A. Abdelhedi, D. Boutat, L. Sbita, and R. Tami, Extended observer to estimate the spreading of contagious disease, 2014 European Control Conference (ECC), pp.1843-1848, 2014.
DOI : 10.1109/ECC.2014.6862172

A. Abdelhedi, D. Boutat, L. Sbita, R. Tami, and D. Liu, Observer design for a class of nonlinear piecewise systems. Application to an epidemic model with treatment, Mathematical Biosciences, vol.271, pp.128-135, 2016.
DOI : 10.1016/j.mbs.2015.11.002

M. Alonso-quesada, R. P. De-la-sen, A. Agarwal, and . Ibeas, An observer-based vaccination control law for an SEIR epidemic model based on feedback linearization techniques for nonlinear systems, Advances in Difference Equations, vol.2012, issue.1, p.2012161, 2012.
DOI : 10.1016/j.jprocont.2010.02.007

J. Alvarez-ramirez, M. Meraz, and J. X. Velasco-hernandez, FEEDBACK CONTROL OF THE CHEMOTHERAPY OF HIV, International Journal of Bifurcation and Chaos, vol.43, issue.09, pp.2207-2219, 2000.
DOI : 10.1006/jtbi.1997.0622

R. M. Anderson and R. M. May, Infectious Diseases of Humans. Dynamics and Control. Oxford science publications, 1991.

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. S. Aronna and P. Bliman, Interval observer for uncertain time-varying SIR-SI model of vector-borne disease URL https, Proc. of European Control Conference, 2018.

S. Audoly, L. D. Angio, M. P. Saccomani, and C. Cobelli, Global identifiability of linear compartmental models-a computer algebra algorithm, IEEE Transactions on Biomedical Engineering, vol.45, issue.1, pp.36-47, 1998.
DOI : 10.1109/10.650350

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

S. Estimators, . Some, and . Systems,

N. G. Becker, Analysis of infectious disease data, 1989.

G. Besançon, Nonlinear observers and applications. Papers based on the presentations at the 28th Grenoble international summer school on control, Lecture Notes in Control and Information Sciences, vol.363, issue.224, 2007.

D. Bichara, N. Cozic, and A. Iggidr, On the estimation of sequestered infected erythrocytes in <em>Plasmodium falciparum</em> malaria patients, Mathematical Biosciences and Engineering, vol.11, issue.4, pp.741-759, 2014.
DOI : 10.3934/mbe.2014.11.741

O. N. Bjørnstad, B. F. Finkenstädt, and B. T. , Dynamics of Measles Epidemics: Estimating Scaling of Transmission Rates Using a Time Series SIR Model, Ecological Monographs, vol.72, issue.2, pp.169-184, 2002.
DOI : 10.2307/3100023

P. Bliman and B. Barros, Interval Observers for SIR Epidemic Models Subject to Uncertain Seasonality, Positive systems, pp.31-39, 2017.
DOI : 10.1007/BF00163027

URL : https://hal.archives-ouvertes.fr/hal-01567474

P. Bliman, D. Efimov, and R. Ushirobira, A class of nonlinear adaptive observers for sir epidemic model, Proc. of European Control Conference, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01724989

V. Capasso and V. Capasso, Mathematical structures of epidemic systems, 1993.
DOI : 10.1007/978-3-540-70514-7

S. Cauchemez and N. M. Ferguson, Likelihood-based estimation of continuous-time epidemic models from time-series data: application to measles transmission in London, Journal of The Royal Society Interface, vol.274, issue.1609, pp.885-897, 2008.
DOI : 10.1098/rspb.2006.3754

S. Cauchemez, F. Carrat, C. Viboud, A. Valleron, and P. Boelle, A Bayesian MCMC approach to study transmission of influenza: application to household longitudinal data, Statistics in Medicine, vol.28, issue.22, pp.3469-3487, 2004.
DOI : 10.1002/sim.1912

W. , Dichotomies in Stability Theory, Lecture Notes in Mathematics, vol.629, 1978.

M. De-la-sen, A. Ibeas, and S. Alonso-quesada, Observer-based vaccination strategy for a true mass action SEIR epidemic model with potential estimation of all the populations. Discrete Dyn, Nat. Soc, vol.743067, issue.19, 2011.

M. Diaby, A. Iggidr, and M. Sy, Observer design for a schistosomiasis model, Mathematical Biosciences, vol.269, pp.17-29, 2015.
DOI : 10.1016/j.mbs.2015.08.008

URL : https://hal.archives-ouvertes.fr/hal-00758712

O. Diekmann and J. Heesterbeek, Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. Wiley series in mathematical and computational biology, 2000.

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

C. Drakeley, P. Corran, P. Coleman, J. Tongren, S. Mcdonald et al., Estimating medium- and long-term trends in malaria transmission by using serological markers of malaria exposure, Proceedings of the National Academy of Sciences of the United States of America, pp.5108-5113, 2005.
DOI : 10.1007/s00436-003-1009-0

URL : http://www.pnas.org/content/102/14/5108.full.pdf

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

B. F. Finkenstädt and B. T. , Time series modelling of childhood diseases: a dynamical systems approach, Journal of the Royal Statistical Society: Series C (Applied Statistics), vol.49, issue.2, pp.187-205, 2000.
DOI : 10.1111/1467-9876.00187

D. Fisman, E. Khoo, and A. Tuite, Early Epidemic Dynamics of the West African 2014 Ebola Outbreak: Estimates Derived with a Simple Two-Parameter Model, PLoS Currents, 2014.
DOI : 10.1371/currents.outbreaks.89c0d3783f36958d96ebbae97348d571

J. Gauthier, H. Hammouri, and S. Othman, A simple observer for nonlinear systems applications to bioreactors, IEEE Transactions on Automatic Control, vol.37, issue.6, pp.875-880, 1992.
DOI : 10.1109/9.256352

P. Gérardin, V. Guernier, J. Perrau, A. Fianu, K. Le-roux et al., Estimating Chikungunya prevalence in La R??union Island outbreak by serosurveys: Two methods for two critical times of the epidemic, BMC Infectious Diseases, vol.213, issue.4, p.1, 2008.
DOI : 10.1016/j.mbs.2008.02.008

A. Guiro, A. Iggidr, D. Ngom, and H. Touré, On the stock estimation for some fishery systems, Reviews in Fish Biology and Fisheries, vol.60, issue.12, pp.313-327, 2009.
DOI : 10.3934/mbe.2008.5.337

URL : https://hal.archives-ouvertes.fr/inria-00595295

H. Guo, M. Y. Li, and Z. Shuai, Global stability of the endemic equilibrium of multigroup SIR epidemic models, Can. Appl. Math. Q, vol.14, issue.3, pp.259-284, 2006.

H. Guo, M. Y. Li, and Z. Shuai, A graph-theoretic approach to the method of global Lyapunov functions, Proceedings of the American Mathematical Society, vol.136, issue.08, pp.2793-2802, 2008.
DOI : 10.1090/S0002-9939-08-09341-6

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

A. Ibeas, M. De-la-sen, S. Alonso-quesada, and I. Zamani, Stability analysis and observer design for discrete-time SEIR epidemic models, Advances in Difference Equations, vol.39, issue.1, p.2015122, 2015.
DOI : 10.1080/00207720701683033

URL : https://advancesindifferenceequations.springeropen.com/track/pdf/10.1186/s13662-015-0459-x?site=advancesindifferenceequations.springeropen.com

A. Iggidr, Encyclopedia of Life Support Systems (EOLSS), chapter Controllability, Observability and Stability of Mathematical Models, 2004.

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

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

H. Inaba, Threshold and stability results for an age-structured epidemic model, Journal of Mathematical Biology, vol.28, issue.4, pp.411-434, 1990.
DOI : 10.1007/BF00178326

J. A. Jacquez and P. Greif, Numerical parameter identifiability and estimability: Integrating identifiability, estimability, and optimal sampling design, Mathematical Biosciences, vol.77, issue.1-2, pp.201-227, 1985.
DOI : 10.1016/0025-5564(85)90098-7

J. A. Jacquez, Compartmental analysis in biology and medicine, 1985.

L. Joseph, T. W. Gyorkos, and L. Coupal, Bayesian Estimation of Disease Prevalence and the Parameters of Diagnostic Tests in the Absence of a Gold Standard, American Journal of Epidemiology, vol.141, issue.3, pp.263-272, 1995.
DOI : 10.1093/oxfordjournals.aje.a117428

B. Kågström, Bounds and perturbation bounds for the matrix exponential, BIT, vol.7, issue.5, pp.39-57, 1977.
DOI : 10.1007/BF01932398

M. J. Keeling and P. Rohani, Modeling infectious diseases in humans and animals, 2008.

W. O. Kermack and A. G. Mckendrick, A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences, pp.700-721, 1927.

T. Kuniya, Global stability analysis with a discretization approach for an age-structured multigroup SIR epidemic model, Nonlinear Analysis: Real World Applications, vol.12, issue.5, pp.2640-2655, 2011.
DOI : 10.1016/j.nonrwa.2011.03.011

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

A. L. Lloyd, The dependence of viral parameter estimates on the assumed viral life cycle: limitations of studies of viral load data, Proceedings of the Royal Society B: Biological Sciences, vol.268, issue.1469, pp.847-854, 1469.
DOI : 10.1098/rspb.2000.1572

D. G. Luenberger, An introduction to observers, IEEE Transactions on Automatic Control, vol.16, issue.6, pp.16596-602, 1971.
DOI : 10.1109/TAC.1971.1099826

H. Nishiura, Mathematical and statistical analyses of the spread of dengue, Dengue Bulletin, vol.30, pp.51-67, 2006.

P. Pongsumpun and I. Tang, Transmission of dengue hemorrhagic fever in an age structured population, Mathematical and Computer Modelling, vol.37, issue.9-10, pp.9-10949, 2003.
DOI : 10.1016/S0895-7177(03)00111-0

R. C. Reiner, T. A. Perkins, C. M. Barker, T. Niu, and L. ,

A. George, J. R. Le-menach, D. Pulliam, C. Bisanzio, C. Buckee et al., A systematic review of mathematical models of mosquito-borne pathogen transmission, Journal of The Royal Society Interface, issue.81, pp.1970-2010

F. Rocha, M. Aguiar, M. O. Souza, and N. Stollenwerk, Time-scale separation and center manifold analysis describing vector-borne disease dynamics, International Journal of Computer Mathematics, issue.10, pp.902105-2125, 2013.

R. Ross, The prevention of malaria, 1911.

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

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, pp.1269-1293, 2014.
DOI : 10.1017/S0950268809002040

R. Tami, D. Boutat, and G. Zheng, Extended output depending normal form, Automatica, vol.49, issue.7, pp.2192-2198, 2013.
DOI : 10.1016/j.automatica.2013.03.025

URL : https://hal.archives-ouvertes.fr/hal-00817332

R. Tami, D. Boutat, G. Zheng, and F. Kratz, Parameters and states estimation for Dengue epidemic model, 2014 European Control Conference (ECC), pp.528-533, 2014.
DOI : 10.1109/ECC.2014.6862173

URL : https://hal.archives-ouvertes.fr/hal-01094912

T. Toni, D. Welch, N. Strelkowa, A. Ipsen, and M. P. Stumpf, Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems, Journal of The Royal Society Interface, vol.24, issue.6, pp.187-202, 2009.
DOI : 10.1093/bioinformatics/btm607

S. Towers, O. Patterson-lomba, and C. Castillo-chavez, Temporal Variations in the Effective Reproduction Number of the 2014 West Africa Ebola Outbreak, PLoS Currents, 2014.
DOI : 10.1371/currents.outbreaks.9e4c4294ec8ce1adad283172b16bc908

J. X. Velasco-hernández, J. A. García, and D. Kirschner, Remarks on modeling hostviral dynamics and treatment Mathematical approaches for emerging and reemerging infectious diseases: An introduction, Proceedings of a tutorial Introduction to epidemiology and immunology, pp.287-308, 2002.

W. Wonham, Linear multivariable control: a geometric approach, 1979.
DOI : 10.1007/978-1-4684-0068-7