E. J. Balder, On equivalence of strong and weak convergence inL 1-spaces under extreme point conditions, Israel Journal of Mathematics, vol.30, issue.1, pp.21-47, 1991.
DOI : 10.1007/978-3-642-88507-5

N. H. Barton and M. Turelli, Spatial Waves of Advance with Bistable Dynamics: Cytoplasmic and Genetic Analogues of Allee Effects, The American Naturalist, vol.178, issue.3, pp.48-75, 2011.
DOI : 10.1086/661246
URL : https://repository.ist.ac.at/554/1/BartonTurelli2011_copy.pdf

A. Braides, A handbook of ?-convergence, Handbook of Differential Equations: Stationary Partial Differential Equations, pp.101-213, 2006.

D. E. Campo-duarte, D. Cardona-salgado, and O. Vasilieva, Establishing wMelPop Wolbachia Infection among Wild Aedes aegypti Females by Optimal Control Approach, Applied Mathematics & Information Sciences, vol.11, issue.4, pp.1-17, 2017.
DOI : 10.18576/amis/110408

D. E. Campo-duarte, O. Vasilieva, D. Cardona-salgado, and M. Svinin, Optimal control approach for establishing wMelPop Wolbachia infection among wild Aedes aegypti populations, Journal of Mathematical Biology, vol.7, issue.58, pp.1907-1950, 2018.
DOI : 10.1186/1756-3305-7-58

C. Carrère, Optimization of an in vitro chemotherapy to avoid resistant tumours, Journal of Theoretical Biology, vol.413, pp.24-33, 2017.
DOI : 10.1016/j.jtbi.2016.11.009

E. Caspari and G. Watson, ON THE EVOLUTIONARY IMPORTANCE OF CYTOPLASMIC STERILITY IN MOSQUITOES, Evolution, vol.88, issue.4, pp.568-570, 1959.
DOI : 10.1111/j.1558-5646.1959.tb03045.x

M. H. Chan and P. S. Kim, Modelling a Wolbachia Invasion Using a Slow???Fast Dispersal Reaction???Diffusion Approach, Bulletin of Mathematical Biology, vol.137, issue.7144, pp.1501-1523, 2013.
DOI : 10.1017/S0950268809002040

R. Cominetti and J. Penot, Tangent sets to unilateral convex sets, C. R. Acad. Sci. Paris Sér. I Math, vol.321, issue.12, pp.1631-1636, 1995.

C. Curtis and T. Adak, Population replacement in culex fatigans by means of cytoplasmic incompatibility: 1. laboratory experiments with non-overlapping generations, Bulletin of the World Health Organization, vol.51, issue.3, pp.249-255, 1974.

G. L. Dutra, L. M. Santos, E. P. Caragata, J. B. Silva, D. A. Villela et al., From Lab to Field: The Influence of Urban Landscapes on the Invasive Potential of Wolbachia in Brazilian Aedes aegypti Mosquitoes, PLOS Neglected Tropical Diseases, vol.2, issue.Suppl 1, p.2015
DOI : 10.1371/journal.pntd.0003689.s003

J. Z. Farkas and P. Hinow, Structured and Unstructured Continuous Models for??Wolbachia Infections, Bulletin of Mathematical Biology, vol.42, issue.8, pp.2067-2088, 2010.
DOI : 10.1111/j.0014-3820.2005.tb01812.x
URL : https://link.springer.com/content/pdf/10.1007%2Fs11538-017-0386-y.pdf

A. Fenton, K. N. Johnson, J. C. Brownlie, and G. D. Hurst, , and a Natural Enemy, The American Naturalist, vol.178, issue.3, pp.333-342, 2011.
DOI : 10.1086/661247

D. A. Focks, D. G. Haile, E. Daniels, and G. A. Mount, Dynamic Life Table Model for Aedes aegypti (Diptera: Culicidae): Analysis of the Literature and Model Development, Journal of Medical Entomology, vol.30, issue.6, pp.1003-1017, 1993.
DOI : 10.1093/jmedent/30.6.1003

R. Fourer, AMPL : a modeling language for mathematical programming, Scientific Pr, 1996.
DOI : 10.1007/978-3-642-83724-1_12

E. Hairer, C. Lubich, and M. Roche, Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations, BIT, vol.18, issue.13, pp.678-700, 1988.
DOI : 10.1007/978-3-642-82175-2

M. Hertig and S. B. Wolbach, Studies on rickettsia-like micro-organisms in insects. The Journal of medical research, p.329, 1924.

M. W. Hirsch and H. Smith, Monotone dynamical systems In Handbook of differential equations: ordinary differential equations, volume II, pp.239-257, 2005.

A. A. Hoffmann, B. L. Montgomery, J. Popovici, I. Iturbe-ormaetxe, P. H. Johnson et al., Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission, Nature, vol.53, issue.7361, pp.476454-457, 1038.
DOI : 10.1603/ME09218

H. Hughes and N. F. Britton, Modelling the Use of Wolbachia to Control Dengue Fever Transmission, Bulletin of Mathematical Biology, vol.310, issue.5, pp.796-818, 2013.
DOI : 10.1126/science.1117607
URL : http://opus.bath.ac.uk/34502/1/bmbrevision.pdf

J. Lamboley, A. Laurain, G. Nadin, and Y. Privat, Properties of optimizers of the principal eigenvalue with indefinite weight and Robin conditions, Calculus of Variations and Partial Differential Equations, vol.38, issue.1, 2016.
DOI : 10.1093/biomet/38.1-2.196
URL : https://hal.archives-ouvertes.fr/hal-01295457

H. Laven, Eradication of Culex pipiens fatigans through Cytoplasmic Incompatibility, Nature, vol.177, issue.5113, pp.383-1967
DOI : 10.1038/216383a0

R. Lees, J. Gilles, J. Hendrichs, M. Vreysen, and K. Bourtzis, Back to the future: the sterile insect technique against mosquito disease vectors, Current Opinion in Insect Science, vol.10, issue.08, pp.156-162
DOI : 10.1016/j.cois.2015.05.011
URL : https://doi.org/10.1016/j.cois.2015.05.011

M. Otero, N. Schweigmann, and H. G. Solari, A Stochastic Spatial Dynamical Model for Aedes Aegypti, Bulletin of Mathematical Biology, vol.2, issue.1, pp.1297-325, 2008.
DOI : 10.1590/S0074-02762004000400002

J. G. Schraiber, A. N. Kaczmarczyk, R. Kwok, M. Park, R. Silverstein et al., Constraints on the use of lifespan-shortening Wolbachia to control dengue fever, Journal of Theoretical Biology, vol.297, pp.26-32, 2012.
DOI : 10.1016/j.jtbi.2011.12.006

M. Strugarek and N. Vauchelet, Reduction to a Single Closed Equation for 2-by-2 Reaction-Diffusion Systems of Lotka--Volterra Type, SIAM Journal on Applied Mathematics, vol.76, issue.5, pp.2060-2080, 2016.
DOI : 10.1137/16M1059217
URL : https://hal.archives-ouvertes.fr/hal-01264980

R. C. Thomé, H. M. Yang, and L. Esteva, Optimal control of Aedes aegypti mosquitoes by the sterile insect technique and insecticide, Mathematical Biosciences, vol.223, issue.1, pp.12-23, 2010.
DOI : 10.1016/j.mbs.2009.08.009

E. Trélat, J. Zhu, and E. Zuazua, Allee Optimal Control of a System in Ecology, Mathematical Models and Methods in Applied Sciences, vol.3, 2017.
DOI : 10.1090/btran/17

A. Wächter and L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Mathematical Programming, vol.10, issue.1, pp.25-57, 2006.
DOI : 10.1007/BFb0120945

J. H. Werren, L. Baldo, and M. E. Clark, Wolbachia: master manipulators of invertebrate biology, Nature Reviews Microbiology, vol.12, issue.10, pp.741-751, 2008.
DOI : 10.1099/ijs.0.64515-0