A. S. Ackleh and L. J. Allen, Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size, Journal of Mathematical Biology, vol.47, issue.2, pp.47-153, 2003.
DOI : 10.1007/s00285-003-0207-9

A. S. Ackleh and L. J. Allen, Competitive exclusion in sis and sir epidemic models with total cross immunity and density-dependent host mortality, Discrete Contin, Dyn. Syst. Ser. B, vol.5, pp.175-188, 2005.

R. A. Amstrong and R. Mcgehee, Competitive exclusion, The American Naturalist, pp.151-170, 1980.

V. Andreasen, J. Lin, and S. A. Levin, The dynamics of cocirculating influenza strains conferring partial cross-immunity, Journal of Mathematical Biology, vol.35, issue.7, pp.825-842, 1997.
DOI : 10.1007/s002850050079

V. Andreasen and A. Pugliese, Pathogen coexistence induced by density-dependent host mortality, J. Theoret. Biol, pp.159-165, 1995.

H. Bremermann and H. R. Thieme, A competitive exclusion principle for pathogen virulence, Journal of Mathematical Biology, vol.11, issue.2, pp.179-190, 1989.
DOI : 10.1007/BF00276102

C. Castillo-chavez, W. Huang, and J. Li, Competitive Exclusion in Gonorrhea Models and Other Sexually Transmitted Diseases, SIAM Journal on Applied Mathematics, vol.56, issue.2, pp.494-508, 1996.
DOI : 10.1137/S003613999325419X

T. Dhirasakdanon and H. R. Thieme, Persistence of vertically transmitted parasite strains which protect against more virulent horizontally transmitted strains, in Modeling and dynamics of infectious diseases, Contemp. Appl. Math. CAM, vol.11, pp.187-215, 2009.

T. Dhirasakdanon and H. R. Thieme, Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites, Mathematical Modelling of Natural Phenomena, vol.5, issue.6, pp.109-138, 2010.
DOI : 10.1051/mmnp/20105606

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, J. A. Heesterbeek, and J. A. Metz, On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations, Journal of Mathematical Biology, vol.28, issue.4, pp.28-365, 1990.
DOI : 10.1007/BF00178324

G. Gause, The struggle for existence, Williams and Wilkins, 1934.

J. Hale, Ordinary differential equations, 1980.

S. Hsu, H. Smith, and P. Waltman, Competitive exclusion and coexistence for competitive systems on ordered banach spaces, Trans. Amer. Math. Soc, p.348, 1996.

A. Iggidr, J. Kamgang, G. Sallet, and J. Tewa, Global Analysis of New Malaria Intrahost Models with a Competitive Exclusion Principle, SIAM Journal on Applied Mathematics, vol.67, issue.1, pp.260-278, 2006.
DOI : 10.1137/050643271
URL : https://hal.archives-ouvertes.fr/inria-00552014

S. Iwami and T. Hara, Global stability of a generalized epidemic model, Journal of Mathematical Analysis and Applications, vol.362, issue.2, pp.286-300, 2010.
DOI : 10.1016/j.jmaa.2009.07.059

J. A. Jacquez, C. P. Simon, and J. Koopman, Core groups and the r0s for subgroups in heterogeneous sis and si models, in Epidemics models : their structure and relation to data, pp.279-301, 1996.

J. Lasalle, Stability theory for ordinary differential equations, Journal of Differential Equations, vol.4, issue.1, pp.41-57, 1968.
DOI : 10.1016/0022-0396(68)90048-X

J. P. Lasalle, The stability of dynamical systems With an appendix: " Limiting equations and stability of nonautonomous ordinary differential equations, Artstein, Regional Conference Series in Applied Mathematics, 1976.

S. Levin and D. Pimentel, Selection of Intermediate Rates of Increase in Parasite-Host Systems, The American Naturalist, vol.117, issue.3, pp.308-315, 1981.
DOI : 10.1086/283708

S. A. Levin, Community Equilibria and Stability, and an Extension of the Competitive Exclusion Principle, The American Naturalist, vol.104, issue.939, pp.413-423, 1970.
DOI : 10.1086/282676

M. Lipsitch and M. A. Nowak, The evolution of virulence in sexually transmitted HIV/AIDS, Journal of Theoretical Biology, vol.174, issue.4, pp.427-440, 1995.
DOI : 10.1006/jtbi.1995.0109

M. Lipsitch, M. A. Nowak, D. Ebert, and R. M. May, The Population Dynamics of Vertically and Horizontally Transmitted Parasites, Proceedings of the Royal Society B: Biological Sciences, vol.260, issue.1359, pp.321-327, 1995.
DOI : 10.1098/rspb.1995.0099

R. May, Stability and Complexity in Model Ecosystems, 1973.

R. M. May and R. M. Anderson, Epidemiology and Genetics in the Coevolution of Parasites and Hosts, Proceedings of the Royal Society B: Biological Sciences, vol.219, issue.1216, pp.281-313, 1983.
DOI : 10.1098/rspb.1983.0075

J. and M. Smith, Models in Ecology, 1974.

S. D. Mylius and O. Diekmann, On evolutionarily stable life histories, optimization and the need to be specific about density dependence, Oikos, pp.74-218, 1995.

H. R. Thieme, Pathogen Competition and Coexistence and the Evolution of Virulence, Mathematics for Life Sciences and Medicine, pp.123-153, 2007.
DOI : 10.1007/978-3-540-34426-1_6

P. Van-den-driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, vol.180, issue.1-2, pp.29-48, 2002.
DOI : 10.1016/S0025-5564(02)00108-6

M. Vidyasagar, Decomposition techniques for large-scale systems with nonadditive interactions: Stability and stabilizability, IEEE Transactions on Automatic Control, vol.25, issue.4, pp.25-773, 1980.
DOI : 10.1109/TAC.1980.1102422

V. Volterra, Variations and Fluctuations of the Number of Individuals in Animal Species living together, ICES Journal of Marine Science, vol.3, issue.1, pp.3-51, 1928.
DOI : 10.1093/icesjms/3.1.3