J. Arino, Disease in metapopulations model, in Modeling and dynamics of infectious diseases, pp.65-123, 2009.

J. Arino and S. Portet, Epidemiological implications of mobility between a large urban centre and smaller satellite cities, Journal of Mathematical Biology, vol.20, issue.3, pp.1243-1265, 2015.
DOI : 10.1007/s10884-008-9111-8

J. Arino and P. Van-den-driessche, Disease spread in metapopulations, Nonlinear dynamics and evolution equations, pp.1-13, 2006.
DOI : 10.1090/fic/048/01

D. Bichara and C. Castillo-chavez, Vector-borne diseases models with residence times ??? A Lagrangian perspective, Mathematical Biosciences, vol.281, pp.128-138, 2016.
DOI : 10.1016/j.mbs.2016.09.006
URL : http://arxiv.org/pdf/1509.08894

D. Bichara, S. A. Holechek, J. Velázquez-castro, A. L. Murillo, and C. Castillo-chavez, On the dynamics of dengue virus type 2 with residence times and vertical transmission, Letters in Biomathematics, vol.57, issue.1, pp.140-160, 2016.
DOI : 10.1099/vir.0.81486-0

D. Bichara, Y. Kang, C. Castillo-chavez, R. Horan, and C. Perrings, SIS and SIR Epidemic Models Under Virtual Dispersal, Bulletin of Mathematical Biology, vol.5, issue.11, pp.77-2004, 2015.
DOI : 10.1097/00007435-197804000-00003
URL : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4749480/pdf

B. Bonzi, A. Fall, A. Iggidr, and G. Sallet, Stability of differential susceptibility and infectivity epidemic models, Journal of Mathematical Biology, vol.124, issue.1, pp.39-64, 2011.
DOI : 10.1017/S0950268800003605
URL : https://hal.archives-ouvertes.fr/inria-00544315

S. P. Blythe and C. Castillo-chavez, Like-with-like preference and sexual mixing models, Mathematical Biosciences, vol.96, issue.2, pp.221-238, 1989.
DOI : 10.1016/0025-5564(89)90060-6

C. Castillo-chavez, D. Bichara, and B. R. Morin, Perspectives on the role of mobility, behavior, and time scales in the spread of diseases, Proceedings of the National Academy of Sciences, pp.14582-14588, 2016.
DOI : 10.1007/s12080-015-0262-z

C. Castillo-chavez and S. Busenberg, A general solution of the problem of mixing of subpopulations and its application to risk-and age-structured epidemic models for the spread of aids, Mathematical Medecine and Biology, vol.8, pp.1-29, 1991.

C. Castillo-chavez and H. R. Thieme, Asymptotically autonomous epidemic models , in Mathematical Population Dynamics: Analysis of Heterogeneity, Volume One: Theory of Epidemics, 1995.

C. Cosner, J. Beier, R. Cantrell, D. Impoinvil, L. Kapitanski et al., The effects of human movement on the persistence of vectorborne diseases, Journal of theoretical biology, pp.258-550, 2009.

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

J. Dushoff and S. Levin, The effects of population heterogeneity on disease invasion, Mathematical Biosciences, vol.128, issue.1-2, pp.25-40, 1995.
DOI : 10.1016/0025-5564(94)00065-8

S. Eckenrode, A. Bakullari, M. L. Metersky, Y. Wang, M. M. Pandolfi et al., Conclusions., Infection Control & Hospital Epidemiology, vol.20, issue.S3, pp.35-38, 2014.
DOI : 10.1056/NEJMoa061115

J. A. Falcón-lezama, R. A. Martínez-vega, P. A. Kuri-morales, J. Ramos-castañeda, and B. Adams, Day-to-Day Population Movement and the Management of Dengue Epidemics, Bulletin of Mathematical Biology, vol.206, issue.3, pp.78-2011, 2016.
DOI : 10.1093/infdis/jis357

E. Fenichel, C. Castillo-chavez, M. G. Ceddia, G. Chowell, P. Gonzalez-parra et al., Adaptive human behavior in epidemiological models, Proceedings of the National Academy of Sciences, vol.339, issue.nov19_1, 2011.
DOI : 10.1136/bmj.b4571
URL : http://www.pnas.org/content/108/15/6306.full.pdf

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

M. Hirsch, The dynamical systems approach to differential equations, Bulletin of the American Mathematical Society, vol.11, issue.1, pp.1-64, 1984.
DOI : 10.1090/S0273-0979-1984-15236-4
URL : http://www.ams.org/bull/1984-11-01/S0273-0979-1984-15236-4/S0273-0979-1984-15236-4.pdf

W. Huang, K. Cooke, and C. Castillo-chavez, Stability and Bifurcation for a Multiple-Group Model for the Dynamics of HIV/AIDS Transmission, SIAM Journal on Applied Mathematics, vol.52, issue.3, pp.835-854, 1992.
DOI : 10.1137/0152047

A. Iggidr, G. Sallet, and M. O. Souza, On the dynamics of a class of multi-group models for vector-borne diseases, Journal of Mathematical Analysis and Applications, vol.441, issue.2, pp.723-743, 2016.
DOI : 10.1016/j.jmaa.2016.04.003
URL : https://hal.archives-ouvertes.fr/hal-01249798

A. Iggidr, G. Sallet, and B. Tsanou, Global Stability Analysis of a Metapopulation SIS Epidemic Model, Mathematical Population Studies, vol.190, issue.1, pp.115-129, 2012.
DOI : 10.1016/j.mbs.2002.11.001
URL : https://hal.archives-ouvertes.fr/hal-00648041

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. 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

V. Kaplan, D. C. Angus, M. F. Griffin, G. Clermont, R. Scott-watson et al., Linde-zwirble, Hospitalized community-acquired pneumonia in the elderly: age-and sex-related patterns of care and outcome in the united states, American journal of respiratory and critical care medicine, pp.165-766, 2002.

W. Kermack and A. Mckendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc., A115, pp.700-721, 1927.

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 and S. Lefschetz, Stability by Liapunov's direct method, 1961.

J. A. Metz and O. Diekmann, The dynamics of physiologically structured populations, 2014.
DOI : 10.1007/978-3-662-13159-6

A. Nold, Heterogeneity in disease-transmission modeling, Mathematical Biosciences, vol.52, issue.3-4, p.227, 1980.
DOI : 10.1016/0025-5564(80)90069-3

C. Perrings, C. Castillo-chavez, G. Chowell, P. Daszak, E. P. Fenichel et al., Merging Economics and Epidemiology to Improve the Prediction and Management of Infectious Disease, EcoHealth, vol.51, issue.4, 2014.
DOI : 10.1257/jel.51.3.689

R. M. Prothero, Disease and Mobility: A Neglected Factor in Epidemiology, International Journal of Epidemiology, vol.6, issue.3, pp.259-267, 1977.
DOI : 10.1093/ije/6.3.259

D. J. Rodríguez and L. Torres-sorando, Models of Infectious Diseases in Spatially Heterogeneous Environments, Bulletin of Mathematical Biology, vol.63, issue.3, pp.547-571, 2001.
DOI : 10.1006/bulm.2001.0231

N. W. Ruktanonchai, D. L. Smith, and P. De-leenheer, Parasite sources and sinks in a patched Ross???Macdonald malaria model with human and mosquito movement: Implications for control, Mathematical Biosciences, vol.279, pp.279-90, 2016.
DOI : 10.1016/j.mbs.2016.06.012

S. Rushton and A. Mautner, The deterministic model of a simple epidemic for more than one community, Biometrika, pp.126-132, 1955.

M. Salmani and P. Van-den-driessche, A model for disease transmission in a patchy environment, DCDS series B, vol.6, pp.185-202, 2006.

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

L. Sattenspiel and C. P. Simon, The spread and persistence of infectious diseases in structured populations, Mathematical Biosciences, vol.90, issue.1-2, pp.341-366, 1987.
DOI : 10.1016/0025-5564(88)90074-0

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

Y. Xiao and X. Zou, Transmission dynamics for vector-borne diseases in a patchy environment, Journal of Mathematical Biology, vol.3, issue.1, pp.113-146, 2014.
DOI : 10.3934/mbe.2013.10.463

J. A. Yorke, H. W. Hethcote, and A. Nold, Dynamics and Control of the Transmission of Gonorrhea, Sexually Transmitted Diseases, vol.5, issue.2, pp.51-56, 1978.
DOI : 10.1097/00007435-197804000-00003