Issue
ESAIM: COCV
Volume 27, 2021
Special issue in honor of Enrique Zuazua's 60th birthday
Article Number 74
Number of page(s) 30
DOI https://doi.org/10.1051/cocv/2021070
Published online 13 July 2021
  1. L. Almeida, M. Duprez, Y. Privat and N. Vauchelet, Mosquito population control strategies for fighting against arboviruses. Math. Biosci. Eng. 16 (2019) 6274. [CrossRef] [PubMed] [Google Scholar]
  2. L. Almeida, Y. Privat, M. Strugarek and N. Vauchelet, Optimal releases for population replacement strategies: application to wolbachia. SIAM J. Math. Anal. 51 (2019) 3170–3194. [Google Scholar]
  3. L. Almeida, A. Haddon, C. Kermorvant, A. Léculier, Y. Privat, M. Strugarek, N. Vauchelet and J.P. Zubelli, Optimal release of mosquitoes to control dengue transmission. ESAIM: Procs 67 (2020) 16–29. [EDP Sciences] [Google Scholar]
  4. N.H. Barton and M. Turelli, Spatial waves of advance with bistable dynamics: cytoplasmic and genetic analogues of Allee effects. Am. Natur. 178 (2011) E48–E75. [Google Scholar]
  5. L. Beal, D. Hill, R. Martin and J. Hedengren, Gekko optimization suite. Processes 6 (2018) 106. [Google Scholar]
  6. P.-A. Bliman, Feedback control principles for biological control of dengue vectors. 18th European Control Conference (ECC), arXiv preprint arXiv:1903.00730 (2019). [Google Scholar]
  7. K. Bourtzis, Wolbachia-based technologies for insect pest population control, in Transgenesis and the management of vector-borne disease. Springer (2008) 104–113. [Google Scholar]
  8. 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. J. Math. Biol. 76 (2018) 1907–1950. [CrossRef] [PubMed] [Google Scholar]
  9. E.D. Conway and J.A. Smoller, A comparison technique for systems of reaction-diffusion equations. Commun. Partial Differ. Equ. 2 (1977) 679–697. [Google Scholar]
  10. G.L.C. Dutra, L.M.B. dos Santos, E.P. Caragata, J.B.L. Silva, D.A.M. Villela, R. Maciel-de Freitas and L. Andrade Moreira, From Lab to Field: the influence of urban landscapes on the invasive potential of Wolbachia in Brazilian Aedes aegypti mosquitoes. PLoS Negl Trop Dis 9 (2015). [Google Scholar]
  11. V.A. Dyck, J. Hendrichs and A. Robinson, Sterile insect technique: principles and practice in area-wide integrated pest management. Springer (2006). [Google Scholar]
  12. L.C. Evans, Vol. 19 of Partial differential equations. American Mathematical Society (AMS), Providence, RI (2010), 2nd edn. [Google Scholar]
  13. J.Z. Farkas and P. Hinow, Structured and unstructured continuous models for wolbachia infections. Bull. Math. Biol. 72 (2010) 2067–2088. [CrossRef] [PubMed] [Google Scholar]
  14. A. Fenton, K.N. Johnson, J.C. Brownlie and G.D.D. Hurst, Solving the wolbachia paradox: modeling the tripartite interaction between host, wolbachia, and a natural enemy. Am. Natur. 178 (2011) 333–342. [Google Scholar]
  15. 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. J. Med. Entomol. 30 (1993) 1003–1017. [Google Scholar]
  16. G. Fu, R. Lees, D. Nimmo, D. Aw, L. Jin, P. Gray, T. Berendonk, H. White-Cooper, S. Scaife, H.K. Phuc, et al., Female-specific flightless phenotype for mosquito control. Proc. Natl. Acad. Sci. 107 (2010) 4550–4554. [Google Scholar]
  17. J. Heinrich and M. Scott, A repressible female-specific lethal genetic system for making transgenic insect strains suitable for a sterile-release program. Proc. Natl. Acad. Sci. 97 (2000) 8229–8232. [Google Scholar]
  18. J.-B. Hiriart-Urruty and C. Lemaréchal, Convex analysis and minimization algorithms. I. Vol. 305 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin (1993). Fundamentals. [Google Scholar]
  19. H. Hughes and N.F. Britton, Modelling the use of wolbachia to control dengue fever transmission. Bull. Math. Biol. 75 (2013) 796–818. [CrossRef] [PubMed] [Google Scholar]
  20. K. Le Balc’h Null-controllability of two species reaction-diffusion system with nonlinear coupling: a new duality method. SIAM J. Control Optim. 57 (2019) 2541–2573. [Google Scholar]
  21. X.J. Li and J.M. Yong, Necessary conditions for optimal control of distributed parameter systems. SIAM J. Control Optim. 29 (1991) 895–908. [Google Scholar]
  22. I. Mazari, D. Ruiz-Balet and E. Zuazua, Constrained control of bistable reaction-diffusion equations: gene-flow and spatially heterogeneous models. Preprint (2020). [Google Scholar]
  23. I. Mazari, G. Nadin and A.I. Toledo Marrero Optimization of the total population size with respect to the initial condition in reaction-diffusion equations. Work inprogress (2021). [Google Scholar]
  24. T.Y. Miyaoka, S. Lenhart and J.F.C.A. Meyer, Optimal control of vaccination in a vector-borne reaction–diffusion model applied to zika virus. J. Math. Biol. 79 (2019) 1077–1104. [CrossRef] [PubMed] [Google Scholar]
  25. G. Nadin and A.I. Toledo Marrero On the maximization problem for solutions of reaction-diffusion equations with respect to their initial data. Math. Model. Nat. Phenom. 15 (2020) 71. [Google Scholar]
  26. T. Ouyang and J. Shi, Exact multiplicity of positive solutions for a class of semilinear problem II. J. Differ. Equ. 158 (1999) 94–151. [Google Scholar]
  27. B. Perthame, Parabolic equations in biology. Growth, reaction, movement and diffusion. Springer, Cham (2015). [Google Scholar]
  28. J. Schraiber, A. Kaczmarczyk, R. Kwok, M. Park, R. Silverstein, F. Rutaganira, T. Aggarwal, M. Schwemmer, C. Hom, R. Grosberg, et al., Constraints on the use of lifespan-shortening Wolbachia to control dengue fever. J. Theor. Biol. 297 (2012) 26–32. [CrossRef] [PubMed] [Google Scholar]
  29. J. Simon, Compact sets in the space Lp(0, T; B). Ann. Mat. Pura Appl. 146 (1987) 65–96. [Google Scholar]
  30. S. Sinkins, Wolbachia and cytoplasmic incompatibility in mosquitoes. Insect Biochem. Mol. Biol. 34 (2004) 723–729. [CrossRef] [PubMed] [Google Scholar]
  31. B. Stoll, H. Bossin, H. Petit, J. Marie and M.A. Cheong Sang Suppression of an isolated population of the mosquito vector aedes polynesiensis on the atoll of tetiaroa, french polynesia, by sustained release of wolbachia-incompatible male mosquitoes. In Conference: ICE - XXV International Congress of Entomology, At Orlando, Florida, USA (2016). [Google Scholar]
  32. M. Strugarek and N. Vauchelet, Reduction to a single closed equation for 2-by-2 reaction-diffusion systems of Lotka-Volterra type. SIAM J. Appl. Math. 76 (2016) 2060–2080. [Google Scholar]
  33. M. Strugarek, N. Vauchelet and J.P. Zubelli, Quantifying the survival uncertainty of wolbachia-infected mosquitoes in a spatial model. Math. Biosci. Eng. 15 (2018) 961–991. [CrossRef] [PubMed] [Google Scholar]
  34. D. Thomas, C. Donnelly, R. Wood and L. Alphey, Insect population control using a dominant, repressible, lethal genetic system. Science 287 (2000) 2474–2476. [CrossRef] [PubMed] [Google Scholar]
  35. A. Wächter and L. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Progr. 106 (2006) 25–57. [CrossRef] [MathSciNet] [Google Scholar]
  36. T.J.P.H. Walker, P.H. Johnson, L.A. Moreira, I. Iturbe-Ormaetxe, F.D. Frentiu, C.J. McMeniman, Y.S. Leong, Y. Dong, J. Axford, P. Kriesner, et al., The wmel wolbachia strain blocks dengue and invades caged aedes aegypti populations. Nature 476 (2011) 450. [CrossRef] [PubMed] [Google Scholar]
  37. H.F. Weinberger, Invariant sets for weakly coupled parabolic and elliptic systems. Rend. Mat. 8 (1975) 295–310. [Google Scholar]
  38. J. Werren, L. Baldo and M. Clark, Wolbachia: master manipulators of invertebrate biology. Nat. Rev. Microbiol. 6 (2008) 741. [CrossRef] [PubMed] [Google Scholar]
  39. X. Zheng et al., Incompatible and sterile insect techniques combined eliminate mosquitoes. Nature 572 (2019) 56–61. [CrossRef] [PubMed] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.