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, 70 A. Fall, A. Iggidr, G. Sallet, and J.J. Tewa, pp.260-276, 2003.
DOI : 10.1137/S0036139902413829

N. Bame, S. Bowong, J. Mbang, G. Sallet, and J. Tewa, Global stability analysis for seis models with n latent classes, Math. Biosci. Eng

E. Beretta and V. Capasso, On the general structure of epidemic systems. Global asymptotic stability, Computers & Mathematics with Applications, vol.12, issue.6, pp.677-694, 1986.
DOI : 10.1016/0898-1221(86)90054-4

E. Beretta and Y. Takeuchi, Global Asymptotic Stability of Lotka???Volterra Diffusion Models with Continuous Time Delay, SIAM Journal on Applied Mathematics, vol.48, issue.3, pp.627-651, 1988.
DOI : 10.1137/0148035

S. Busenberg and P. Van-den-driessche, A Method for Proving the Non-existence of Limit Cycles, Journal of Mathematical Analysis and Applications, vol.172, issue.2, pp.463-479, 1993.
DOI : 10.1006/jmaa.1993.1037

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.365-382, 1990.
DOI : 10.1007/BF00178324

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

K. Dietz, The estimation of the basic reproduction number for infectious diseases, Statistical Methods in Medical Research, vol.154, issue.1, pp.23-41, 1993.
DOI : 10.1177/096228029300200103

L. Esteva and C. Vargas, A model for dengue disease with variable human population, Journal of Mathematical Biology, vol.38, issue.3, pp.220-240, 1998.
DOI : 10.1007/s002850050147

B. S. Goh, Global Stability in Many-Species Systems, The American Naturalist, vol.111, issue.977, pp.135-143, 1977.
DOI : 10.1086/283144

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

A. Gumel, C. C. Mccluskey, and J. Watmough, An sveir model for assessing the potential impact of an imperfect anti-sars vaccine, Math. Biosci. Eng, vol.3, 2006.

H. Guo and M. Li, Global dynamics of a staged progression model for infectious diseases, Mathematical Biosciences and Engineering, vol.3, issue.3, pp.513-525, 2006.
DOI : 10.3934/mbe.2006.3.513

G. W. Harrison, Global stability of predator-prey interactions, Journal of Mathematical Biology, vol.18, issue.2, pp.159-171, 1979.
DOI : 10.1007/BF00279719

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

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

H. W. Hethcote and H. R. Thieme, Stability of the endemic equilibrium in epidemic models with subpopulations, Mathematical Biosciences, vol.75, issue.2, pp.205-227, 1985.
DOI : 10.1016/0025-5564(85)90038-0

H. W. Hethcote, Qualitative analyses of communicable disease models, Mathematical Biosciences, vol.28, issue.3-4, pp.335-356, 1976.
DOI : 10.1016/0025-5564(76)90132-2

M. Hirsch, Systems of Differential Equations That are Competitive or Cooperative. IV: Structural Stability in Three-Dimensional Systems, SIAM Journal on Mathematical Analysis, vol.21, issue.5, pp.1125-1234, 1990.
DOI : 10.1137/0521067

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

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, 2006.
DOI : 10.3934/mbe.2006.3.89
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.598.5827

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. Hyman and J. Li, An intuitive formulation for the reproductive number for the spread of diseases in heterogeneous populations, Mathematical Biosciences, vol.167, issue.1, 2000.
DOI : 10.1016/S0025-5564(00)00025-0

J. Hyman and J. Li, Differential susceptibility and infectivity epidemic models, Mathematical Biosciences and Engineering, vol.3, issue.1, pp.626-644, 2005.
DOI : 10.3934/mbe.2006.3.89
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.598.5827

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, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00591683

A. Iggidr, J. Mbang, and G. Sallet, Stability analysis of within-host parasite models with delays, Mathematical Biosciences, vol.209, issue.1, 2007.
DOI : 10.1016/j.mbs.2007.01.008
URL : https://hal.archives-ouvertes.fr/inria-00552051

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, 1988.
DOI : 10.1016/0025-5564(88)90031-4

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

A. Korobeinikov and P. Maini, A Lyapunov function and global properties for SIR and SEIR epidemiolgical models with nonlinear incidence, Math. Biosci. Eng, vol.1, pp.57-60, 2004.

A. Korobeinikov and P. Maini, Non-linear incidence and stability of infectious disease models, Mathematical Medicine and Biology, vol.22, issue.2, pp.113-128, 2005.
DOI : 10.1093/imammb/dqi001

A. Korobeinikov, Lyapunov functions and global properties for SEIR and SEIS epidemic models, Mathematical Medicine and Biology, vol.21, issue.2, pp.75-83, 2004.
DOI : 10.1093/imammb/21.2.75
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.549.150

A. Lajmanovich and J. Yorke, A deterministic model for gonorrhea in a nonhomogeneous population, Mathematical Biosciences, vol.28, issue.3-4, pp.221-236, 1976.
DOI : 10.1016/0025-5564(76)90125-5

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

W. M. Liu, H. W. Hethcote, and S. A. Levin, Dynamical behavior of epidemiological models with nonlinear incidence rates, 72 A. Fall, A. Iggidr, G. Sallet, and J.J. Tewa, pp.359-380, 1987.
DOI : 10.1007/BF00277162

M. Y. Li, J. R. Graef, L. Wang, and J. Karsai, Global dynamics of a SEIR model with varying total population size, Mathematical Biosciences, vol.160, issue.2, pp.191-213, 1999.
DOI : 10.1016/S0025-5564(99)00030-9

M. Y. Li, J. S. Muldowney, and P. Van-den-driessche, Global stability for the SEIR model in epidemiology, Mathematical Biosciences, vol.125, issue.2, pp.409-425, 1999.
DOI : 10.1016/0025-5564(95)92756-5

M. Y. Li and J. S. Muldowney, Global stability for the SEIR model in epidemiology, Mathematical Biosciences, vol.125, issue.2, pp.155-164, 1995.
DOI : 10.1016/0025-5564(95)92756-5

M. Y. Li, H. L. Smith, and L. Wang, Global dynamics an SEIR epidemic model with vertical transmission, SIAM J. Appl. Math, vol.62, pp.58-69, 2001.

M. Y. Li and L. Wang, Global stability in some SEIR epidemic models, in Mathematical approaches for emerging and reemerging infectious diseases: models, methods, and theory, Math. Appl, vol.126, pp.295-311, 1999.

M. Li and J. S. Muldowney, On R.A. Smith's Autonomous Convergence Theorem, Rocky Mountain Journal of Mathematics, vol.25, issue.1, pp.365-379, 1995.
DOI : 10.1216/rmjm/1181072289
URL : https://hal.archives-ouvertes.fr/jpa-00228424

Y. Li and J. S. Muldowney, On Bendixson???s Criterion, Journal of Differential Equations, vol.106, issue.1, pp.27-39, 1993.
DOI : 10.1006/jdeq.1993.1097

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.

C. C. Mccluskey, Lyapunov functions for tuberculosis models with fast and slow progression, Mathematical Biosciences and Engineering, vol.3, issue.4, 2006.
DOI : 10.3934/mbe.2006.3.603

C. Mccluskey and P. Van-den-driessche, Global Analysis of Two Tuberculosis Models, Journal of Dynamics and Differential Equations, vol.16, issue.1, pp.139-166, 2004.
DOI : 10.1023/B:JODY.0000041283.66784.3e

C. Mccluskey, A model of HIV/AIDS with staged progression and amelioration, Mathematical Biosciences, vol.181, issue.1, pp.1-16, 2003.
DOI : 10.1016/S0025-5564(02)00149-9

J. Mena-lorca and H. W. Hethcote, Dynamic models of infectious diseases as regulators of population sizes, J. Math. Biol, vol.30, pp.693-716, 1992.

J. S. Muldowney, Compound matrices and ordinary differential equations, Rocky Mountain Journal of Mathematics, vol.20, issue.4, pp.857-872, 1990.
DOI : 10.1216/rmjm/1181073047

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, Periodic orbits of competitive and cooperative systems, Journal of Differential Equations, vol.65, issue.3, pp.361-373, 1986.
DOI : 10.1016/0022-0396(86)90024-0

R. Smith, Synopsis, Proc. Roy. Soc. Edinburgh, pp.235-259, 1986.
DOI : 10.1073/pnas.35.7.408

Y. Takeuchi and N. Adachi, The existence of globally stable equilibria of ecosystems of the generalized Volterra type, Journal of Mathematical Biology, vol.42, issue.4, pp.401-415, 1980.
DOI : 10.1007/BF00276098

H. R. Thieme, Global asymptotic stability in epidemic models, Equadiff 82, Proc. int. Conf. 1017 in Lectures Notes in Biomath, pp.608-615, 1982.
DOI : 10.1007/BF02320701

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

R. Varga, Factorization and normalized iterative methods, in Boundary problems in differential equations, pp.121-142, 1960.