Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes

This paper proposes a bidimensional modeling framework for Wolbachia invasion, assuming imperfect maternal transmission, incomplete cytoplasmic incompatibility, and direct infection loss due to thermal stress. Our model adapts to various Wolbachia strains and retains all properties of higher-dimensi...

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Autores:
Cardona Salgado, Daiver
Sepúlveda Salcedo, Lilian Sofía
Orozco-Gonzales, Jose L.
dos Santos Benedito, Antone
Pio Ferreira, Claudia
de Oliveira Florentino, Helenice
Vasilieva, Olga
Tipo de recurso:
Article of investigation
Fecha de publicación:
2024
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
eng
OAI Identifier:
oai:red.uao.edu.co:10614/16205
Acceso en línea:
https://hdl.handle.net/10614/16205
https://doi.org/10.1016/j.mbs.2024.109190
https://red.uao.edu.co/
Palabra clave:
Wolbachia
Aedes aegypti
Population dynamics
Imperfect maternal transmission
Incomplete CI
Infection loss
Stable coexistence
Pitch-fork bifurcation
Dinámica poblacional
Transmisión materna imperfecta
CI incompleto
Pérdida por infección
Coexistencia estable
Bifurcación en horquilla
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openAccess
License
Derechos reservados - Elsevier, 2024
id REPOUAO2_654534643e553dc47b9a74752a528bed
oai_identifier_str oai:red.uao.edu.co:10614/16205
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repository_id_str
dc.title.eng.fl_str_mv Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes
dc.title.translated.spa.fl_str_mv Comparación de la persistencia a largo plazo de diferentes cepas de Wolbachia después de la liberación de mosquitos portadores de bacterias
title Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes
spellingShingle Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes
Wolbachia
Aedes aegypti
Population dynamics
Imperfect maternal transmission
Incomplete CI
Infection loss
Stable coexistence
Pitch-fork bifurcation
Dinámica poblacional
Transmisión materna imperfecta
CI incompleto
Pérdida por infección
Coexistencia estable
Bifurcación en horquilla
title_short Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes
title_full Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes
title_fullStr Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes
title_full_unstemmed Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes
title_sort Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes
dc.creator.fl_str_mv Cardona Salgado, Daiver
Sepúlveda Salcedo, Lilian Sofía
Orozco-Gonzales, Jose L.
dos Santos Benedito, Antone
Pio Ferreira, Claudia
de Oliveira Florentino, Helenice
Vasilieva, Olga
dc.contributor.author.none.fl_str_mv Cardona Salgado, Daiver
Sepúlveda Salcedo, Lilian Sofía
Orozco-Gonzales, Jose L.
dos Santos Benedito, Antone
Pio Ferreira, Claudia
de Oliveira Florentino, Helenice
Vasilieva, Olga
dc.subject.proposal.eng.fl_str_mv Wolbachia
Aedes aegypti
Population dynamics
Imperfect maternal transmission
Incomplete CI
Infection loss
Stable coexistence
Pitch-fork bifurcation
topic Wolbachia
Aedes aegypti
Population dynamics
Imperfect maternal transmission
Incomplete CI
Infection loss
Stable coexistence
Pitch-fork bifurcation
Dinámica poblacional
Transmisión materna imperfecta
CI incompleto
Pérdida por infección
Coexistencia estable
Bifurcación en horquilla
dc.subject.proposal.spa.fl_str_mv Dinámica poblacional
Transmisión materna imperfecta
CI incompleto
Pérdida por infección
Coexistencia estable
Bifurcación en horquilla
description This paper proposes a bidimensional modeling framework for Wolbachia invasion, assuming imperfect maternal transmission, incomplete cytoplasmic incompatibility, and direct infection loss due to thermal stress. Our model adapts to various Wolbachia strains and retains all properties of higher-dimensional models. The conditions for the durable coexistence of Wolbachia-carrying and wild mosquitoes are expressed using the model’s parameters in a compact closed form. When the Wolbachia bacterium is locally established, the size of the remanent wild population can be assessed by a direct formula derived from the model. The model was tested for four Wolbachia strains undergoing laboratory and field trials to control mosquito-borne diseases: wMel, wMelPop, wAlbB, and wAu. As all these bacterial strains affect the individual fitness of mosquito hosts differently and exhibit different levels of resistance to temperature variations, the model helped to conclude that: (1) the wMel strain spreads faster in wild mosquito populations; (2) the wMelPop exhibits lower resilience but also guarantees the smallest size of the remanent wild population; (3) the wAlbB strain performs better at higher ambient temperatures than others; (4) the wAu strain is not sustainable and cannot persist in the wild mosquito population despite its resistance to high temperatures
publishDate 2024
dc.date.issued.none.fl_str_mv 2024
dc.date.accessioned.none.fl_str_mv 2025-07-08T16:13:14Z
dc.date.available.none.fl_str_mv 2025-07-08T16:13:14Z
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.eng.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.content.eng.fl_str_mv Text
dc.type.driver.eng.fl_str_mv info:eu-repo/semantics/article
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dc.identifier.citation.eng.fl_str_mv Cardona Salgado, D.; Sepúlveda Salcedo, L. S.; dos Santos Benedito, A.; Pio Ferreira, C.; de Oliveira Florentino, H. y Vasilieva, O. (2024). Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes. Mathematical Biosciences. Vol. 372. 16 p. https://doi.org/10.1016/j.mbs.2024.109190
dc.identifier.issn.spa.fl_str_mv 00255564
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10614/16205
dc.identifier.doi.spa.fl_str_mv https://doi.org/10.1016/j.mbs.2024.109190
dc.identifier.eissn.spa.fl_str_mv 18793134
dc.identifier.instname.spa.fl_str_mv Universidad Autónoma de Occidente
dc.identifier.reponame.spa.fl_str_mv Respositorio Educativo Digital UAO
dc.identifier.repourl.none.fl_str_mv https://red.uao.edu.co/
identifier_str_mv Cardona Salgado, D.; Sepúlveda Salcedo, L. S.; dos Santos Benedito, A.; Pio Ferreira, C.; de Oliveira Florentino, H. y Vasilieva, O. (2024). Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes. Mathematical Biosciences. Vol. 372. 16 p. https://doi.org/10.1016/j.mbs.2024.109190
00255564
18793134
Universidad Autónoma de Occidente
Respositorio Educativo Digital UAO
url https://hdl.handle.net/10614/16205
https://doi.org/10.1016/j.mbs.2024.109190
https://red.uao.edu.co/
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.citationendpage.spa.fl_str_mv 16
dc.relation.citationstartpage.spa.fl_str_mv 1
dc.relation.citationvolume.spa.fl_str_mv 372
dc.relation.ispartofjournal.spa.fl_str_mv Mathematical Biosciences
dc.relation.references.none.fl_str_mv [1] G. Bian, Y. Xu, P. Lu, Y. Xie, Z. Xi, The endosymbiotic bacterium Wolbachia induces resistance to dengue virus in Aedes aegypti, PLoS Pathogens 6 (4) (2010) e1000833.
[2] L. Dutra, M. Rocha, F. Dias, S. Mansur, E. Caragata, L. Moreira, Wolbachia blocks currently circulating zika virus isolates in Brazilian Aedes aegypti mosquitoes, Cell Host Microbe 19 (6) (2016) 771–774.
[3] L. Moreira, I. Iturbe-Ormaetxe, J. Jeffery, G. Lu, A. Pyke, L. Hedges, B. Rocha, S. Hall-Mendelin, A. Day, M. Riegler, L. Hugo, K. Johnson, B. Kay, E. McGraw, A. van den Hurk, P. Ryan, S. O’Neill, A Wolbachia symbiont in Aedes aegypti limits infection with dengue, chikungunya, and plasmodium, Cell 139 (7) (2009) 1268–1278.
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[7] S. Ogunlade, M. Meehan, A. Adekunle, D. Rojas, O. Adegboye, E. McBryde, A review: Aedes-borne arboviral infections, controls and Wolbachia-based strategies, Vaccines 9 (1) (2021) 32.
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[12] P. Ross, I. Wiwatanaratanabutr, J. Axford, V. White, N. Endersby-Harshman, A. Hoffmann, Wolbachia infections in Aedes aegypti differ markedly in their response to cyclical heat stress, PLoS Pathogens 13 (1) (2017) e1006006.
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[14] T. Walker, P. Johnson, L. Moreira, I. Iturbe-Ormaetxe, F. Frentiu, C. McMeniman, Y. Leong, Y. Dong, J. Axford, P. Kriesner, A. Lloyd, S. Ritchie, S. O’Neill, A. Hoffmann, The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations, Nature 476 (7361) (2011) 450–453.
[15] J. Ulrich, J. Beier, G. Devine, L. Hugo, Heat sensitivity of wMel Wolbachia during Aedes aegypti development, PLoS Negl. Trop. Dis. 10 (7) (2016) e0004873.
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[19] A. dos Santos Benedito, C.P. Ferreira, H. de Oliveira Florentino, Establishing the coexistence of Wolbachia-carrying and wild Aedes aegypti. Populations by feedback linearization, Appl. Math. 17 (3) (2023) 521–533.
[20] J. Farkas, S. Gourley, R. Liu, A.-A. Yakubu, Modelling Wolbachia infection in a sex-structured mosquito population carrying West Nile virus, J. Math. Biol. 75 (2017) 621–647.
[21] C.P. Ferreira, Aedes aegypti and Wolbachia interaction: population persistence in an environment changing, Theor. Ecol. 13 (2) (2020) 137–148.
[22] D. Li, H. Wan, The threshold infection level for Wolbachia invasion in a two-sex mosquito population model, Bull. Math. Biol. 81 (7) (2019) 2596–2624.
[23] Y. Li, X. Liu, Modeling and control of mosquito-borne diseases with Wolbachia and insecticides, Theor. Popul. Biol. 132 (2020) 82–91.
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[41] A. Hoffmann, P.A Ross, G. Rašić, Wolbachia strains for disease control: ecological and evolutionary considerations, Evol. Appl. 8 (8) (2015) 751–768.
[42] M. Mancini, T. Ant, C. Herd, D. Gingell, S. Murdochy, E. Mararo, S. Sinkins, High-temperature cycles result in maternal transmission and dengue infection differences between Wolbachia strains in Aedes aegypti, Mbio 12 (6) (2021) e00250–21.
[43] X. Liang, C. Tan, Qiang. Sun, Zhang, P. Wong, M. Li, K. Mak, A. Martín- Park, Y. Contreras-Perera, H. Puerta-Guardo, P. Manrique-Saide, L. Ng, Z. Xi, Wolbachia wAlbB remains stable in Aedes aegypti over 15 years but exhibits genetic background-dependent variation in virus blocking, PNAS Nexus 1 (4) (2022) pgac203.
[44] T. Nguyen, H. Nguyen, T. Nguyen, S. Vu, N. Tran, T. Le, Q. Vien, T. Bui, H. Le, S. Kutcher, T. Hurst, T. Duong, J. Jeffery, J. Darbro, B. Kay, I. Iturbe-Ormaetxe, J. Popovici, B. Montgomery, A. Turley, F. Zigterman, H. Cook, P. Cook, P. Johnson, P. Ryan, C. Paton, S. Ritchie, C. Simmons, S. O’Neill, A. Hoffmann, Field evaluation of the establishment potential of wMelPop Wolbachia in Australia and Vietnam for dengue control, Parasites Vectors 8 (2015) 1–14.
[45] K. Gunasekaran, C. Sadanandane, D. Panneer, A. Kumar, M. Rahi, S. Dinesh, B. Vijayakumar, M. Krishnaraja, S. Subbarao, P. Jambulingam, Sensitivity of wMel and wAlbB Wolbachia infections in Aedes aegypti Puducherry (Indian) strains to heat stress during larval development, Parasites Vectors 15 (1) (2022) 1–10.
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dc.rights.spa.fl_str_mv Derechos reservados - Elsevier, 2024
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https://creativecommons.org/licenses/by-nc-nd/4.0/
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spelling Cardona Salgado, Daivervirtual::6094-1Sepúlveda Salcedo, Lilian Sofíavirtual::6095-1Orozco-Gonzales, Jose L.dos Santos Benedito, AntonePio Ferreira, Claudiade Oliveira Florentino, HeleniceVasilieva, Olga2025-07-08T16:13:14Z2025-07-08T16:13:14Z2024Cardona Salgado, D.; Sepúlveda Salcedo, L. S.; dos Santos Benedito, A.; Pio Ferreira, C.; de Oliveira Florentino, H. y Vasilieva, O. (2024). Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoes. Mathematical Biosciences. Vol. 372. 16 p. https://doi.org/10.1016/j.mbs.2024.10919000255564https://hdl.handle.net/10614/16205https://doi.org/10.1016/j.mbs.2024.10919018793134Universidad Autónoma de OccidenteRespositorio Educativo Digital UAOhttps://red.uao.edu.co/This paper proposes a bidimensional modeling framework for Wolbachia invasion, assuming imperfect maternal transmission, incomplete cytoplasmic incompatibility, and direct infection loss due to thermal stress. Our model adapts to various Wolbachia strains and retains all properties of higher-dimensional models. The conditions for the durable coexistence of Wolbachia-carrying and wild mosquitoes are expressed using the model’s parameters in a compact closed form. When the Wolbachia bacterium is locally established, the size of the remanent wild population can be assessed by a direct formula derived from the model. The model was tested for four Wolbachia strains undergoing laboratory and field trials to control mosquito-borne diseases: wMel, wMelPop, wAlbB, and wAu. As all these bacterial strains affect the individual fitness of mosquito hosts differently and exhibit different levels of resistance to temperature variations, the model helped to conclude that: (1) the wMel strain spreads faster in wild mosquito populations; (2) the wMelPop exhibits lower resilience but also guarantees the smallest size of the remanent wild population; (3) the wAlbB strain performs better at higher ambient temperatures than others; (4) the wAu strain is not sustainable and cannot persist in the wild mosquito population despite its resistance to high temperatures16 páginasapplication/pdfengElsevierPaíses bajosDerechos reservados - Elsevier, 2024https://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_abf2Comparing the long-term persistence of different Wolbachia strains after the release of bacteria-carrying mosquitoesComparación de la persistencia a largo plazo de diferentes cepas de Wolbachia después de la liberación de mosquitos portadores de bacteriasArtículo de revistahttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85161372Mathematical Biosciences[1] G. Bian, Y. Xu, P. Lu, Y. Xie, Z. Xi, The endosymbiotic bacterium Wolbachia induces resistance to dengue virus in Aedes aegypti, PLoS Pathogens 6 (4) (2010) e1000833.[2] L. Dutra, M. Rocha, F. Dias, S. Mansur, E. Caragata, L. Moreira, Wolbachia blocks currently circulating zika virus isolates in Brazilian Aedes aegypti mosquitoes, Cell Host Microbe 19 (6) (2016) 771–774.[3] L. Moreira, I. Iturbe-Ormaetxe, J. Jeffery, G. Lu, A. Pyke, L. Hedges, B. Rocha, S. Hall-Mendelin, A. Day, M. Riegler, L. Hugo, K. Johnson, B. Kay, E. McGraw, A. van den Hurk, P. Ryan, S. O’Neill, A Wolbachia symbiont in Aedes aegypti limits infection with dengue, chikungunya, and plasmodium, Cell 139 (7) (2009) 1268–1278.[4] T. Ant, C. Herd, V. Geoghegan, A. Hoffmann, S. Sinkins, The Wolbachia strain wAu provides highly efficient virus transmission blocking in Aedes aegypti, PLoS Pathogens 14 (1) (2018) e1006815.[5] I. Dorigatti, C. McCormack, G. Nedjati-Gilani, N. 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Dis. 15 (2) (2021) e0009179.WolbachiaAedes aegyptiPopulation dynamicsImperfect maternal transmissionIncomplete CIInfection lossStable coexistencePitch-fork bifurcationDinámica poblacionalTransmisión materna imperfectaCI incompletoPérdida por infecciónCoexistencia estableBifurcación en horquillaComunidad generalPublication72f68479-5914-43da-8996-02353d27d5dcvirtual::6094-1aeb47892-e365-4668-9322-a97426768e27virtual::6095-172f68479-5914-43da-8996-02353d27d5dcvirtual::6094-1aeb47892-e365-4668-9322-a97426768e27virtual::6095-1https://scholar.google.com.co/citations?user=KcfKIyEAAAAJ&hl=esvirtual::6094-1https://scholar.google.com.co/citations?user=u2HFR6AAAAAJ&hl=esvirtual::6095-10000-0003-4828-9360virtual::6094-10000-0002-7052-1851virtual::6095-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0001474886virtual::6094-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000277746virtual::6095-1ORIGINALComparing_the_long-term_persistence_of_different_Wolbachia_strains_after_the_release_of_bacteria-carrying_mosquitoes.pdfComparing_the_long-term_persistence_of_different_Wolbachia_strains_after_the_release_of_bacteria-carrying_mosquitoes.pdfArchivo texto completo del artículo de revista, PDFapplication/pdf1233869https://red.uao.edu.co/bitstreams/a1bf7c81-cc82-40e5-bd9f-a39189748b3e/download66ee90b73aaa18efb8f3fad60b3b2aa2MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81672https://red.uao.edu.co/bitstreams/5b213a5c-5644-4b50-b3d5-0c95a52319a9/download6987b791264a2b5525252450f99b10d1MD52TEXTComparing_the_long-term_persistence_of_different_Wolbachia_strains_after_the_release_of_bacteria-carrying_mosquitoes.pdf.txtComparing_the_long-term_persistence_of_different_Wolbachia_strains_after_the_release_of_bacteria-carrying_mosquitoes.pdf.txtExtracted texttext/plain109461https://red.uao.edu.co/bitstreams/825545cc-3eb2-4e8f-9e60-c0b69aa8ec41/downloadbcbfa36affeb92bd9a9254181dabe913MD53THUMBNAILComparing_the_long-term_persistence_of_different_Wolbachia_strains_after_the_release_of_bacteria-carrying_mosquitoes.pdf.jpgComparing_the_long-term_persistence_of_different_Wolbachia_strains_after_the_release_of_bacteria-carrying_mosquitoes.pdf.jpgGenerated Thumbnailimage/jpeg15584https://red.uao.edu.co/bitstreams/40648979-b2ad-4a80-acbc-12635bfae300/download0a4cd5e99969582928fedd17463d4c54MD5410614/16205oai:red.uao.edu.co:10614/162052025-07-10 03:01:54.624https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos reservados - Elsevier, 2024open.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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