P. Adda, J. Dimi, A. Iggidr, J. Kamgang, G. Sallet et al., General models of host-parasite systems. global analysis, DCDS series B, vol.8, pp.1-17, 2007.

J. Arino, C. C. Mccluskey, and P. Van-den-driessche, Global Results for an Epidemic Model with Vaccination that Exhibits Backward Bifurcation, SIAM Journal on Applied Mathematics, vol.64, issue.1, pp.260-276, 2003.
DOI : 10.1137/S0036139902413829

N. Bame, S. Bowong, J. Mbang, G. Sallet, and J. Tewa, Global stability for SEIS models with n latent classes, Math. Biosci. Eng, vol.5, pp.20-33, 2008.

N. P. Bhatia and G. P. Szegö, Dynamical systems: Stability theory and applications, Lecture Notes in Mathematics, vol.35, issue.35, 1967.
DOI : 10.1007/BFb0080630

M. C. De-jong, O. Diekmann, and H. Heesterbeek, How does transmission of infection depend on population size ?, in Epidemic models . Their structure and relation to data, pp.85-94, 1995.

P. , D. Leenheer, and S. S. Pilyugin, Multistrain virus dynamics with mutations: a global analysis, Mathematical Medicine and Biology, vol.25, pp.285-322, 2008.

O. Diekmann and J. A. Heesterbeek, Mathematical epidemiology of infectious diseases Model building, analysis and interpretation, Wiley Series in Mathematical and Computational Biology, 2000.

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

W. J. Edmunds, G. F. Medley, and D. J. Nokes, THE TRANSMISSION DYNAMICS AND CONTROL OF HEPATITIS B VIRUS IN THE GAMBIA, Statistics in Medicine, vol.15, issue.20, pp.2215-2233, 1996.
DOI : 10.1002/(SICI)1097-0258(19961030)15:20<2215::AID-SIM369>3.0.CO;2-2

S. Gandon, M. J. Mackinnon, S. Nee, and A. F. Read, Imperfect vaccines and the evolution of pathogen virulence, Nature, vol.414, issue.6865, pp.414-751, 2001.
DOI : 10.1038/414751a

S. Gandon and D. Troy, The evolutionary epidemiology of vaccination, Journal of The Royal Society Interface, vol.17, issue.7-8, pp.803-817, 2007.
DOI : 10.1016/S0264-410X(98)00313-2

A. Gumel, C. C. Mccluskey, and P. Van-den-driessche, Mathematical Study of a Staged-Progression HIV Model with Imperfect Vaccine, Bulletin of Mathematical Biology, vol.303, issue.5, pp.2105-2128, 2006.
DOI : 10.1007/s11538-006-9095-7

J. A. Heesterbeek, A brief history of R 0 and a recipe for its calculation, Acta Biotheoretica, vol.50, issue.3, pp.189-204, 2002.
DOI : 10.1023/A:1016599411804

J. A. Heesterbeek and K. Dietz, The concept of R 0 in epidemic theory, pp.89-110, 1996.

J. Hyman and J. Li, Differential susceptibility epidemic models, Journal of Mathematical Biology, vol.42, issue.6, pp.626-644, 2005.
DOI : 10.1007/s00285-004-0301-7
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.616.626

J. Hyman, J. Li, and E. Stanley, The Initialization and Sensitivity of Multigroup Models for the Transmission of HIV, Journal of Theoretical Biology, vol.208, issue.2, pp.227-249, 2001.
DOI : 10.1006/jtbi.2000.2214

J. M. Hyman and J. Li, Threshold Conditions for the Spread of the HIV Infection in Age-structured Populations of Homosexual Men, Journal of Theoretical Biology, vol.166, issue.1, pp.9-31, 1994.
DOI : 10.1006/jtbi.1994.1002

J. M. Hyman and J. Li, The reproductive number for an HIV model with differential infectivity and staged progression, Linear Algebra and its Applications, vol.398, pp.101-116, 2005.
DOI : 10.1016/j.laa.2004.07.017

J. M. Hyman and J. Li, Differential susceptibility and infectivity epidemic models, Mathematical Biosciences and Engineering, vol.3, issue.1, pp.89-100, 2006.
DOI : 10.3934/mbe.2006.3.89
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.598.5827

J. M. Hyman, J. Li, and E. Stanley, The differential infectivity and staged progression models for the transmission of HIV, Mathematical Biosciences, vol.155, issue.2, pp.77-109, 1999.
DOI : 10.1016/S0025-5564(98)10057-3

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

A. Iggidr, J. Mbang, G. Sallet, and J. Tewa, multi-compartment models, DCDS series B, pp.506-519, 2007.

J. A. Jacquez, Modeling with compartments, 1999.

J. A. Jacquez and C. P. Simon, Qualitative Theory of Compartmental Systems, SIAM Review, vol.35, issue.1, pp.43-79, 1993.
DOI : 10.1137/1035003

J. A. Jacquez, C. P. Simon, and J. Koopman, The reproduction number in deterministic models of contagious diseases, Comment. Theor. Biol, vol.2, 1991.

J. A. Jacquez, C. P. Simon, J. Koopman, L. Sattenspiel, and T. Perry, Modeling and analyzing HIV transmission: the effect of contact patterns, Mathematical Biosciences, vol.92, issue.2, p.92, 1988.
DOI : 10.1016/0025-5564(88)90031-4

A. Korobeinikov and P. Maini, A lyapunov function and global properties for sir and seir epidemiological models with nonlinear incidence, Mathematical Biosciences and Engineering, vol.1, pp.57-60, 2004.

A. Korobeinikov and G. Wake, Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models, Applied Mathematics Letters, vol.15, issue.8, pp.955-960, 2002.
DOI : 10.1016/S0893-9659(02)00069-1

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.

X. Lin and J. W. So, Global stability of the endemic equilibrium and uniform persistence in epidemic models with subpopulations, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, vol.12, issue.03, pp.282-295, 1993.
DOI : 10.1016/0025-5564(85)90047-1

D. G. Luenberger, Introduction to dynamic systems. Theory, models, and applications, 1979.

Z. Ma, J. Liu, and J. Li, Stability analysis for differential infectivity epidemic models, Nonlinear Anal. : Real world applications, pp.841-856, 2003.

H. Mccallum, N. Barlow, and J. Hone, How should pathogen transmission be modelled?, Trends in Ecology & Evolution, vol.16, issue.6, pp.295-300, 2001.
DOI : 10.1016/S0169-5347(01)02144-9

C. P. Simon and J. A. Jacquez, Reproduction Numbers and the Stability of Equilibria of SI Models for Heterogeneous Populations, SIAM Journal on Applied Mathematics, vol.52, issue.2, pp.541-576, 1992.
DOI : 10.1137/0152030

H. Smith, Monotone dynamical systems. An introduction ot the theory of competitive and cooperative systems, 1995.

H. R. Thieme, Mathematics in population biology, Princeton Series in Theoretical and Computational Biology, 2003.

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

J. Wilson, D. Nokes, and W. Carman, Current status of HBV vaccine escape variants - a mathematical model of their epidemiology, Journal of Viral Hepatitis, vol.5, issue.s2, 1998.
DOI : 10.1016/S0140-6736(95)90272-4

J. N. Wilson, D. J. Nokes, and W. F. Carman, Predictions of the emergence of vaccine-resistant hepatitis B in The Gambia using a mathematical model, Epidemiology and Infection, vol.124, issue.2, pp.295-307, 2000.
DOI : 10.1017/S0950268800003605