Asymptotic Profiles of the Steady States for an SIS Epidemic Patch Model, SIAM Journal on Applied Mathematics, vol.67, issue.5, pp.1283-1309, 2007. ,
DOI : 10.1137/060672522
A secular equation for the eigenvalues of a diagonal matrix perturbation, Linear Algebra and its Applications, vol.246, issue.49, 1996. ,
DOI : 10.1016/0024-3795(94)00314-9
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
Quarantine in a multi-species epidemic model with spatial dynamics, Mathematical Biosciences, vol.206, issue.1, 2006. ,
DOI : 10.1016/j.mbs.2005.09.002
The basic reproduction number in a multicity compartmental model. Lect. Notes Contr, Inf. Sci, vol.294, pp.135-142, 2003. ,
A multi-city epidemic model, Mathematical Population Studies, vol.70, issue.3, pp.175-193, 2003. ,
DOI : 10.1016/S0025-5564(02)00108-6
Disease spread in metapopulations, Nonlinear dynamics and evolution equations, pp.1-13, 2006. ,
DOI : 10.1090/fic/048/01
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
Multiple endemic equilibria for a multipatch ross-macdonald model with fast migrations, Proc. 10th Biennal CARI Congress, 2010. ,
When individual behaviour matters: homogeneous and network models in epidemiology, Journal of The Royal Society Interface, vol.33, issue.9, pp.879-891, 2007. ,
DOI : 10.1038/30918
An attempt at large-scale influenza epidemic modelling by means of a computer ,
Computer modelling of influenza epidemics for the whole country (USSR), Advances in Applied Probability, vol.180, issue.02, pp.224-226, 1971. ,
DOI : 10.1017/S0001867800037903
Nonnegative matrices in the mathematical sciences, Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.9, 1994. ,
DOI : 10.1137/1.9781611971262
Stability Theory of Dynamical Systems, 1970. ,
DOI : 10.1007/978-3-642-62006-5
Tuberculosis Transmission Model with Chemoprophylaxis and Treatment, Bulletin of Mathematical Biology, vol.74, issue.1, pp.1163-1191, 2008. ,
DOI : 10.1007/s11538-008-9295-4
Tuberculosis : Pathogenis, protection and control, 1994. ,
DOI : 10.1128/9781555818357
Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework, Journal of Molecular Medicine, vol.76, issue.9, p.76, 1998. ,
DOI : 10.1007/s001090050260
Epidemic spreading in correlated complex networks, Phys. Rev. E, issue.047104, p.66, 2002. ,
Parameter estimation based synchronization for an epidemic model with application to tuberculosis in Cameroon, Physics Letters A, vol.374, issue.44 ,
DOI : 10.1016/j.physleta.2010.09.008
Mathematical analysis of a tuberculosis model with differential infectivity, Communications in Nonlinear Science and Numerical Simulation, vol.14, issue.11, 2009. ,
DOI : 10.1016/j.cnsns.2009.02.017
Asymptotically autonomous epidemic models, Mathematical Population Dynamics : Analysis of Heterogeneity, 1995. ,
A two-patch model of Gambian sleeping sickness : application to vector control strategies in a village and plantations, Acta Biotheoretica, vol.46, issue.3, pp.207-229, 1998. ,
DOI : 10.1023/A:1001776926167
Modeling the world-wide spread of pandemic influenza, PLoS Med, vol.4, issue.95, 2007. ,
Reaction???diffusion processes and metapopulation models in heterogeneous??networks, Nature Physics, vol.6, issue.4, 2007. ,
DOI : 10.1103/PhysRevE.71.027103
Invasion threahold in heterogeneous metapopulation networks, Phys. Rev. Lett, vol.99, 2007. ,
Epidemic modelling in metapopulation systems with heterogeneous pattern : theory and simulations, J. Theor. Biol, vol.251, issue.450, 2008. ,
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
Agreement dynamics on small-world networks, Europhys. Lett, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00020240
How does transmission of infection depend on population size ? Epidemic models. Their structure and relation to data, pp.85-94, 1995. ,
Mathematical epidemiology of infectious diseases Model building, analysis and interpre- tation, 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
A mathematical model for malaria involving differential susceptibility, exposedness and infectivity of human host, Journal of Biological Dynamics, vol.34, issue.6, pp.574-598, 2009. ,
DOI : 10.1016/S0025-5564(02)00108-6
URL : https://hal.archives-ouvertes.fr/hal-00385593
control, but not elimination, Int. J. Tuberc. Lung Dis, vol.45, pp.146-152, 2000. ,
Population dynamics of mosquito-borne disease: effects of flies which bite some people more frequently than others, Transactions of the Royal Society of Tropical Medicine and Hygiene, vol.80, issue.1, pp.69-77, 1986. ,
DOI : 10.1016/0035-9203(86)90199-9
A Model for Tuberculosis with Exogenous Reinfection, Theoretical Population Biology, vol.57, issue.3, pp.235-147, 2000. ,
DOI : 10.1006/tpbi.2000.1451
Disease propagation in connected host populations with density-dependent dynamics: the case of the Feline Leukemia Virus, Journal of Theoretical Biology, vol.223, issue.4, pp.465-475, 2003. ,
DOI : 10.1016/S0022-5193(03)00122-X
URL : https://hal.archives-ouvertes.fr/hal-00427417
The Metapopulation Dynamics of an Infectious Disease: Tuberculosis in Possums, Theoretical Population Biology, vol.61, issue.1, pp.15-29, 2002. ,
DOI : 10.1006/tpbi.2001.1553
A core group model for disease transmission, Mathematical Biosciences, vol.128, issue.1-2, pp.41-55, 1995. ,
DOI : 10.1016/0025-5564(94)00066-9
Backward bifurcation in epidemic control, Mathematical Biosciences, vol.146, issue.1, pp.15-35, 1997. ,
DOI : 10.1016/S0025-5564(97)00027-8
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
The Mathematics of Infectious Diseases, SIAM Review, vol.42, issue.4, pp.599-653, 2000. ,
DOI : 10.1137/S0036144500371907
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
Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets, SIAM Journal on Mathematical Analysis, vol.13, issue.2, pp.167-179, 1982. ,
DOI : 10.1137/0513013
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
Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere, SIAM Journal on Mathematical Analysis, vol.16, issue.3, pp.423-439, 1985. ,
DOI : 10.1137/0516030
Systems of differential equations which are competitive or cooperative: III. Competing species, Nonlinearity, vol.1, issue.1, pp.51-71, 1988. ,
DOI : 10.1088/0951-7715/1/1/003
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
Monotone dynamical systems, Handbook of differential equations : ordinary differential equations ,
Analysis of a patchy sis epidemic model, 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00552197
Metapopulation sis epidemic model, Proc. 9th Biennal CARI Congress, 2008. ,
URL : https://hal.archives-ouvertes.fr/inria-00595397
Global Stability Analysis of a Metapopulation SIS Epidemic Model, Mathematical Population Studies, vol.190, issue.1, 2011. ,
DOI : 10.1080/08898480.2012.693844
URL : https://hal.archives-ouvertes.fr/hal-00648041
Modeling with compartments, BioMedware, 1999. ,
Qualitative Theory of Compartmental Systems, SIAM Review, vol.35, issue.1, pp.43-79, 1993. ,
DOI : 10.1137/1035003
Local stability analysis of spatially homogeneous solutions of multi-patch systems, Journal of Mathematical Biology, vol.41, issue.3, pp.232-252, 2004. ,
DOI : 10.1007/s002850000048
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
Analysis and Monte Carlo simulations of a model for the spread of infectious diseases in heterogeneous metapopulations, Physical Review E, vol.80, issue.4 ,
DOI : 10.1103/PhysRevE.80.041920
Global asymptotic stability for the disease free equilibrium for epidemiological models, Comptes Rendus Mathematique, vol.341, issue.7, p.341, 2005. ,
DOI : 10.1016/j.crma.2005.07.015
Networks and epidemic models, Journal of The Royal Society Interface, vol.2, issue.4, 2005. ,
DOI : 10.1098/rsif.2005.0051
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1578276
Small World Effect in an Epidemiological Model, Physical Review Letters, vol.86, issue.13, 2001. ,
DOI : 10.1103/PhysRevLett.86.2909
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
Stability Analysis of Nonlinear Systems, 1989. ,
DOI : 10.1007/978-3-319-27200-9
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. ,
Stability of nonautonomous systems, Nonlinear Analysis: Theory, Methods & Applications, vol.1, issue.1, pp.83-91, 1976. ,
DOI : 10.1016/0362-546X(76)90011-0
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
Spatiotemporal dynamics of epidemics: synchrony in metapopulation models, Mathematical Biosciences, vol.188, issue.1-2, pp.1-16, 2004. ,
DOI : 10.1016/j.mbs.2003.09.003
Spatial Heterogeneity in Epidemic Models, Journal of Theoretical Biology, vol.179, issue.1, 1996. ,
DOI : 10.1006/jtbi.1996.0042
Spatial Heterogeneity in Epidemic Models, Journal of Theoretical Biology, vol.179, issue.1, pp.1-11, 1996. ,
DOI : 10.1006/jtbi.1996.0042
Spatiotemporal dynamics of epidemics : synchrony in metapopulation models, Math Biosci, vol.188, pp.1-16, 2004. ,
Stochasticity and heterogeneity in host-vector models, J R Soc Interface, vol.4, issue.16, pp.851-863, 2007. ,
The theory of Island biogeography, 1967. ,
DOI : 10.1515/9781400881376
A biologic basis for integrated malaria control, Am J Trop Med Hyg, vol.67, pp.571-578, 2002. ,
Comparing epidemic tuberculosis in demographically distinct heterogeneous populations, Mathematical Biosciences, vol.180, issue.1-2, pp.161-185, 2002. ,
DOI : 10.1016/S0025-5564(02)00133-5
Mathematical Biology II : Spatial models and biomedical applications, Interdisciplinary Applied Mathematics, vol.18, 2003. ,
Analysis of weighted networks, Physical Review E, vol.70, issue.5, 1996. ,
DOI : 10.1103/PhysRevE.70.056131
Clustering and preferential attachment in growing networks, Physical Review E, vol.64, issue.2, 2001. ,
DOI : 10.1103/PhysRevE.64.025102
The Structure and Function of Complex Networks, SIAM Review, vol.45, issue.2, pp.167-256, 2003. ,
DOI : 10.1137/S003614450342480
Random graphs with arbitrary degree distributions and their applications, Physical Review E, vol.64, issue.2, p.64, 2001. ,
DOI : 10.1103/PhysRevE.64.026118
Epidemic Spreading in Scale-Free Networks, Physical Review Letters, vol.86, issue.14, 2001. ,
DOI : 10.1103/PhysRevLett.86.3200
Endemic disease in environments with spatially heterogeneous host populations, Mathematical Biosciences, vol.63, issue.2, pp.289-302, 1983. ,
DOI : 10.1016/0025-5564(82)90044-X
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
The prevention of malaria, 1911. ,
Periodicity and synchronization in blood-stage malaria infection, J. Math. Biol, 2010. ,
The effect of global travel on the spread of SARS, Mathematical Biosciences and Engineering, vol.3, issue.1, pp.205-218, 2006. ,
DOI : 10.3934/mbe.2006.3.205
A mathematical model for the global spread of influenza, Math Biosci, vol.75, issue.1, pp.3-22, 1985. ,
Continuous-time formulation of reaction-diffusion processes on heterogeneous metapopulations, Physical Review E, vol.78, issue.1, p.78, 2008. ,
DOI : 10.1103/PhysRevE.78.012902
Modelling the Spread of Infectious Diseases in Complex Metapopulations, Mathematical Modelling of Natural Phenomena, vol.5, issue.6, 2010. ,
DOI : 10.1051/mmnp/20105602
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
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
Relative stability and stability of closed sets, In Lect. Notes Math, vol.9, issue.2, pp.185-189, 1970. ,
DOI : 10.1007/BFb0059936
Global stabilization of nonlinear cascade systems, Systems & Control Letters, vol.14, issue.4 ,
DOI : 10.1016/0167-6911(90)90056-Z
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
Management of Tuberculosis in the United States, New England Journal of Medicine, vol.345, issue.3, pp.189-200, 2001. ,
DOI : 10.1056/NEJM200107193450307
Monotone dynamical systems. An introduction of the theory of competitive and cooperative systems, AMS, vol.41, 1995. ,
DOI : 10.1090/surv/041
An epidemiologic model of the incidence of acute illness in plasmodium falciparum malaria, Am J Trop Med Hyg, vol.75, issue.2, pp.56-62, 2006. ,
Global burden of tuberculosis ,
Tuberculosis, pathogenis, Protection and control, pp.47-59, 1994. ,
Mathematics in population biology Princeton Series in Theoretical and Computational Biology, 2003. ,
Models of spatio-temporal dynamics in malaria, Ecological Modelling, vol.104, issue.2-3, pp.231-240, 1997. ,
DOI : 10.1016/S0304-3800(97)00135-X
Analysis of the spread of tuberculosis in heterogeneous complex metapopulations complex metapopulations . under review : Mathematical and Computer Modelling, 2011. ,
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
matrix iterative analysis, 1962. ,
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
Threshold of disease transmission in a patch environment, Journal of Mathematical Analysis and Applications, vol.285, issue.1, pp.321-335, 2002. ,
DOI : 10.1016/S0022-247X(03)00428-1
An epidemic model in a patchy environment, Mathematical Biosciences, vol.190, issue.1, 2004. ,
DOI : 10.1016/j.mbs.2002.11.001
collective dynamics of 'small world' networks, Nature, vol.393, issue.6684, pp.440-442, 1998. ,
DOI : 10.1038/30918
1. S'il existe v > 0 tel que Av ? ?v alors ?(A) ? ? ,