Buttazzo, G. ; Casas, E. ; de Teresa, L. ; Glowinski, R. ; Leugering, G. ; Trélat, E. ; Zhang, X.(éd.)
In this article, we are interested in the analysis and simulation of solutions to an optimal control problem motivated by population dynamics issues. In order to control the spread of mosquito-borne arboviruses, the population replacement technique consists in releasing into the environment mosquitoes infected with the Wolbachia bacterium, which greatly reduces the transmission of the virus to the humans. Spatial releases are then sought in such a way that the infected mosquito population invades the uninfected mosquito population. Assuming very high mosquito fecundity rates, we first introduce an asymptotic model on the proportion of infected mosquitoes and then an optimal control problem to determine the best spatial strategy to achieve these releases. We then analyze this problem, including the optimality of natural candidates and carry out first numerical simulations in one dimension of space to illustrate the relevance of our approach.
Keywords: Reaction-diffusion equation, optimal control, second order optimality conditions
@article{COCV_2021__27_1_A76_0,
author = {Duprez, Michel and H\'elie, Romane and Privat, Yannick and Vauchelet, Nicolas},
editor = {Buttazzo, G. and Casas, E. and de Teresa, L. and Glowinski, R. and Leugering, G. and Tr\'elat, E. and Zhang, X.},
title = {Optimization of spatial control strategies for population replacement, application to {\protect\emph{Wolbachia}}},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021070},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021070/}
}
TY - JOUR AU - Duprez, Michel AU - Hélie, Romane AU - Privat, Yannick AU - Vauchelet, Nicolas ED - Buttazzo, G. ED - Casas, E. ED - de Teresa, L. ED - Glowinski, R. ED - Leugering, G. ED - Trélat, E. ED - Zhang, X. TI - Optimization of spatial control strategies for population replacement, application to Wolbachia JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021070/ DO - 10.1051/cocv/2021070 LA - en ID - COCV_2021__27_1_A76_0 ER -
%0 Journal Article %A Duprez, Michel %A Hélie, Romane %A Privat, Yannick %A Vauchelet, Nicolas %E Buttazzo, G. %E Casas, E. %E de Teresa, L. %E Glowinski, R. %E Leugering, G. %E Trélat, E. %E Zhang, X. %T Optimization of spatial control strategies for population replacement, application to Wolbachia %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021070/ %R 10.1051/cocv/2021070 %G en %F COCV_2021__27_1_A76_0
Duprez, Michel; Hélie, Romane; Privat, Yannick; Vauchelet, Nicolas. Optimization of spatial control strategies for population replacement, application to Wolbachia. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 74. doi: 10.1051/cocv/2021070
[1] , , and , Mosquito population control strategies for fighting against arboviruses. Math. Biosci. Eng. 16 (2019) 6274.
[2] , , and , Optimal releases for population replacement strategies: application to wolbachia. SIAM J. Math. Anal. 51 (2019) 3170–3194.
[3] , , , , , , and , Optimal release of mosquitoes to control dengue transmission. ESAIM: Procs 67 (2020) 16–29.
[4] and , Spatial waves of advance with bistable dynamics: cytoplasmic and genetic analogues of Allee effects. Am. Natur. 178 (2011) E48–E75.
[5] , , and , Gekko optimization suite. Processes 6 (2018) 106.
[6] , Feedback control principles for biological control of dengue vectors. 18th European Control Conference (ECC), arXiv preprint (2019). | arXiv
[7] , Wolbachia-based technologies for insect pest population control, in Transgenesis and the management of vector-borne disease. Springer (2008) 104–113.
[8] , , and , Optimal control approach for establishing wmelpop wolbachia infection among wild aedes aegypti populations. J. Math. Biol. 76 (2018) 1907–1950.
[9] and , A comparison technique for systems of reaction-diffusion equations. Commun. Partial Differ. Equ. 2 (1977) 679–697.
[10] , , , , , and , 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).
[11] , and , Sterile insect technique: principles and practice in area-wide integrated pest management. Springer (2006).
[12] , Vol. 19 of Partial differential equations. American Mathematical Society (AMS), Providence, RI (2010), 2nd edn.
[13] and , Structured and unstructured continuous models for wolbachia infections. Bull. Math. Biol. 72 (2010) 2067–2088.
[14] , , and , Solving the wolbachia paradox: modeling the tripartite interaction between host, wolbachia, and a natural enemy. Am. Natur. 178 (2011) 333–342.
[15] , , and , Dynamic life table model for Aedes aegypti (Diptera: Culicidae): analysis of the literature and model development. J. Med. Entomol. 30 (1993) 1003–1017.
[16] , , , , , , , , , , et al., Female-specific flightless phenotype for mosquito control. Proc. Natl. Acad. Sci. 107 (2010) 4550–4554.
[17] and , 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.
[18] and , Convex analysis and minimization algorithms. I. Vol. 305 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin (1993). Fundamentals.
[19] and , Modelling the use of wolbachia to control dengue fever transmission. Bull. Math. Biol. 75 (2013) 796–818.
[20] Null-controllability of two species reaction-diffusion system with nonlinear coupling: a new duality method. SIAM J. Control Optim. 57 (2019) 2541–2573.
[21] and , Necessary conditions for optimal control of distributed parameter systems. SIAM J. Control Optim. 29 (1991) 895–908.
[22] , and , Constrained control of bistable reaction-diffusion equations: gene-flow and spatially heterogeneous models. Preprint (2020).
[23] , and Optimization of the total population size with respect to the initial condition in reaction-diffusion equations. Work inprogress (2021).
[24] , and , Optimal control of vaccination in a vector-borne reaction–diffusion model applied to zika virus. J. Math. Biol. 79 (2019) 1077–1104.
[25] and On the maximization problem for solutions of reaction-diffusion equations with respect to their initial data. Math. Model. Nat. Phenom. 15 (2020) 71.
[26] and , Exact multiplicity of positive solutions for a class of semilinear problem II. J. Differ. Equ. 158 (1999) 94–151.
[27] , Parabolic equations in biology. Growth, reaction, movement and diffusion. Springer, Cham (2015).
[28] , , , , , , , , , , et al., Constraints on the use of lifespan-shortening Wolbachia to control dengue fever. J. Theor. Biol. 297 (2012) 26–32.
[29] , Compact sets in the space L$$(0, T; B). Ann. Mat. Pura Appl. 146 (1987) 65–96.
[30] , Wolbachia and cytoplasmic incompatibility in mosquitoes. Insect Biochem. Mol. Biol. 34 (2004) 723–729.
[31] , , , and 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).
[32] and , 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.
[33] , and , Quantifying the survival uncertainty of wolbachia-infected mosquitoes in a spatial model. Math. Biosci. Eng. 15 (2018) 961–991.
[34] , , and , Insect population control using a dominant, repressible, lethal genetic system. Science 287 (2000) 2474–2476.
[35] and , On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Progr. 106 (2006) 25–57.
[36] , , , , , , , , , , et al., The wmel wolbachia strain blocks dengue and invades caged aedes aegypti populations. Nature 476 (2011) 450.
[37] , Invariant sets for weakly coupled parabolic and elliptic systems. Rend. Mat. 8 (1975) 295–310.
[38] , and , Wolbachia: master manipulators of invertebrate biology. Nat. Rev. Microbiol. 6 (2008) 741.
[39] et al., Incompatible and sterile insect techniques combined eliminate mosquitoes. Nature 572 (2019) 56–61.
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