediting: Integrating Immunity's Roles in Cancer Suppression and Promotion, Science, vol.144, issue.5, pp.1565-1570, 2011.
DOI : 10.1016/j.cell.2011.02.013

R. M. Sutherland, B. Sordat, J. Bamat, H. Gabbert, B. Bourrat et al., Oxygenation and differentiation in multicellular spheroids of human, Cancer Res, vol.46, pp.5320-5329, 1986.

R. H. Thomlinson and L. H. Gray, The Histological Structure of Some Human Lung Cancers and the Possible Implications for Radiotherapy, British Journal of Cancer, vol.9, issue.4, pp.539-549, 1955.
DOI : 10.1038/bjc.1955.55

L. Viger, F. Denis, M. Rosalie, and C. Letellier, A cancer model for the angiogenic switch, Journal of Theoretical Biology, vol.360, pp.21-33, 2014.
DOI : 10.1016/j.jtbi.2014.06.020

URL : https://hal.archives-ouvertes.fr/hal-01544737

M. Welter, K. Bartha, and H. Rieger, Emergent vascular network inhomogeneities and resulting blood flow patterns in a growing tumor, Journal of Theoretical Biology, vol.250, issue.2, pp.257-280, 2008.
DOI : 10.1016/j.jtbi.2007.09.031

M. Welter, K. Bartha, and H. Rieger, Vascular remodelling of an arterio-venous blood vessel network during solid tumour growth, Journal of Theoretical Biology, vol.259, issue.3, pp.405-422, 2009.
DOI : 10.1016/j.jtbi.2009.04.005

URL : https://hal.archives-ouvertes.fr/hal-00554603

L. Viger, Spatial avascular growth of tumor in a homogeneous environment, Journal of Theoretical Biology, vol.416, pp.99-112, 2017.
DOI : 10.1016/j.jtbi.2016.12.011

URL : https://hal.archives-ouvertes.fr/hal-01611148