B. Adams and D. D. Kapan, Man Bites Mosquito: Understanding the Contribution of Human Movement to Vector-Borne Disease Dynamics, PLoS ONE, vol.3, issue.8, p.6763, 2009.
DOI : 10.1371/journal.pone.0006763.s001

M. Alvim, A. Iggidr, J. Koiler, G. Sallet, M. L. Penna et al., Onset of a vector borne disease due to human circulation?uniform, local and network reproduction ratios, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00839351

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

N. Bailey, The Mathematical Theory of Infectious Diseases and its Applications, 1975.

L. Cai, S. Guo, X. Li, and M. Ghosh, Global dynamics of a dengue epidemic mathematical model, Chaos, Solitons & Fractals, vol.42, issue.4, pp.2297-2304, 2009.
DOI : 10.1016/j.chaos.2009.03.130

C. Cosner, J. Beier, R. Cantrell, D. Impoinvil, L. Kapitanski et al., The effects of human movement on the persistence of vector-borne diseases, Journal of Theoretical Biology, vol.258, issue.4, pp.550-560, 2009.
DOI : 10.1016/j.jtbi.2009.02.016

O. Diekmann and J. 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.365-382, 1990.
DOI : 10.1007/BF00178324

K. Dietz, Transmission and control of arbovirus diseases, pp.104-121, 1975.

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

L. Esteva and C. Vargas, Analysis of a dengue disease transmission model, Mathematical Biosciences, vol.150, issue.2, pp.131-151, 1998.
DOI : 10.1016/S0025-5564(98)10003-2

H. Freedman, S. Ruan, and M. Tang, Uniform persistence and flows near a closed positively invariant set, Journal of Dynamics and Differential Equations, vol.8, issue.4, pp.583-600, 1994.
DOI : 10.1007/BF02218848

M. Gatto, L. Mari, E. Bertuzzo, R. Casagrandi, L. Righetto et al., Generalized reproduction numbers and the prediction of patterns in waterborne disease, Proceedings of the National Academy of Sciences, vol.109, issue.48, pp.19703-19708, 2012.
DOI : 10.1073/pnas.1217567109

G. Hasibeder and C. Dye, Population dynamics of mosquito-borne disease: Persistence in a completely heterogeneous environment, Theoretical Population Biology, vol.33, issue.1, pp.31-53, 1988.
DOI : 10.1016/0040-5809(88)90003-2

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 and J. Yorke, Gonorrhea : transmission dynamics and control, Lect. Notes Biomath, vol.56, 1984.
DOI : 10.1007/978-3-662-07544-9

M. W. Hirsch and H. L. Smith, Monotone dynamical systems In Handbook of differential equations: ordinary differential equations, pp.239-357, 2005.

N. A. Honorio, R. M. Nogueira, C. T. Codeco, M. S. Carvalho, O. G. Cruz et al., Spatial Evaluation and Modeling of Dengue Seroprevalence and Vector Density in Rio de Janeiro, Brazil, PLoS Neglected Tropical Diseases, vol.72, issue.11, p.545, 2009.
DOI : 10.1371/journal.pntd.0000545.s001

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

L. Lambrechts, T. W. Scott, and D. J. Gubler, Consequences of the Expanding Global Distribution of Aedes albopictus for Dengue Virus Transmission, PLoS Neglected Tropical Diseases, vol.2, issue.5, p.646, 2010.
DOI : 10.1371/journal.pntd.0000646.s001

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

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

A. M. Powers, A. C. Brault, R. B. Tesh, and S. C. Weaver, Re-emergence of chikungunya and o???nyong-nyong viruses: evidence for distinct geographical lineages and distant evolutionary relationships, Journal of General Virology, vol.81, issue.2, pp.81471-81480, 2000.
DOI : 10.1099/0022-1317-81-2-471

R. Ross, The prevention of malaria, 1911.

S. Rushton and A. J. Mautner, THE DETERMINISTIC MODEL OF A SIMPLE EPIDEMIC FOR MORE THAN ONE COMMUNITY, Biometrika, vol.42, issue.1-2, pp.126-132, 1955.
DOI : 10.1093/biomet/42.1-2.126

D. L. Smith, K. E. Battle, S. I. Hay, C. M. Barker, T. W. Scott et al., Ross, Macdonald, and a Theory for the Dynamics and Control of Mosquito-Transmitted Pathogens, PLoS Pathogens, vol.3, issue.4, pp.1002588-1002592
DOI : 10.1371/journal.ppat.1002588.s001

D. L. Smith, F. E. Dushoff, and . Mckenzie, The risk of a mosquito-borne infection in a heterogeneous environment, PLoS Biol, issue.11, p.368, 2004.

H. L. Smith, Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, Mathematical Surveys and Monographs, vol.41, issue.174, 1995.
DOI : 10.1090/surv/041

M. O. Souza, Multiscale analysis for a vector-borne epidemic model, Journal of Mathematical Biology, vol.137, issue.8, 2013.
DOI : 10.1007/s00285-013-0666-6

S. T. Stoddard, A. C. Morrison, G. M. Vazquez-prokopec, V. Paz-soldan, T. J. Kochel et al., The Role of Human Movement in the Transmission of Vector-Borne Pathogens, PLoS Neglected Tropical Diseases, vol.82, issue.6, pp.481-488, 2009.
DOI : 10.1371/journal.pntd.0000481.s002

M. Teurlai, R. Huy, B. Cazelles, R. Duboz, C. Baehr et al., Can Human Movements Explain Heterogeneous Propagation of Dengue Fever in Cambodia?, PLoS Neglected Tropical Diseases, vol.123, issue.12, pp.1957-2012
DOI : 10.1371/journal.pntd.0001957.s009

URL : https://hal.archives-ouvertes.fr/hal-01495165

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

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

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

H. Yang, H. Wei, and X. Li, Global stability of an epidemic model for vector-borne disease, Inria RESEARCH CENTRE NANCY ? GRAND EST 615 rue du Jardin Botanique CS20101 54603 Villers-lès-Nancy Cedex Publisher Inria Domaine de Voluceau -Rocquencourt BP 105 -78153 Le Chesnay Cedex inria.fr ISSN, pp.279-292, 2010.
DOI : 10.1007/s11424-010-8436-7