D. , A. E. Dupont-rouzeyrol, M. Magal, P. Olivier, D. Ruan et al., The impact of different antibiotic regimens on the emergence of antimicrobial-resistant bacteria, PLoS One, vol.3, issue.12, p.4036, 2008.

N. Bacaër and C. Sokhna, A reaction-diffusion system modeling the spread of resistance to an antimalarial drug, Math. Biosc. Eng, vol.2, issue.2, pp.227-238, 2005.

G. Barles, Solutions de viscosité etéquationsetéquations de Hamilton-Jacobi, Collec. SMAI, 2002.

G. Barles, S. Mirrahimi, and B. Perthame, Concentration in Lotka-Volterra Parabolic or Integral Equations: A General Convergence Result, Methods and Applications of Analysis, vol.16, issue.3, pp.321-340, 2009.
DOI : 10.4310/MAA.2009.v16.n3.a4
URL : https://hal.archives-ouvertes.fr/hal-00391982

G. Barles and B. Perthame, Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics, Recent Developments in Nonlinear Partial Differential Equations, pp.57-68, 2007.
DOI : 10.1090/conm/439/08463

I. Bozic, T. Antal, H. Ohtsuki, H. Carter, D. Kim et al., Accumulation of driver and passenger mutations during tumor progression, Proc. Natl. Acad. Sci. USA, pp.107-1854518550, 2010.
DOI : 10.1073/pnas.1010978107

A. Calsinà and S. Cuadrado, A model for the adaptive dynamics of the maturation age, Ecological Modelling, vol.133, issue.1-2, pp.33-43, 2000.
DOI : 10.1016/S0304-3800(00)00278-7

N. Champagnat, R. Ferrì-ere, and S. Méléard, Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models, Theoretical Population Biology, vol.69, issue.3, pp.297-321, 2006.
DOI : 10.1016/j.tpb.2005.10.004
URL : https://hal.archives-ouvertes.fr/inria-00164784

J. Clairambault, Modelling Physiological and Pharmacological Control on Cell Proliferation to Optimise Cancer Treatments, Mathematical Modelling of Natural Phenomena, vol.4, issue.3, pp.12-67, 2009.
DOI : 10.1051/mmnp/20094302

M. G. Crandall, H. Ishii, and P. Lions, user's guide to viscosity solutions\\ of second order\\ partial differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992.
DOI : 10.1090/S0273-0979-1992-00266-5

T. Day and R. Bonduriansky, A Unified Approach to the Evolutionary Consequences of Genetic and Nongenetic Inheritance, The American Naturalist, vol.178, issue.2, pp.18-36, 2011.
DOI : 10.1086/660911

O. Diekmann, A beginner's guide to adaptive dynamics, Mathematical Modelling of Population Dynamics, pp.47-86, 2004.
DOI : 10.4064/bc63-0-2

O. Diekmann, P. Jabin, S. Mischler, and B. Perthame, The dynamics of adaptation: An illuminating example and a Hamilton???Jacobi approach, Theoretical Population Biology, vol.67, issue.4, pp.257-271, 2005.
DOI : 10.1016/j.tpb.2004.12.003

E. R. Fearon and B. Vogelstein, A genetic model for colorectal tumorigenesis, Cell, vol.61, issue.5, pp.759-767, 1990.
DOI : 10.1016/0092-8674(90)90186-I

W. H. Fleming and H. M. Soner, Controlled markov processes and vicosity solutions, Applications of Mathematics, vol.25, 1993.

J. Foo and F. Michor, Evolution of Resistance to Targeted Anti-Cancer Therapies during Continuous and Pulsed Administration Strategies, PLoS Computational Biology, vol.107, issue.11, p.1000557, 2009.
DOI : 10.1371/journal.pcbi.1000557.t001

J. Foo and F. Michor, Evolution of resistance to anti-cancer therapy during general dosing schedules, Journal of Theoretical Biology, vol.263, issue.2, pp.179-188, 2010.
DOI : 10.1016/j.jtbi.2009.11.022

E. C. Friedberg, G. C. Walker, W. Siede, R. D. Wood, R. A. Schultz et al., DNA repair and mutagenesis, 2005.

R. A. Gatenby, A change of strategy in the war on cancer, Nature, vol.5, issue.7246, pp.508-509, 2009.
DOI : 10.1038/459508a

R. A. Gatenby, A. S. Silva, R. J. Gillies, and B. R. Frieden, Adaptive Therapy, Cancer Research, vol.69, issue.11, pp.4894-4903, 2009.
DOI : 10.1158/0008-5472.CAN-08-3658

J. Goldie and A. Coldman, Drug resistance in cancer: mechanisms and models, 1998.
DOI : 10.1017/CBO9780511666544

R. Gomulkiewicz and R. D. Holt, When does Evolution by Natural Selection Prevent Extinction?, Evolution, vol.49, issue.1, pp.201-207, 1995.
DOI : 10.2307/2410305

M. M. Gottesman, T. Fojo, and S. E. Bates, MULTIDRUG RESISTANCE IN CANCER: ROLE OF ATP-DEPENDENT TRANSPORTERS, Nature Reviews Cancer, vol.2, issue.1, pp.48-58, 2002.
DOI : 10.1038/nrc706

M. Greaves and C. C. Maley, Clonal evolution in cancer, Nature, vol.69, issue.7381, pp.481-306, 2012.
DOI : 10.1038/nature10762

P. Jabin, On selection dynamics for competitive interactions, Journal of Mathematical Biology, vol.49, issue.4, pp.493-517, 2011.
DOI : 10.1007/s00285-010-0370-8
URL : https://hal.archives-ouvertes.fr/hal-00602077

C. A. Jerez, Metal Extraction and Biomining. The Desk Encyclopedia of Microbiology, pp.762-775

M. Kimmel, Control Theory Approach to Cancer Chemotherapy: Benefiting from Phase Dependence and Overcoming Drug Resistance, Tutorials in Mathematical Biosciences III, Lect. Notes Math. 1872, pp.185-221, 2006.
DOI : 10.1007/11561606_5

N. L. Komarova and D. Wodarz, Drug resistance in cancer: Principles of emergence and prevention, Proceedings of the National Academy of Sciences, vol.102, issue.27, pp.9714-9719, 2005.
DOI : 10.1073/pnas.0501870102

M. Kivisaar, Stationary phase mutagenesis: mechanisms that accelerate adaptation of microbial populations under environmental stress, Environmental Microbiology, vol.259, issue.10, pp.814-827, 2003.
DOI : 10.1038/88740

V. Lemesle, L. Mailleret, and M. Vaissayre, Role of Spatial and Temporal Refuges in the Evolution of Pest Resistance to Toxic Crops, Acta Biotheoretica, vol.24, issue.2-3, pp.89-102, 2010.
DOI : 10.1007/s10441-010-9102-0

A. Lorz, S. Mirrahimi, and B. Perthame, Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations, Communications in Partial Differential Equations, vol.69, issue.6, pp.1071-1098, 2011.
DOI : 10.1051/mmnp:2008029

F. Mccormick, Cancer therapy based on oncogene addiction, Journal of Surgical Oncology, vol.23, issue.6, pp.464-467, 2011.
DOI : 10.1002/jso.21749

P. Magal and G. F. Webb, Mutation, selection and recombination in a model of phenotype evolution, Discrete Contin. Dynam. Systems, vol.6, issue.1, pp.221-236, 2000.

C. Marzac, ATP Binding Cassette transporters associated with chemoresistance: transcriptional profiling in extreme cohorts and their prognostic impact in a cohort of 281 acute myeloid leukemia patients, Haematologica, vol.96, issue.9, pp.1293-1301, 2011.
DOI : 10.3324/haematol.2010.031823
URL : https://hal.archives-ouvertes.fr/hal-00647621

J. Pasquier, P. Magal, C. Boulangé-lecomte, G. F. Webb, L. Foll et al., Consequences of cell-to-cell P-glycoprotein transfer on acquired multidrug resistance in breast cancer: a cell population dynamics model, Biology Direct, vol.6, issue.1, p.5, 2011.
DOI : 10.1186/1745-6150-6-5

B. Perthame, Transport equations in biology. Series 'Frontiers in Mathematics, 2007.

B. Perthame and G. Barles, Dirac concentrations in Lotka-Volterra parabolic PDEs, Indiana University Mathematics Journal, vol.57, issue.7, pp.3275-3301, 2008.
DOI : 10.1512/iumj.2008.57.3398
URL : https://hal.archives-ouvertes.fr/hal-00168404

K. J. Pienta, N. Mcgregor, R. Axelrod, and D. E. Axelrod, Ecological Therapy for Cancer: Defining Tumors Using an Ecosystem Paradigm Suggests New Opportunities for Novel Cancer Treatments, Translational Oncology, vol.1, issue.4, pp.158-164, 2008.
DOI : 10.1593/tlo.08178

A. Rafii, P. Mirshahi, M. Poupot, A. Faussat, A. Simon et al., Oncologic Trogocytosis of an Original Stromal Cells Induces Chemoresistance of Ovarian Tumours, PLoS ONE, vol.171, issue.2, p.3894, 2008.
DOI : 10.1371/journal.pone.0003894.s002

K. W. Scotto, Transcriptional regulation of ABC drug transporters, Oncogene, vol.22, issue.47, pp.7496-7511, 2003.
DOI : 10.1038/sj.onc.1206950

N. P. Shah, C. T. Tran, F. Y. Lee, P. Chan, D. Norris et al., Overriding Imatinib Resistance with a Novel ABL Kinase Inhibitor, Science, vol.305, issue.5682, pp.399-401, 2004.
DOI : 10.1126/science.1099480

A. S. Silva and R. A. Gatenby, A theoretical quantitative model for evolution of cancer chemotherapy resistance, Biology Direct, vol.5, issue.1, p.25, 2010.
DOI : 10.1186/1745-6150-5-25

K. Sprouffske, J. W. Pepper, and C. C. Maley, Accurate Reconstruction of the Temporal Order of Mutations in Neoplastic Progression, Cancer Prevention Research, vol.4, issue.7, pp.1135-1144, 2011.
DOI : 10.1158/1940-6207.CAPR-10-0374

A. G. Terry and S. A. Gourley, Perverse Consequences of Infrequently Culling a Pest, Bulletin of Mathematical Biology, vol.53, issue.2, pp.1666-1695, 2010.
DOI : 10.1007/s11538-009-9492-9

C. Tomasetti and D. Levy, An elementary approach to modeling drug resistance in cancer, Mathematical Biosciences and Engineering, vol.7, issue.4, pp.905-923, 2010.
DOI : 10.3934/mbe.2010.7.905

C. Tomasetti and D. Levy, Drug Resistance always Depends on the Turnover Rate, IFMBE Proceedings, vol.32, pp.552-555, 2010.
DOI : 10.1007/978-3-642-14998-6_141

D. C. Zhou, S. Ramond, F. Viguié, A. Faussat, R. Zittoun et al., Sequential emergence ofMRP- andMDR1-gene over-expression as well asMDR1-gene translocation in homoharringtonine-selected K562 human leukemia cell lines, International Journal of Cancer, vol.50, issue.3, pp.365-371, 1996.
DOI : 10.1002/(SICI)1097-0215(19960126)65:3<365::AID-IJC15>3.0.CO;2-9