M. H. Biswas, L. T. Paiva, and M. D. De-pinho, A SEIR model for control of infectious diseases with constraints, Mathematical Biosciences and Engineering, vol.11, issue.4, 2014.
DOI : 10.3934/mbe.2014.11.761

URL : https://hal.archives-ouvertes.fr/hal-01067316

C. Büskens and H. Maurer, SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control, Journal of Computational and Applied Mathematics, vol.120, issue.1-2, pp.85-108, 2000.
DOI : 10.1016/S0377-0427(00)00305-8

F. Clarke, Optimization and Nonsmooth Analysis, 1983.
DOI : 10.1137/1.9781611971309

F. Clarke, Functional Analysis, Calculus of Variations and Optimal Control
DOI : 10.1007/978-1-4471-4820-3

URL : https://hal.archives-ouvertes.fr/hal-00865914

F. Clarke and M. De-pinho, Optimal Control Problems with Mixed Constraints, SIAM Journal on Control and Optimization, vol.48, issue.7, pp.4500-4524, 2010.
DOI : 10.1137/090757642

URL : https://hal.archives-ouvertes.fr/hal-00863285

P. Van-den-driessche, Some epidemiologocal models with delays, Dept. of Mathematics and Statistics, 1994.

P. Falugi, E. Kerrigan, and E. Van-wyk, Imperial College London Optimal Control Software User Guide (ICLOCS), 2010.

R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL: A Modeling Language for Mathematical Programming, 1993.

H. Gaff and E. Schaefer, Optimal control applied to vaccination and treatment strategies for various epidemiological models, Mathematical Bioscieneces and Engineering, vol.6, pp.469-492, 2009.

G. N. Galbraith and R. B. Vinter, Lipschits continuity of optimal controls for state constrained problems, SIAM J. Control Optimization, pp.42-1727, 2003.

R. F. Hartl, S. P. Sethi, and R. G. Vickson, A Survey of the Maximum Principles for Optimal Control Problems with State Constraints, SIAM Review, vol.37, issue.2, pp.181-218, 1995.
DOI : 10.1137/1037043

M. R. Hestenes, Calculus of Variations and Optimal Control Theory, 1980.

H. W. Hethcote, , PARAMETER ESTIMATION, AND APPLICATIONS, In: Mathematical Understanding of Infectious Disease Dynamics, vol.16, issue.1, pp.1-61, 2008.
DOI : 10.1142/9789812834836_0001

D. Kirschner, S. Lenhart, and S. Serbin, Optimal control of the chemotherapy of HIV, Journal of Mathematical Biology, vol.35, issue.7, pp.775-792, 1996.
DOI : 10.1007/s002850050076

U. Ledzewicz and H. Schättler, On optimal singular control for a general SIR?model with vaccination and treatment, Discrete and Continuous Dynamical Systems, pp.981-990

S. Lenhart and J. T. Workman, Optimal Control Applied to Biological Models, 2007.

H. Maurer, On Optimal Control Problems with Bounded State Variables and Control Appearing Linearly, SIAM Journal on Control and Optimization, vol.15, issue.3, pp.345-362, 1977.
DOI : 10.1137/0315023

H. Maurer, On the Minimum Principle for optimal control problems with state constraints, 1979.

H. Maurer, C. Büskens, J. R. Kim, and Y. Kaya, Optimization methods for the verification of second order sufficient conditions for bang-bang controls, Optimal Control Applications and Methods, vol.191, issue.3, pp.129-156, 2005.
DOI : 10.1002/oca.756

H. Maurer and N. P. Osmolovskii, Second-order conditions for optimal control problems with mixed control-state constraints and control appearing linearly, 52nd IEEE Conference on Decision and Control, pp.514-519, 2013.
DOI : 10.1109/CDC.2013.6759933

URL : https://hal.archives-ouvertes.fr/hal-01067546

H. Maurer and S. Pickenhain, Second-order sufficient conditions for control problems with mixed control-state constraints, Journal of Optimization Theory and Applications, vol.32, issue.3, pp.649-667, 1995.
DOI : 10.1007/BF02192163

H. Maurer and G. Vossen, Sufficient Conditions and Sensitivity Analysis for Optimal Bang-Bang Control Problems with State Constraints, Proceedings of the 23rd IFIP Conference on System Modeling and Optimization, pp.82-99, 2009.
DOI : 10.1007/s10107-004-0559-y

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.515.3534

R. M. Neilan and S. Lenhart, An Introduction to Optimal Control with an Application in Disease Modeling, DIMACS Series in Discrete Mathematics, pp.75-67, 2010.

N. P. Osmolovskii and H. Maurer, Applications to Regular and Bang-Bang Control: Second- Order Necessary and Sufficient Optimality Conditions in Calculus of Variations and Optimal Control, SIAM Advances in Design and Control, 2013.
DOI : 10.1137/1.9781611972368

L. T. Paiva, Optimal Control in Constrained and Hybrid Nonlinear Systems, 2013.

L. S. Pontryagin, V. G. Boltyanski, R. V. Gramkrelidze, and E. F. Miscenko, The Mathematical Theory of Optimal Processes, 1964.

H. Schaettler and U. Ledzewicz, Geometric Optimal Control. Theory, Methods and Examples

H. Schaettler, U. Ledzewicz, and H. Maurer, Sufficient conditions for strong local optimality in optimal control problems with L2-type objectives and control constraints Discrete and Continuous Dynamical Systems -Series B, pp.2657-2679, 2014.

C. J. Silva and D. F. Torres, Optimal control strategies for tubercolosis treatment: A case study in Angola, Numerical Algebra, Control and Optimization, vol.2, issue.3, pp.601-617, 2010.

A. Wächter and L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Mathematical Programming, pp.25-57, 2006.