Implementation of control strategies for sterile insect techniques

In this paper, we propose a sex-structured entomological model that serves as a basis for design of control strategies relying on releases of sterile male mosquitoes (Aedes spp) and aiming at elimination of the wild vector population in some target locality. We consider different types of releases (...

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Autores:
Cardona Salgado, Daiver
Vasillieva, Olga
Bliman, Pierre-Alexandre
Dumont, Yves
Tipo de recurso:
Article of journal
Fecha de publicación:
2019
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
eng
OAI Identifier:
oai:red.uao.edu.co:10614/11561
Acceso en línea:
http://hdl.handle.net/10614/11561
https://doi.org/10.1016/j.mbs.2019.06.002
Palabra clave:
Control biológico de plagas
Pests - Biological control
Sterile insect technique
Periodic impulsive control
Open-loop and closed-loop control
Global stability
Exponential convergence
Saturated control
Rights
openAccess
License
Derechos Reservados - Universidad Autónoma de Occidente
id REPOUAO2_c23d70e9ccea662be913284d66e4cbde
oai_identifier_str oai:red.uao.edu.co:10614/11561
network_acronym_str REPOUAO2
network_name_str RED: Repositorio Educativo Digital UAO
repository_id_str
dc.title.eng.fl_str_mv Implementation of control strategies for sterile insect techniques
title Implementation of control strategies for sterile insect techniques
spellingShingle Implementation of control strategies for sterile insect techniques
Control biológico de plagas
Pests - Biological control
Sterile insect technique
Periodic impulsive control
Open-loop and closed-loop control
Global stability
Exponential convergence
Saturated control
title_short Implementation of control strategies for sterile insect techniques
title_full Implementation of control strategies for sterile insect techniques
title_fullStr Implementation of control strategies for sterile insect techniques
title_full_unstemmed Implementation of control strategies for sterile insect techniques
title_sort Implementation of control strategies for sterile insect techniques
dc.creator.fl_str_mv Cardona Salgado, Daiver
Vasillieva, Olga
Bliman, Pierre-Alexandre
Dumont, Yves
dc.contributor.author.none.fl_str_mv Cardona Salgado, Daiver
Vasillieva, Olga
Bliman, Pierre-Alexandre
Dumont, Yves
dc.subject.lemb.spa.fl_str_mv Control biológico de plagas
topic Control biológico de plagas
Pests - Biological control
Sterile insect technique
Periodic impulsive control
Open-loop and closed-loop control
Global stability
Exponential convergence
Saturated control
dc.subject.lemb.eng.fl_str_mv Pests - Biological control
dc.subject.proposal.eng.fl_str_mv Sterile insect technique
Periodic impulsive control
Open-loop and closed-loop control
Global stability
Exponential convergence
Saturated control
description In this paper, we propose a sex-structured entomological model that serves as a basis for design of control strategies relying on releases of sterile male mosquitoes (Aedes spp) and aiming at elimination of the wild vector population in some target locality. We consider different types of releases (constant and periodic impulsive), providing sufficient conditions to reach elimination. However, the main part of the paper is focused on the study of the periodic impulsive control in different situations. When the size of wild mosquito population cannot be assessed in real time, we propose the so-called open-loop control strategy that relies on periodic impulsive releases of sterile males with constant release size. Under this control mode, global convergence towards the mosquito-free equilibrium is proved on the grounds of sufficient condition that relates the size and frequency of releases. If periodic assessments (either synchronized with the releases or more sparse) of the wild population size are available in real time, we propose the so-called closed-loop control strategy, under which the release size is adjusted in accordance with the wild population size estimate. Finally, we propose a mixed control strategy that combines open-loop and closed-loop strategies. This control mode renders the best result, in terms of overall time needed to reach elimination and the number of releases to be effectively carried out during the whole release campaign, while requiring for a reasonable amount of released sterile insects
publishDate 2019
dc.date.accessioned.none.fl_str_mv 2019-11-25T14:06:07Z
dc.date.available.none.fl_str_mv 2019-11-25T14:06:07Z
dc.date.issued.none.fl_str_mv 2019-08
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.doi.spa.fl_str_mv https://doi.org/10.1016/j.mbs.2019.06.002
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https://doi.org/10.1016/j.mbs.2019.06.002
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.citationvolume.none.fl_str_mv 34
dc.relation.cites.none.fl_str_mv Bliman, P. A., Cardona-Salgado, D., Dumont, Y., & Vasilieva, O. (2019). Implementation of control strategies for sterile insect techniques. Mathematical biosciences. 314 , 43-60. https://doi.org/10.1016/j.mbs.2019.06.002
dc.relation.ispartofjournal.eng.fl_str_mv Mathematical Biosciences
dc.relation.references.none.fl_str_mv [1] V.A. Dyck, J. Hendrichs, A.S. Robinson, The Sterile Insect Technique, Principles and Practice in Area-Wide Integrated Pest Management, Springer, Dordrecht, 2006.
[2] M. Hertig, S.B. Wolbach, Studies on rickettsia-like micro-organisms in insects, J. Med. Res. 44 (3) (1924) 329.
[3] K. Bourtzis, Wolbachia-based technologies for insect pest population control, Advances in Experimental Medicine and Biology, 627 Springer, New York, NY, 2008.
[4] S.P. Sinkins, Wolbachia and cytoplasmic incompatibility in mosquitoes, Insect Biochem. Mol. Biol. 34 (7) (2004) 723–729. Molecular and population biology of mosquitoes
[5] J.L. Rasgon, T.W. Scott, Wolbachia and cytoplasmic incompatibility in the California Culex pipiens mosquito species complex: parameter estimates and infection dynamics in natural populations, Genetics 165 (4) (2003) 2029–2038.
[6] J.G. Schraiber, A.N. Kaczmarczyk, R. Kwok, M. Park, R. Silverstein, F.U. Rutaganira, T. Aggarwal, M.A. Schwemmer, C.L. Hom, R.K. Grosberg, S.J. Schreiber, Constraints on the use of lifespan-shortening Wolbachia to control dengue fever, J. Theor. Biol. 297 (2012) 26–32.
[7] L.A. Moreira, I. Iturbe-Ormaetxe, J.A. Jeffery, G. Lu, A.T. Pyke, L.M. Hedges, B.C. Rocha, S. Hall-Mendelin, A. Day, M. Riegler, L.E. Hugo, K.N. Johnson, B.H. Kay, E.A. McGraw, A.F. van den Hurk, P.A. Ryan, S.L. O’Neill, A Wolbachia symbiont in Aedes aegypti limits infection with dengue, chikungunya, and plasmodium, Cell 139 (7) (2009) 1268–1278.
[8] C. Dufourd, Y. Dumont, Modeling and simulations of mosquito dispersal. the case of Aedes albopictus, Biomath 1209262 (2012) 1–7.
[9] C. Dufourd, Y. Dumont, Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control, Comput. Math. Appl. 66 (9) (2013) 1695–1715.
[10] Y. Dumont, J.M. Tchuenche, Mathematical studies on the sterile insect technique for the Chikungunya disease and Aedes albopictus, J. Math. Biol. 65 (5) (2012) 809–855.
[11] M. Huang, X. Song, J. Li, Modelling and analysis of impulsive releases of sterile mosquitoes, J. Biol. Dyn. 11 (1) (2017) 147–171.
[12] J. Li, Z. Yuan, Modelling releases of sterile mosquitoes with different strategies, J. Biol. Dyn. 9 (1) (2015) 1–14.
[13] M. Strugarek, H. Bossin, Y. Dumont, On the use of the sterile insect release technique to reduce or eliminate mosquito populations, Appl. Math. Model. (2018), https://doi.org/10.1016/j.apm.2018.11.026. http://www.sciencedirect.com/science/article/pii/S0307904X18305638
[14] D.E. Campo-Duarte, D. Cardona-Salgado, O. Vasilieva, Establishing wMelPop Wolbachia infection among wild Aedes aegypti females by optimal control approach, Appl. Math. Inf. Sci. 11 (4) (2017) 1011–1027, https://doi.org/10.18576/amis/110408.
[15] D.E. Campo-Duarte, O. Vasilieva, D. Cardona-Salgado, M. Svinin, Optimal control approach for establishing wMelPop Wolbachia infection among wild Aedes aegyptipopulations, J. Math. Biol. 76 (7) (2018) 1907–1950.
[16] J.Z. Farkas, S.A. Gourley, R. Liu, A.-A. Yakubu, Modelling Wolbachia infection in a sex-structured mosquito population carrying West Nile virus, J. Math. Biol. 75 (3) (2017) 621–647.
[17] J.Z. Farkas, P. Hinow, Structured and unstructured continuous models for Wolbachia infections, Bull. Math. Biol. 72 (8) (2010) 2067–2088.
[18] A. Fenton, K.N. Johnson, J.C. Brownlie, G.D.D. Hurst, Solving the wolbachia paradox: modeling the tripartite interaction between host, wolbachia, and a natural enemy, Am. Nat. 178 (2011) 333–342.
[19] H. Hughes, N.F. Britton, Modeling the use of Wolbachia to control dengue fever transmission, Bull. Math. Biol. 75 (2013) 796–818.
[20] G. Nadin, M. Strugarek, N. Vauchelet, Hindrances to bistable front propagation: application to Wolbachia invasion, J. Math. Biol. 76 (6) (2018) 1489–1533, https://doi.org/10.1007/s00285-017-1181-y.
[21] M. Strugarek, N. Vauchelet, J. Zubelli, Quantifying the survival uncertainty of Wolbachia-infected mosquitoes in a spatial model, Math. Biosci. Eng. 15(4) (2018) 961–991.
[22] H.L. Smith, Monotone Dynamical Systems: an Introduction to the Theory of Competitive and Cooperative Systems, Providence, R.I.: American Mathematical Society, 1995.
[23] R. Anguelov, Y. Dumont, J. Lubuma, Mathematical modeling of sterile insect technology for control of anopheles mosquito, Comput. Math. Appl. 64 (3) (2012) 374–389.
[24] J. Koiller, M. Da Silva, M. Souza, C. Codeço, A. Iggidr, G. Sallet, Aedes, Wolbachia and Dengue, Research Report RR-8462, Inria Nancy - Grand Est (Villers-lès-Nancy, France), 2014. https://hal.inria.fr/hal-00939411
[25] P.-A. Bliman, M.S. Aronna, F.C. Coelho, M.A.H.B. da Silva, Ensuring successful introduction of Wolbachia in natural populations of Aedes aegypti by means of feedback control, J. Math. Biol. 76 (5) (2018) 1269–1300.
[26] P.-A. Bliman, Feedback control principles for biological control of dengue vectors, arXiv preprint arXiv:/1903.00730(2019).
[27] L. Gouagna, J. Dehecq, D. Fontenille, Y. Dumont, S. Boyer, Seasonal variation in size estimates of Aedes albopictus population based on standard mark-release-recapture experiments in an urban area on Reunion Island, Acta Tropica 143 (2015) 89–96.
[28] K. Cooke, P. van den Driessche, X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol. 39 (4) (1999) 332–352, https://doi.org/10.1007/s002850050194.
[29] L. Perko, Differential Equations and Dynamical Systems, Springer-Verlag, 2006.
dc.rights.spa.fl_str_mv Derechos Reservados - Universidad Autónoma de Occidente
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spelling Cardona Salgado, Daivervirtual::1175-1Vasillieva, Olga8192a3cb04cd7d52c219424345b35dc3Bliman, Pierre-Alexandre04409da18d2ed8ec31008212a98665d1Dumont, Yvesaf7acf9f6add184b3beef7fea8d68997Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí2019-11-25T14:06:07Z2019-11-25T14:06:07Z2019-080025-5564http://hdl.handle.net/10614/11561https://doi.org/10.1016/j.mbs.2019.06.002In this paper, we propose a sex-structured entomological model that serves as a basis for design of control strategies relying on releases of sterile male mosquitoes (Aedes spp) and aiming at elimination of the wild vector population in some target locality. We consider different types of releases (constant and periodic impulsive), providing sufficient conditions to reach elimination. However, the main part of the paper is focused on the study of the periodic impulsive control in different situations. When the size of wild mosquito population cannot be assessed in real time, we propose the so-called open-loop control strategy that relies on periodic impulsive releases of sterile males with constant release size. Under this control mode, global convergence towards the mosquito-free equilibrium is proved on the grounds of sufficient condition that relates the size and frequency of releases. If periodic assessments (either synchronized with the releases or more sparse) of the wild population size are available in real time, we propose the so-called closed-loop control strategy, under which the release size is adjusted in accordance with the wild population size estimate. Finally, we propose a mixed control strategy that combines open-loop and closed-loop strategies. This control mode renders the best result, in terms of overall time needed to reach elimination and the number of releases to be effectively carried out during the whole release campaign, while requiring for a reasonable amount of released sterile insectsapplication/pdf18 páginasengElsevierDerechos Reservados - Universidad Autónoma de Occidentehttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_abf2reponame:Repositorio Institucional UAOImplementation of control strategies for sterile insect techniquesArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTREFinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Control biológico de plagasPests - Biological controlSterile insect techniquePeriodic impulsive controlOpen-loop and closed-loop controlGlobal stabilityExponential convergenceSaturated control34Bliman, P. A., Cardona-Salgado, D., Dumont, Y., & Vasilieva, O. (2019). Implementation of control strategies for sterile insect techniques. Mathematical biosciences. 314 , 43-60. https://doi.org/10.1016/j.mbs.2019.06.002Mathematical Biosciences[1] V.A. Dyck, J. Hendrichs, A.S. Robinson, The Sterile Insect Technique, Principles and Practice in Area-Wide Integrated Pest Management, Springer, Dordrecht, 2006.[2] M. Hertig, S.B. Wolbach, Studies on rickettsia-like micro-organisms in insects, J. Med. Res. 44 (3) (1924) 329.[3] K. Bourtzis, Wolbachia-based technologies for insect pest population control, Advances in Experimental Medicine and Biology, 627 Springer, New York, NY, 2008.[4] S.P. Sinkins, Wolbachia and cytoplasmic incompatibility in mosquitoes, Insect Biochem. Mol. Biol. 34 (7) (2004) 723–729. Molecular and population biology of mosquitoes[5] J.L. Rasgon, T.W. Scott, Wolbachia and cytoplasmic incompatibility in the California Culex pipiens mosquito species complex: parameter estimates and infection dynamics in natural populations, Genetics 165 (4) (2003) 2029–2038.[6] J.G. Schraiber, A.N. Kaczmarczyk, R. Kwok, M. Park, R. Silverstein, F.U. Rutaganira, T. Aggarwal, M.A. Schwemmer, C.L. Hom, R.K. Grosberg, S.J. Schreiber, Constraints on the use of lifespan-shortening Wolbachia to control dengue fever, J. Theor. Biol. 297 (2012) 26–32.[7] L.A. Moreira, I. Iturbe-Ormaetxe, J.A. Jeffery, G. Lu, A.T. Pyke, L.M. Hedges, B.C. Rocha, S. Hall-Mendelin, A. Day, M. Riegler, L.E. Hugo, K.N. Johnson, B.H. Kay, E.A. McGraw, A.F. van den Hurk, P.A. Ryan, S.L. O’Neill, A Wolbachia symbiont in Aedes aegypti limits infection with dengue, chikungunya, and plasmodium, Cell 139 (7) (2009) 1268–1278.[8] C. Dufourd, Y. Dumont, Modeling and simulations of mosquito dispersal. the case of Aedes albopictus, Biomath 1209262 (2012) 1–7.[9] C. Dufourd, Y. Dumont, Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control, Comput. Math. Appl. 66 (9) (2013) 1695–1715.[10] Y. Dumont, J.M. Tchuenche, Mathematical studies on the sterile insect technique for the Chikungunya disease and Aedes albopictus, J. Math. Biol. 65 (5) (2012) 809–855.[11] M. Huang, X. Song, J. Li, Modelling and analysis of impulsive releases of sterile mosquitoes, J. Biol. Dyn. 11 (1) (2017) 147–171.[12] J. Li, Z. Yuan, Modelling releases of sterile mosquitoes with different strategies, J. Biol. Dyn. 9 (1) (2015) 1–14.[13] M. Strugarek, H. Bossin, Y. Dumont, On the use of the sterile insect release technique to reduce or eliminate mosquito populations, Appl. Math. Model. (2018), https://doi.org/10.1016/j.apm.2018.11.026. http://www.sciencedirect.com/science/article/pii/S0307904X18305638[14] D.E. Campo-Duarte, D. Cardona-Salgado, O. Vasilieva, Establishing wMelPop Wolbachia infection among wild Aedes aegypti females by optimal control approach, Appl. Math. Inf. Sci. 11 (4) (2017) 1011–1027, https://doi.org/10.18576/amis/110408.[15] D.E. Campo-Duarte, O. Vasilieva, D. Cardona-Salgado, M. Svinin, Optimal control approach for establishing wMelPop Wolbachia infection among wild Aedes aegyptipopulations, J. Math. Biol. 76 (7) (2018) 1907–1950.[16] J.Z. Farkas, S.A. Gourley, R. Liu, A.-A. Yakubu, Modelling Wolbachia infection in a sex-structured mosquito population carrying West Nile virus, J. Math. Biol. 75 (3) (2017) 621–647.[17] J.Z. Farkas, P. Hinow, Structured and unstructured continuous models for Wolbachia infections, Bull. Math. Biol. 72 (8) (2010) 2067–2088.[18] A. Fenton, K.N. Johnson, J.C. Brownlie, G.D.D. Hurst, Solving the wolbachia paradox: modeling the tripartite interaction between host, wolbachia, and a natural enemy, Am. Nat. 178 (2011) 333–342.[19] H. Hughes, N.F. Britton, Modeling the use of Wolbachia to control dengue fever transmission, Bull. Math. Biol. 75 (2013) 796–818.[20] G. Nadin, M. Strugarek, N. Vauchelet, Hindrances to bistable front propagation: application to Wolbachia invasion, J. Math. Biol. 76 (6) (2018) 1489–1533, https://doi.org/10.1007/s00285-017-1181-y.[21] M. Strugarek, N. Vauchelet, J. Zubelli, Quantifying the survival uncertainty of Wolbachia-infected mosquitoes in a spatial model, Math. Biosci. Eng. 15(4) (2018) 961–991.[22] H.L. Smith, Monotone Dynamical Systems: an Introduction to the Theory of Competitive and Cooperative Systems, Providence, R.I.: American Mathematical Society, 1995.[23] R. Anguelov, Y. Dumont, J. Lubuma, Mathematical modeling of sterile insect technology for control of anopheles mosquito, Comput. Math. Appl. 64 (3) (2012) 374–389.[24] J. Koiller, M. Da Silva, M. Souza, C. Codeço, A. Iggidr, G. Sallet, Aedes, Wolbachia and Dengue, Research Report RR-8462, Inria Nancy - Grand Est (Villers-lès-Nancy, France), 2014. https://hal.inria.fr/hal-00939411[25] P.-A. Bliman, M.S. Aronna, F.C. Coelho, M.A.H.B. da Silva, Ensuring successful introduction of Wolbachia in natural populations of Aedes aegypti by means of feedback control, J. Math. Biol. 76 (5) (2018) 1269–1300.[26] P.-A. Bliman, Feedback control principles for biological control of dengue vectors, arXiv preprint arXiv:/1903.00730(2019).[27] L. Gouagna, J. Dehecq, D. Fontenille, Y. Dumont, S. Boyer, Seasonal variation in size estimates of Aedes albopictus population based on standard mark-release-recapture experiments in an urban area on Reunion Island, Acta Tropica 143 (2015) 89–96.[28] K. Cooke, P. van den Driessche, X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol. 39 (4) (1999) 332–352, https://doi.org/10.1007/s002850050194.[29] L. Perko, Differential Equations and Dynamical Systems, Springer-Verlag, 2006.Publication72f68479-5914-43da-8996-02353d27d5dcvirtual::1175-172f68479-5914-43da-8996-02353d27d5dcvirtual::1175-1https://scholar.google.com.co/citations?user=KcfKIyEAAAAJ&hl=esvirtual::1175-10000-0003-4828-9360virtual::1175-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0001474886virtual::1175-1CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://red.uao.edu.co/bitstreams/10c5cfc1-e02d-4e4e-838c-9a2580bebd35/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/cb7de6e9-0a32-4a06-bb7c-c3a3941f28e9/download20b5ba22b1117f71589c7318baa2c560MD5310614/11561oai:red.uao.edu.co:10614/115612024-03-01 14:58:13.926https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos Reservados - Universidad Autónoma de Occidentemetadata.onlyhttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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