Optimal release programs for dengue prevention using aedes aegypti mosquitoes transinfected with wmel or wmelpop wolbachia strains

In this paper, we propose a dengue transmission model of SIR(S)-SI type that accounts for two sex-structured mosquito populations: the wild mosquitoes (males and females that are Wol- bachia-free), and those deliberately infected with either wMel or wMelPop strain of Wolbachia. This epidemiological...

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Autores:
Cardona Salgado, Daiver
Campo Duarte, Doris Elena
Sepúlveda Salcedo, Lilian Sofía
Vasilieva, Olga
Svinin, Mikhail
Tipo de recurso:
Article of journal
Fecha de publicación:
2021
Institución:
Universidad Autónoma de Occidente
Repositorio:
RED: Repositorio Educativo Digital UAO
Idioma:
eng
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oai:red.uao.edu.co:10614/13901
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https://hdl.handle.net/10614/13901
https://red.uao.edu.co/
Palabra clave:
Virus del dengue
Modelos matemáticos
Dengue viruses
Mathematical models
Aedes aegypti mosquitoes
Sex-structured model
Dengue transmission model
Wolbachia-based biocontrol
wMelPop and wMel strains
Optimal control
Optimal release program
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openAccess
License
Derechos reservados - AIMS Press, 2021
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oai_identifier_str oai:red.uao.edu.co:10614/13901
network_acronym_str REPOUAO2
network_name_str RED: Repositorio Educativo Digital UAO
repository_id_str
dc.title.eng.fl_str_mv Optimal release programs for dengue prevention using aedes aegypti mosquitoes transinfected with wmel or wmelpop wolbachia strains
title Optimal release programs for dengue prevention using aedes aegypti mosquitoes transinfected with wmel or wmelpop wolbachia strains
spellingShingle Optimal release programs for dengue prevention using aedes aegypti mosquitoes transinfected with wmel or wmelpop wolbachia strains
Virus del dengue
Modelos matemáticos
Dengue viruses
Mathematical models
Aedes aegypti mosquitoes
Sex-structured model
Dengue transmission model
Wolbachia-based biocontrol
wMelPop and wMel strains
Optimal control
Optimal release program
title_short Optimal release programs for dengue prevention using aedes aegypti mosquitoes transinfected with wmel or wmelpop wolbachia strains
title_full Optimal release programs for dengue prevention using aedes aegypti mosquitoes transinfected with wmel or wmelpop wolbachia strains
title_fullStr Optimal release programs for dengue prevention using aedes aegypti mosquitoes transinfected with wmel or wmelpop wolbachia strains
title_full_unstemmed Optimal release programs for dengue prevention using aedes aegypti mosquitoes transinfected with wmel or wmelpop wolbachia strains
title_sort Optimal release programs for dengue prevention using aedes aegypti mosquitoes transinfected with wmel or wmelpop wolbachia strains
dc.creator.fl_str_mv Cardona Salgado, Daiver
Campo Duarte, Doris Elena
Sepúlveda Salcedo, Lilian Sofía
Vasilieva, Olga
Svinin, Mikhail
dc.contributor.author.none.fl_str_mv Cardona Salgado, Daiver
Campo Duarte, Doris Elena
Sepúlveda Salcedo, Lilian Sofía
Vasilieva, Olga
Svinin, Mikhail
dc.subject.armarc.spa.fl_str_mv Virus del dengue
Modelos matemáticos
topic Virus del dengue
Modelos matemáticos
Dengue viruses
Mathematical models
Aedes aegypti mosquitoes
Sex-structured model
Dengue transmission model
Wolbachia-based biocontrol
wMelPop and wMel strains
Optimal control
Optimal release program
dc.subject.armarc.eng.fl_str_mv Dengue viruses
Mathematical models
dc.subject.proposal.eng.fl_str_mv Aedes aegypti mosquitoes
Sex-structured model
Dengue transmission model
Wolbachia-based biocontrol
wMelPop and wMel strains
Optimal control
Optimal release program
description In this paper, we propose a dengue transmission model of SIR(S)-SI type that accounts for two sex-structured mosquito populations: the wild mosquitoes (males and females that are Wol- bachia-free), and those deliberately infected with either wMel or wMelPop strain of Wolbachia. This epidemiological model has four possible outcomes: with or without Wolbachia and with or without dengue. To reach the desired outcome, with Wolbachia and without dengue, we employ the dynamic optimization approach and then design optimal programs for releasing Wolbachia-carrying male and female mosquitoes. Our discussion is focused on advantages and drawbacks of two Wolbachia strains, wMelPop and wMel, that are recommended for dengue prevention and control. On the one hand, the wMel strain guarantees a faster population replacement, ensures durable Wolbachia persistence in the wild mosquito population, and requiters fewer releases. On the other hand, the wMelPop strain displays better results for averting dengue infections in the human population
publishDate 2021
dc.date.issued.none.fl_str_mv 2021-03
dc.date.accessioned.none.fl_str_mv 2022-05-20T17:19:53Z
dc.date.available.none.fl_str_mv 2022-05-20T17:19:53Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.type.content.eng.fl_str_mv Text
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dc.identifier.issn.spa.fl_str_mv 15471063
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10614/13901
dc.identifier.instname.spa.fl_str_mv Universidad Autónoma de Occidente
dc.identifier.reponame.spa.fl_str_mv Repositorio Educativo Digital
dc.identifier.repourl.spa.fl_str_mv https://red.uao.edu.co/
identifier_str_mv 15471063
Universidad Autónoma de Occidente
Repositorio Educativo Digital
url https://hdl.handle.net/10614/13901
https://red.uao.edu.co/
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.citationendpage.spa.fl_str_mv 2990
dc.relation.citationissue.spa.fl_str_mv 3
dc.relation.citationstartpage.spa.fl_str_mv 2952
dc.relation.citationvolume.spa.fl_str_mv 18
dc.relation.cites.spa.fl_str_mv Cardona Salgado, D., Campo Duarte, D. E., Sepúlveda Salcedo, L. S., Vasilieva, O., Svinin, M. (2021). Optimal release programs for dengue prevention using Aedes aegypti mosquitoes transinfected with wMel or wMelPop Wolbachia strains. Mathematical Biosciences and Engineering. Vol 18 (3), pp. 2952-2990.
dc.relation.ispartofjournal.eng.fl_str_mv Mathematical Biosciences and Engineering
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 Pathog., 6 (2010), e1000833.
2. J. Kamtchum-Tatuene, B. Makepeace, L. Benjamin, M. Baylis, T. Solomon, The potential role of Wolbachia in controlling the transmission of emerging human arboviral infections, Current Opin. Infect. Diseases, 30 (2017), 108.
3. L. Moreira, I. Iturbe-Ormaetxe, J. Jeffery, G. Lu, A. Pyke, L. Hedges, et al., A Wolbachia symbiont in Aedes aegypti limits infection with dengue, chikungunya, and plasmodium, Cell, 139 (2009), 1268–1278.
4. T. Walker, P. Johnson, L. Moreira, I. Iturbe-Ormaetxe, F. Frentiu, C. McMeniman, et al., The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations, Nature, 476 (2011), 450–453.
5. I. Dorigatti, C. McCormack, G. Nedjati-Gilani, N. Ferguson, Using Wolbachia for dengue control: Insights from modelling, Trends Parasitol., 34 (2018), 102–113.
6. Scott A Ritchie, Michael Townsend, Chris J Paton, Ashley G Callahan, Ary A Hoffmann, Application of wMelPop Wolbachia strain to crash local populations of Aedes aegypti, PLoS Negl. Trop Dis., 9 (2015), e0003930.
7. N. Ferguson, D. Kien, H. Clapham, R. Aguas, V. Trung, T. Chau, et al., Modeling the impact on virus transmission of Wolbachia-mediated blocking of dengue virus infection of Aedes aegypti. Sci. Translat. Med., 7 (2015), 279ra37.
8. M. Woolfit, I. Iturbe-Ormaetxe, J. Brownlie, T. Walker, M. Riegler, A. Seleznev, et al., Genomic evolution of the pathogenic Wolbachia strain, wMelPop, Genome Biol. Evolut., 5 (2013), 2189– 2204.
9. Doris E. Campo-Duarte, Olga Vasilieva, Daiver Cardona-Salgado, Mikhail Svinin, Optimal control methods for establishing wMelPop Wolbachia infection among wild Aedes aegypti populations, J. Math. Biol., 76 (2018), 1907–1950.
10. Daiver Cardona-Salgado, Doris E. Campo-Duarte, Lilian S. Sepulveda-Salcedo, Olga Vasilieva, Wolbachia-based biocontrol for dengue reduction using dynamic optimization approach, Appl. Math. Model., 82 (2020), 125–149.
11. H. Hughes, N. Britton. Modelling the use of Wolbachia to control dengue fever transmission, Bullet. Math. Biol.,75 (2013), 796–818.
12. Meksianis Ndii, Roslyn Hickson, David Allingham, G. N. Mercer. Modelling the transmission dynamics of dengue in the presence of Wolbachia, Math. Biosci., 262 (2015),157–166.
13. N. Bailey, The mathematical theory of infectious diseases and its applications, Charles Griffin & Company Ltd, Bucks, U.K., 1975.
14. Hal Caswell, Daniel E. Weeks. Two-sex models: Chaos, extinction, and other dynamic consequences of sex, Am. Natural., 128 (1986), 707–735.
15. J. N. Liles, Effects of mating or association of the sexes on longevity in Aedes aegypti (L.), Mosquito News, 25 (1965), 434–439.
16. J. Werren, L. Baldo, M. Clark. Wolbachia: Master manipulators of invertebrate biology. Nat. Rev. Microbiol., 6 (2008), 741.
17. L. Almeida, A. Haddon, C. Kermorvant, A. Leculier, Y. Privat, M. Strugarek, et al., Optimal ´ release of mosquitoes to control dengue transmission, ESAIM Proceed. Surveys, 67 (2020), 16– 29.
18. J. Schraiber, A. Kaczmarczyk, R. Kwok, M. Park, R. Silverstein, F. Rutaganira, et al., Constraints on the use of lifespan-shortening Wolbachia to control dengue fever, J. Theoret. Biol., 297 (2012), 26–32.
19. M. Turelli, Cytoplasmic incompatibility in populations with overlapping generations, Evolution, 64 (2010), 232–241.
20. L. Almeida, M. Duprez, Y. Privat, N. Vauchelet. Mosquito population control strategies for fighting against arboviruses, Math. Biosci. Eng., 16 (2019), 6274–6297.
21. L. Almeida, Y. Privat, M. Strugarek, N. Vauchelet. Optimal releases for population replacement strategies: Application to Wolbachia, SIAM J. Math. Anal., 51 (2019), 3170–3194.
22. P.-A. Bliman, M. S. Aronna, F. C. Coelho, Moacyr A. H. Da Silva, Ensuring successful introduction of Wolbachia in natural populations of Aedes aegypti by means of feedback control, J. Math. Biol., 76 (2018), 1269–1300.
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48. P. Hancock, S. Sinkins, H. Godfray, Population dynamic models of the spread of Wolbachia. Am. Natural., 177 (2011), 323–333.
49. L. Styer, S. Minnick, A. Sun, T. Scott. Mortality and reproductive dynamics of Aedes aegypti (Diptera: Culicidae) fed human blood, Vector-borne Zoonot. Diseases, 7 (2007), 86–98.
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dc.rights.spa.fl_str_mv Derechos reservados - AIMS Press, 2021
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rights_invalid_str_mv Derechos reservados - AIMS Press, 2021
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spelling Cardona Salgado, Daivervirtual::1169-1Campo Duarte, Doris Elenavirtual::1000-1Sepúlveda Salcedo, Lilian Sofíavirtual::4683-1Vasilieva, Olga31f6a4db00254953edddbca148e36487Svinin, Mikhailcebfbd9cdab50bbe6233c8c30761320e2022-05-20T17:19:53Z2022-05-20T17:19:53Z2021-0315471063https://hdl.handle.net/10614/13901Universidad Autónoma de OccidenteRepositorio Educativo Digitalhttps://red.uao.edu.co/In this paper, we propose a dengue transmission model of SIR(S)-SI type that accounts for two sex-structured mosquito populations: the wild mosquitoes (males and females that are Wol- bachia-free), and those deliberately infected with either wMel or wMelPop strain of Wolbachia. This epidemiological model has four possible outcomes: with or without Wolbachia and with or without dengue. To reach the desired outcome, with Wolbachia and without dengue, we employ the dynamic optimization approach and then design optimal programs for releasing Wolbachia-carrying male and female mosquitoes. Our discussion is focused on advantages and drawbacks of two Wolbachia strains, wMelPop and wMel, that are recommended for dengue prevention and control. On the one hand, the wMel strain guarantees a faster population replacement, ensures durable Wolbachia persistence in the wild mosquito population, and requiters fewer releases. On the other hand, the wMelPop strain displays better results for averting dengue infections in the human population39 páginasapplication/pdfengAIMS PressDerechos reservados - AIMS Press, 2021https://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_abf2Optimal release programs for dengue prevention using aedes aegypti mosquitoes transinfected with wmel or wmelpop wolbachia strainsArtículo 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/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Virus del dengueModelos matemáticosDengue virusesMathematical modelsAedes aegypti mosquitoesSex-structured modelDengue transmission modelWolbachia-based biocontrolwMelPop and wMel strainsOptimal controlOptimal release program29903295218Cardona Salgado, D., Campo Duarte, D. E., Sepúlveda Salcedo, L. S., Vasilieva, O., Svinin, M. (2021). Optimal release programs for dengue prevention using Aedes aegypti mosquitoes transinfected with wMel or wMelPop Wolbachia strains. Mathematical Biosciences and Engineering. Vol 18 (3), pp. 2952-2990.Mathematical Biosciences and Engineering1. G. Bian, Y. Xu, P. Lu, Y. Xie, Z. Xi, The endosymbiotic bacterium Wolbachia induces resistance to dengue virus in Aedes aegypti, PLoS Pathog., 6 (2010), e1000833.2. J. Kamtchum-Tatuene, B. Makepeace, L. Benjamin, M. Baylis, T. Solomon, The potential role of Wolbachia in controlling the transmission of emerging human arboviral infections, Current Opin. Infect. Diseases, 30 (2017), 108.3. L. Moreira, I. Iturbe-Ormaetxe, J. Jeffery, G. Lu, A. Pyke, L. Hedges, et al., A Wolbachia symbiont in Aedes aegypti limits infection with dengue, chikungunya, and plasmodium, Cell, 139 (2009), 1268–1278.4. T. Walker, P. Johnson, L. Moreira, I. Iturbe-Ormaetxe, F. Frentiu, C. McMeniman, et al., The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations, Nature, 476 (2011), 450–453.5. I. Dorigatti, C. McCormack, G. Nedjati-Gilani, N. Ferguson, Using Wolbachia for dengue control: Insights from modelling, Trends Parasitol., 34 (2018), 102–113.6. Scott A Ritchie, Michael Townsend, Chris J Paton, Ashley G Callahan, Ary A Hoffmann, Application of wMelPop Wolbachia strain to crash local populations of Aedes aegypti, PLoS Negl. Trop Dis., 9 (2015), e0003930.7. N. Ferguson, D. Kien, H. Clapham, R. Aguas, V. Trung, T. Chau, et al., Modeling the impact on virus transmission of Wolbachia-mediated blocking of dengue virus infection of Aedes aegypti. Sci. Translat. Med., 7 (2015), 279ra37.8. M. Woolfit, I. Iturbe-Ormaetxe, J. Brownlie, T. Walker, M. Riegler, A. Seleznev, et al., Genomic evolution of the pathogenic Wolbachia strain, wMelPop, Genome Biol. Evolut., 5 (2013), 2189– 2204.9. Doris E. Campo-Duarte, Olga Vasilieva, Daiver Cardona-Salgado, Mikhail Svinin, Optimal control methods for establishing wMelPop Wolbachia infection among wild Aedes aegypti populations, J. Math. Biol., 76 (2018), 1907–1950.10. Daiver Cardona-Salgado, Doris E. Campo-Duarte, Lilian S. Sepulveda-Salcedo, Olga Vasilieva, Wolbachia-based biocontrol for dengue reduction using dynamic optimization approach, Appl. Math. Model., 82 (2020), 125–149.11. H. Hughes, N. Britton. Modelling the use of Wolbachia to control dengue fever transmission, Bullet. Math. Biol.,75 (2013), 796–818.12. Meksianis Ndii, Roslyn Hickson, David Allingham, G. N. Mercer. Modelling the transmission dynamics of dengue in the presence of Wolbachia, Math. Biosci., 262 (2015),157–166.13. N. Bailey, The mathematical theory of infectious diseases and its applications, Charles Griffin & Company Ltd, Bucks, U.K., 1975.14. Hal Caswell, Daniel E. Weeks. Two-sex models: Chaos, extinction, and other dynamic consequences of sex, Am. Natural., 128 (1986), 707–735.15. J. N. Liles, Effects of mating or association of the sexes on longevity in Aedes aegypti (L.), Mosquito News, 25 (1965), 434–439.16. J. Werren, L. Baldo, M. Clark. Wolbachia: Master manipulators of invertebrate biology. Nat. Rev. Microbiol., 6 (2008), 741.17. L. Almeida, A. Haddon, C. Kermorvant, A. Leculier, Y. Privat, M. Strugarek, et al., Optimal ´ release of mosquitoes to control dengue transmission, ESAIM Proceed. Surveys, 67 (2020), 16– 29.18. J. Schraiber, A. Kaczmarczyk, R. Kwok, M. Park, R. Silverstein, F. Rutaganira, et al., Constraints on the use of lifespan-shortening Wolbachia to control dengue fever, J. Theoret. Biol., 297 (2012), 26–32.19. M. Turelli, Cytoplasmic incompatibility in populations with overlapping generations, Evolution, 64 (2010), 232–241.20. L. Almeida, M. Duprez, Y. Privat, N. Vauchelet. Mosquito population control strategies for fighting against arboviruses, Math. Biosci. Eng., 16 (2019), 6274–6297.21. L. Almeida, Y. 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Model., 81 (2020), 296–319.Comunidad generalPublication72f68479-5914-43da-8996-02353d27d5dcvirtual::1169-15d52813a-b7be-448d-bc24-492faea43f0fvirtual::1000-1aeb47892-e365-4668-9322-a97426768e27virtual::4683-15d52813a-b7be-448d-bc24-492faea43f0fvirtual::1000-172f68479-5914-43da-8996-02353d27d5dcvirtual::1169-1aeb47892-e365-4668-9322-a97426768e27virtual::4683-1https://scholar.google.com.co/citations?user=KcfKIyEAAAAJ&hl=esvirtual::1169-1https://scholar.google.com/citations?hl=es&user=wyuT448AAAAJvirtual::1000-1https://scholar.google.com.co/citations?user=u2HFR6AAAAAJ&hl=esvirtual::4683-10000-0003-4828-9360virtual::1169-10000-0001-6832-9265virtual::1000-10000-0002-7052-1851virtual::4683-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0001474886virtual::1169-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0001349182virtual::1000-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000277746virtual::4683-1LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/6f04c08a-0f81-4b20-a9ae-63ce22fcaf86/download20b5ba22b1117f71589c7318baa2c560MD52ORIGINALOptimal release programs for dengue prevention using Aedes aegypti mosquitoes transinfected with wMel or wMelPop Wolbachia strains.pdfOptimal release programs for dengue prevention using Aedes aegypti mosquitoes transinfected with wMel or wMelPop Wolbachia strains.pdfTexto archivo completo del artículo de revista, PDFapplication/pdf2995289https://red.uao.edu.co/bitstreams/e8c08aa2-00d5-431b-9e67-0e748cf45176/download3d08f843403a44e451c4c85b4d5f762dMD53TEXTOptimal release programs for dengue prevention using Aedes aegypti mosquitoes transinfected with wMel or wMelPop Wolbachia strains.pdf.txtOptimal release programs for dengue prevention using Aedes aegypti mosquitoes transinfected with wMel or wMelPop Wolbachia strains.pdf.txtExtracted texttext/plain111335https://red.uao.edu.co/bitstreams/226e7478-0d62-4db0-ace0-e8b01c6e3463/download2a60f2f23521a33a18219ef84537cdc2MD54THUMBNAILOptimal release programs for dengue prevention using Aedes aegypti mosquitoes transinfected with wMel or wMelPop Wolbachia strains.pdf.jpgOptimal release programs for dengue prevention using Aedes aegypti mosquitoes transinfected with wMel or wMelPop Wolbachia strains.pdf.jpgGenerated Thumbnailimage/jpeg14819https://red.uao.edu.co/bitstreams/111c640b-d2d7-4071-a456-81016cba9963/download78fc4cf889ca957252fd8d5c43f7b280MD5510614/13901oai:red.uao.edu.co:10614/139012024-03-15 08:58:22.364https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos reservados - AIMS Press, 2021open.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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