]. L. Alp14 and . Alphey, Genetic Control of Mosquitoes, Annual Review of Entomology, vol.59, issue.1, pp.205-224, 2014.

. S. Bagdg-+-13-]-m, C. Blagrove, C. D. Arias-goeta, A. Genua, S. P. Failloux et al., A Wolbachia w Mel Transinfection in Aedes albopictus Is Not Detrimental to Host Fitness and Inhibits Chikungunya Virus, PLoS Neglected Tropical Diseases, vol.7, issue.3, p.2152, 2013.

]. S. Bgb-+-13, P. W. Bhatt, O. J. Gething, J. P. Brady, A. W. Messina et al., The global distribution and burden of dengue Adaptation, speciation and hybrid zones, Nature Nature, vol.496, issue.341, pp.504-507497, 1989.

S. [. Barton and . Rouhani, THE PROBABILITY OF FIXATION OF A NEW KARYOTYPE IN A CONTINUOUS POPULATION, Evolution, vol.28, issue.3, pp.499-517, 1991.
DOI : 10.1073/pnas.72.12.5061

M. [. Barton and . 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

P. [. Chan and . 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. Cms-+-11-]-p, J. W. Crain, E. Mains, Y. Suh, P. H. Huang et al., Wolbachia infections that reduce immature insect survival: Predicted impacts on population replacement, BMC Evolutionary Biology, vol.11, issue.1, pp.1-10, 2011.

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

Y. Du and H. Matano, Convergence and sharp thresholds for propagation in nonlinear diffusion problems, Journal of the European Mathematical Society, vol.12, pp.279-312, 2010.
DOI : 10.4171/JEMS/198

A. [. Erd?-os, ]. A. Rényifjbh11, K. N. Fenton, J. C. Johnson, G. D. Brownlie et al., On a classical problem of probability theory Solving the Wolbachia paradox: modeling the tripartite interaction between host, Wolbachia, and a natural enemy, Magyar Tudományos Akadémia Matematikai Kutató Intézetének Közleményei, pp.215-220333, 1961.

N. [. Hughes and . 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

H. [. Hancock and . Godfray, Modelling the spread of Wolbachia in spatially heterogeneous environments, Journal of The Royal Society Interface, vol.178, issue.3, 2012.
DOI : 10.1086/661247

]. P. Hsg11a, S. P. Hancock, H. C. Sinkins, and . Godfray, Population dynamic models of the spread of Wolbachia, The American Naturalist, vol.177, issue.3, pp.323-333, 2011.

P. A. Hancock, S. P. Sinkins, H. C. Godfrayjoh15-]-k, and . Johnson, Strategies for Introducing Wolbachia to Reduce Transmission of Mosquito-Borne Diseases, The Impact of Wolbachia on Virus Infection in Mosquitoes. Viruses, pp.1-105705, 2011.
DOI : 10.1371/journal.pntd.0001024.s008

M. [. Jansen, H. C. Turelli, and . Godfray, Stochastic spread of Wolbachia, Proceedings of the Royal Society B: Biological Sciences, vol.13, issue.7, pp.2752769-2776, 1652.
DOI : 10.1111/j.1365-294X.2004.02203.x

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2605827

]. R. Mdfsscldo10, R. Maciel-de-freitas, C. T. Souza-santos, R. Codeço, . Lourenço-de et al., Influence of the spatial distribution of human hosts and large size containers on the dispersal of the mosquito Aedes aegypti within the first gonotrophic cycle, Medical and Veterinary Entomology, vol.24, pp.74-82, 2010.

[. Matano and P. Polá?ik, Dynamics of nonnegative solutions of one-dimensional reaction???diffusion equations with localized initial data. Part I: A general quasiconvergence theorem and its consequences, Communications in Partial Differential Equations, vol.4, issue.5, pp.785-811, 2016.
DOI : 10.1090/S0894-0347-05-00504-7

X. [. Muratov and . Zhong, Threshold phenomena for symmetric-decreasing radial solutions of reaction-diffusion equations. Discrete and Continuous Dynamical Systems, pp.915-944, 2017.

T. Ouyang and J. Shi, Exact Multiplicity of Positive Solutions for a Class of Semilinear Problems, Journal of Differential Equations, vol.146, issue.1, pp.121-156, 1998.
DOI : 10.1006/jdeq.1998.3414

T. Ouyang and J. Shi, Exact multiplicity of positive solutions for a class of semilinear problem, II, Journal of Differential Equations, vol.158, issue.1, pp.94-151, 1999.
DOI : 10.1016/S0022-0396(99)80020-5

N. [. Otero, H. G. Schweigmann, and . 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

]. P. Pol11 and . Polacik, Threshold solutions and sharp transitions for nonautonomous parabolic equations on R N . Archive for Rational Mechanics and Analysis Speciation and the " Shifting Balance " in a continuous population, Theoretical Population Biology, vol.199, issue.31, pp.69-97465, 1987.

N. [. Strugarek and . 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

]. M. Tur10 and . Turelli, Cytoplasmic incompatibility in populations with overlapping generations, Evolution, vol.64, issue.1, pp.232-241, 2010.

S. [. Vavre and . Charlat, Making (good) use of Wolbachia: what the models say, Current Opinion in Microbiology, vol.15, issue.3, pp.263-268, 2012.
DOI : 10.1016/j.mib.2012.03.005

URL : https://hal.archives-ouvertes.fr/hal-00763517

. A. Vcf-+-15-]-d, C. T. Villela, F. Codeço, G. A. Figueiredo, R. Garcia et al., A Bayesian Hierarchical Model for Estimation of Abundance and Spatial Density of Aedes aegypti, PLoS ONE, vol.10, issue.4, p.2015

]. T. Wjm-+-11, P. H. Walker, L. A. Johnson, I. Moreira, F. D. Iturbe-ormaetxe et al., The w Mel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations, Nature, issue.7361, pp.476450-453, 2011.

H. L. Yeap, P. Mee, T. Walker, A. R. Weeks, S. L. O-'neill et al., Dynamics of the "Popcorn" Wolbachia Infection in Outbred Aedes aegypti Informs Prospects for Mosquito Vector Control, Dynamics of the " Popcorn " Wolbachia Infection in Outbred Aedes aegypti Informs Prospects for Mosquito Vector Control, pp.583-595, 2011.
DOI : 10.1534/genetics.110.122390

. L. Yreh-+-16-]-h, G. Yeap, N. M. Rasic, S. F. Endersby-harshman, E. Lee et al., Mitochondrial DNA variants help monitor the dynamics of Wolbachia invasion into host populations, Heredity, vol.116, issue.3, pp.265-276, 2016.

]. A. Zla06 and . Zlatos, Sharp transition between extinction and propagation of reaction, J. Amer. Math. Soc, vol.19, pp.251-263, 2006.