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
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
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
The Mathematical Theory of Infectious Diseases and its Applications, 1975. ,
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
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
Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. Wiley series in mathematical and computational biology, 2000. ,
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
Transmission and control of arbovirus diseases, pp.104-121, 1975. ,
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
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
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
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
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
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
Gonorrhea : transmission dynamics and control, Lect. Notes Biomath, vol.56, 1984. ,
DOI : 10.1007/978-3-662-07544-9
Monotone dynamical systems In Handbook of differential equations: ordinary differential equations, pp.239-357, 2005. ,
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
Qualitative Theory of Compartmental Systems, SIAM Review, vol.35, issue.1, pp.43-79, 1993. ,
DOI : 10.1137/1035003
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
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
Introduction to dynamic systems. Theory, models, and applications, 1979. ,
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
The prevention of malaria, 1911. ,
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
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
The risk of a mosquito-borne infection in a heterogeneous environment, PLoS Biol, issue.11, p.368, 2004. ,
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
Multiscale analysis for a vector-borne epidemic model, Journal of Mathematical Biology, vol.137, issue.8, 2013. ,
DOI : 10.1007/s00285-013-0666-6
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
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
Global asymptotic stability in epidemic models, Proc. int. Conf. number 1017 in Lectures Notes in Biomath, pp.608-615, 1982. ,
DOI : 10.1007/BF02320701
Mathematics in population biology Princeton Series in Theoretical and Computational Biology, 2003. ,
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
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
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