J. Arino, J. Davis, D. Hartley, R. Jordan, J. Miller et al., A multi-species epidemic model with spatial dynamics, Mathematical Medicine and Biology, vol.22, issue.2, pp.129-142, 2005.
DOI : 10.1093/imammb/dqi003

J. Arino, R. Jordan, and P. Van-den-driessche, Quarantine in a multi-species epidemic model with spatial dynamics, Mathematical Biosciences, vol.206, issue.1, pp.46-60, 2007.
DOI : 10.1016/j.mbs.2005.09.002

J. Arino and P. Van-den-driessche, A multi-city epidemic model, Mathematical Population Studies, vol.70, issue.3, pp.175-193, 2003.
DOI : 10.1016/S0025-5564(02)00108-6

M. Artzrouni, Transmission Probabilities and Reproduction Numbers for Sexually Transmitted Infections with Variable Infectivity: Application to the Spread of HIV Between Low- and High-Activity Populations, Mathematical Population Studies, vol.38, issue.4, pp.266-287, 2009.
DOI : 10.1097/00002030-200406180-00010

URL : https://hal.archives-ouvertes.fr/hal-00866918

P. Auger, E. Kouokam, G. Sallet, M. Tchuente, and B. Tsanou, The Ross???Macdonald model in a patchy environment, Mathematical Biosciences, vol.216, issue.2, pp.123-131, 2008.
DOI : 10.1016/j.mbs.2008.08.010

A. Berman and R. J. Plemmons, Nonnegative matrices in the mathematical sciences, Classics in Applied Mathematics, vol.9, 1994.
DOI : 10.1137/1.9781611971262

C. Castillo-chavez and H. R. Thieme, Asymptotically autonomous epidemic models In Mathematical Population Dynamics : Analysis of heterogeneity, One: Theory of Epidemics. Canada: Wuerz, pp.33-50, 1995.

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. Heesterbeek, Mathematical epidemiology of infectious diseases . Model building, analysis and interpretation, Wiley Series in Mathematical and Computational Biology, 1999.

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

H. W. Hethcote, The Mathematics of Infectious Diseases, SIAM Review, vol.42, issue.4, pp.599-653, 2000.
DOI : 10.1137/S0036144500371907

M. W. Hirsch, The dynamical systems approach to differential equations. Bulletin (New Series) of The, pp.1-64, 1984.

A. Iggidr, K. Niri, and G. Sallet, Analysis of a patchy sis epidemic model, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00552197

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

Y. Jin and W. Wang, The effect of population dispersal on the spread of a disease, Journal of Mathematical Analysis and Applications, vol.308, issue.1, pp.343-364, 2005.
DOI : 10.1016/j.jmaa.2005.01.034

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.

R. Norman and R. G. Bowers, A Host-Host-Pathogen Model with Vaccination and its Application to Target and Reservoir Hosts, Mathematical Population Studies, vol.8, issue.1, pp.31-56, 2007.
DOI : 10.1016/S0895-7177(03)90088-4

L. Sattenspiel and K. Dietz, A structured epidemic model incorporating geographic mobility among regions, Mathematical Biosciences, vol.128, issue.1-2, pp.71-91, 1995.
DOI : 10.1016/0025-5564(94)00068-B

R. Varga, Matrix iterative analysis. (Prentice-Hall Series in Automatic Computation ), 1962.

M. Vidyasagar, Decomposition techniques for large-scale systems with nonadditive interactions: Stability and stabilizability, IEEE Transactions on Automatic Control, vol.25, issue.4, pp.773-779, 1980.
DOI : 10.1109/TAC.1980.1102422

W. Wang and X. Zhao, An epidemic model in a patchy environment, Mathematical Biosciences, vol.190, issue.1, pp.97-112, 2004.
DOI : 10.1016/j.mbs.2002.11.001