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dc.contributor.authorCardona Salgado, Daiver
dc.contributor.authorCampo Duarte, Doris Elena
dc.contributor.authorSvinin, Mikhail
dc.contributor.authorVasilieva, Olga
dc.coverage.spatialUniversidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí
dc.date.accessioned2019-11-01T20:57:14Z
dc.date.available2019-11-01T20:57:14Z
dc.date.issued2018-02-10
dc.identifier.issn0303-6812spa
dc.identifier.urihttp://hdl.handle.net/10614/11386
dc.description.abstractWolbachia-based biocontrol has recently emerged as a potential method for prevention and control of dengue and other vector-borne diseases. Major vector species, such as Aedes aegypti females, when deliberately infected with Wolbachia become less capable of getting viral infections and transmitting the virus to human hosts. In this paper, we propose an explicit sex-structured population model that describes an interaction of uninfected (wild) male and female mosquitoes and those deliberately infected with wMelPop strain of Wolbachia in the same locality. This particular strain of Wolbachia is regarded as the best blocker of dengue and other arboviral infections. However, wMelPop strain of Wolbachia also causes the loss of individual fitness in Aedes aegypti mosquitoes. Our model allows for natural introduction of the decision (or control) variable, and we apply the optimal control approach to simulate wMelPop Wolbachia infestation of wild Aedes aegypti populations. The control action consists in continuous periodic releases of mosquitoes previously infected with wMelPop strain of Wolbachia in laboratory conditions. The ultimate purpose of control is to find a tradeoff between reaching the population replacement in minimum time and with minimum cost of the control effort. This approach also allows us to estimate the number of Wolbachia-carrying mosquitoes to be released in day-by-day control action. The proposed method of biological control is safe to human health, does not contaminate the environment, does not make harm to non-target species, and preserves their interaction with mosquitoes in the ecosystemeng
dc.formatapplication/pdfeng
dc.format.extent44 páginasspa
dc.language.isoengeng
dc.publisherSpringer Verlageng
dc.rightsDerechos Reservados - Universidad Autónoma de Occidentespa
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/eng
dc.sourcereponame:Repositorio Institucional UAOspa
dc.titleOptimal control approach for establishing wMelPop wolbachia infection among wild aedes aegypti populationseng
dc.typeArtículo de revistaspa
dc.subject.armarcDenguespa
dc.subject.armarcAnimales vectoresspa
dc.subject.armarcAnimals as carriers of diseaseeng
dc.identifier.doihttps://doi.org/10.1007/s00285-018-1213-2spa
dc.relation.citationendpage1950
dc.relation.citationissue7
dc.relation.citationstartpage1907
dc.relation.citationvolume76
dc.relation.citesCampo-Duarte, D. E., Vasilieva, O., Cardona-Salgado, D., & Svinin, M. (2018). Optimal control approach for establishing wMelPop Wolbachia infection among wild Aedes aegypti populations. Journal of mathematical biology, 76(7), 1907-1950. https://doi.org/10.1007/s00285-018-1213-2spa
dc.relation.ispartofjournalMathematical Biology, volumen 76, issue 7, páginas 1907-1950, 2018eng
dc.relation.referencesAscher UM, Mattheij RMM, Russell RD (1988) Numerical solution of boundary value problems for ordinary differential equations. Prentice Hall series in computational mathematics. Prentice Hall Inc., Englewood Cliffs
dc.relation.referencesBarton N, Turelli M (2011) Spatial waves of advance with bistable dynamics: cytoplasmic and genetic analogues of Allee effects. Am Nat 178(3):E48–E75
dc.relation.referencesBian G, Xu Y, Lu P, Xie Y, Xi Z (2010) The endosymbiotic bacterium Wolbachia induces resistance to dengue virus in Aedes aegypti. PLoS Pathog 6(4):e1000,833
dc.relation.referencesBlayneh K, Cao Y, Kwon HD (2009) Optimal control of vector-borne diseases: treatment and prevention. Discrete Contin Dyn Syst B 11(3):587–611. https://doi.org/10.3934/dcdsb.2009.11.587
dc.relation.referencesBliman PA, Aronna MS, da Silva MA, et al (2015) Global stabilizing feedback law for a problem of biological control of mosquito-borne diseases. In: 2015 54th IEEE conference on decision and control (CDC). IEEE, pp 3206–3211
dc.relation.referencesBrauer F, Castillo-Chávez C (2012) Mathematical models in population biology and epidemiology. Texts Appl Math. https://doi.org/10.1007/978-1-4614-1686-9
dc.relation.referencesBrown JE, McBride CS, Johnson P, Ritchie S, Paupy C, Bossin H, Lutomiah J, Fernandez-Salas I, Ponlawat A, Cornel AJ, Black WC, Gorrochotegui-Escalante N, Urdaneta-Marquez L, Sylla M, Slotman M, Murray KO, Walker C, Powell JR (2011) Worldwide patterns of genetic differentiation imply multiple “domestications” of Aedes aegypti, a major vector of human diseases. Proc R Soc B Biol Sci 278(1717):2446–2454
dc.relation.referencesBryson A, Ho YC (1975) Applied optimal control: optimization, estimation and control. Halsted Press Book, New York
dc.relation.referencesBull JJ, Turelli M (2013) Wolbachia versus dengue evolutionary forecasts. Evol Med Public Health 2013(1):197–207
dc.relation.referencesCampo-Duarte DE, Cardona-Salgado D, Vasilieva O (2017a) Establishing wMelPop Wolbachia infection among wild Aedes aegypti females by optimal control approach. Appl Math Inf Sci 11(4):1011–1027. https://doi.org/10.18576/amis/110408
dc.relation.referencesCampo-Duarte DE,Vasilieva O, Cardona-SalgadoD(2017b) Optimal control for enhancement ofWolbachia frequency among Aedes aegypti females. Int J Pure Appl Math 112(2):219–238. https://doi.org/10.12732/ijpam.v112i2.1
dc.relation.referencesCastillo-Chávez C, Feng Z, Huang W (2002) On the computation of Ro and its role on global stability. In: Castillo-Chávez C, Blower S, Driessche P, Kirschner D, Yakubu A (eds)Mathematical approaches for emerging and reemerging infectious diseases: an introduction, vol 125. Springer, Berlin, pp 229–250
dc.relation.referencesCaswell H, Weeks DE (1986) Two-sex models: chaos, extinction, and other dynamic consequences of sex. Am Nat 128(5):707–735
dc.relation.referencesChan M, Johansson MA (2012) The incubation periods of dengue viruses. PloS ONE 7(11):e50,972
dc.relation.referencesCoelho FC, Codeço CT,GomesMGM(2011)ABayesian framework for parameter estimation in dynamical models. PloS ONE 6(5):e19,616
dc.relation.referencesDenlinger DL, Armbruster PA (2014) Mosquito diapause. Ann Rev Entomol 59:73–93
dc.relation.referencesDiekmann O, Heesterbeek J (2000) Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. Wiley, Hoboken Wiley Series in Mathematical & Computational Biology
dc.relation.referencesDiekmann O, Heesterbeek J, Metz J (1990) On the definition and the computation of the basic reproduction ratio Ro in models for infectious diseases in heterogeneous populations. J Math Biol 28(4):365–382
dc.relation.referencesDomínguez MC, Ludueña-Almeida FF, Almirón WR (2000) Dinámica poblacional de Aedes aegypti (Diptera: Culicidae) en Córdoba capital [Population dynamics of Aedes aegypti (Diptera: Culicidae) in Cordoba capital]. Revista de la Sociedad Entomológica Argentina 59(1–4):41–50
dc.relation.referencesDutraHLC,Rocha MN,Dias FBS, Mansur SB,Caragata EP,Moreira LA(2016)Wolbachia blocks currently circulating Zika virus isolates in Brazilian Aedes aegypti mosquitoes. Cell Host Microbe 19(6):771–774
dc.relation.referencesDye C (1984) Models for the population dynamics of the yellow fever mosquito, Aedes aegypti. J Anim Ecol 53(1):247–268
dc.relation.referencesFarkas JZ, Hinow P (2010) Structured and unstructured continuous models for Wolbachia infections. Bull Math Biol 72(8):2067–2088
dc.relation.referencesFarkas JZ, Gourley SA, Liu R, Yakubu AA (2017) Modelling Wolbachia infection in a sex-structured mosquito population carrying West Nile virus. J Math Biol 75(3):621–647. https://doi.org/10.1007/s00285-017-1096-7
dc.relation.referencesFarkas M (2001) Dynamical models in biology. Elsevier, Amsterdam
dc.relation.referencesFerguson NM, Kien DTH, Clapham H, Aguas R, Trung VT, Chau TNB, Popovici J, Ryan PA, O’Neill SL, McGraw EA, Long VT, Dui LT, Nguyen HL, Vinh Chau NV,Wills B, Simmons CP (2015) Modeling the impact on virus transmission ofWolbachia-mediated blocking of dengue virus infection of Aedes aegypti. Sci Transl Med 7(279):279ra37–279ra37
dc.relation.referencesFleming W, Rishel R (1975) Deterministic and stochastic optimal control. Springer, New York
dc.relation.referencesFrentiu FD,Walker T, O’Neill SL (2014a) Biological control of dengue andWolbachia-based strategies. In: Gubler D, Ooi E, Vasudevan S, Farrar J (eds) Dengue and dengue hemorrhagic fever, 2nd edn. CAB Books, CABI
dc.relation.referencesFrentiu FD, Zakir T, Walker T, Popovici J, Pyke AT, van den Hurk A, McGraw EA, O’Neill SL (2014b) Limited dengue virus replication in field-collected Aedes aegypti mosquitoes infected withWolbachia. PLoS Negl Trop Dis 8(2):e2688
dc.relation.referencesGarg D, PattersonMA, DarbyCL, Francolin C, HuntingtonGT,HagerWW,RaoAV(2009) Direct trajectory optimization and costate estimation of general optimal control problems using a Radau pseudospectral method. In: Proceedings of the AIAA guidance, navigation, and control conference and exhibit
dc.relation.referencesHancock PA, Godfray HCJ (2012) Modelling the spread of Wolbachia in spatially heterogeneous environments. J R Soc Interface 9(76):3045–3054
dc.relation.referencesHancock PA, Sinkins SP, Godfray HCJ (2011a) Population dynamic models of the spread of Wolbachia. Am Nat 177(3):323–333
dc.relation.referencesHancock PA, Sinkins SP, Godfray HCJ (2011b) Strategies for introducingWolbachia to reduce transmission of mosquito-borne diseases. PLoS Negl Trop Dis 5(4):e1024
dc.relation.referencesHilgenboecker K, Hammerstein P, Schlattmann P, Telschow A, Werren JH (2008) How many species are infected with Wolbachia?—A statistical analysis of current data. FEMS Microbiol Lett 281(2):215–220
dc.relation.referencesHoffmann A, Montgomery B, Popovici J, Iturbe-Ormaetxe I, Johnson P, Muzzi F, Greenfield M, Durkan M, Leong Y, Dong Y, Cook H, Axford J, Callahan A, Kenny N, Omodei C,McGraw E, Ryan P, Ritchie S, Turelli M, O’Neill S (2011) Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission. Nature 476(7361):454–457
dc.relation.referencesHoffmann AA (2014) Facilitating Wolbachia invasions. Austral Entomol 53(2):125–132
dc.relation.referencesHoffmann AA, Turelli M (2013) Facilitating Wolbachia introductions into mosquito populations through insecticide-resistance selection. Proc R Soc Lond B Biol Sci 280(1760):20130371
dc.relation.referencesHughes H, Britton NF (2013) Modelling the use of Wolbachia to control dengue fever transmission. Bull Math Biol 75(5):796–818
dc.relation.referencesHurst TP, Pittman G, O’Neill SL, Ryan PA, Le Nguyen H, Kay BH (2012) Impacts of Wolbachia infection on predator prey relationships: evaluating survival and horizontal transfer between wMelPop infected Aedes aegypti and its predators. J Med Entomol 49(3):624–630
dc.relation.referencesJansen CC, Beebe NW (2010) The dengue vector Aedes aegypti: what comes next. Microbes Infect 12(4):272–279
dc.relation.referencesKeyfitz N (1972) The mathematics of sex and marriage. In: Proceedings of the sixth Berkeley symposium on mathematical statistics and probability, vol 4. University of California Press, Berkeley, pp 89–108
dc.relation.referencesKobayashi Y, Telschow A (2010) Cytoplasmic feminizing elements in a two-population model: infection dynamics, gene flowmodification, and the spread of autosomal suppressors. J Evolut Biol 23(12):2558–2568
dc.relation.referencesKoiller J, Da Silva M, Souza M, Codeço C, Iggidr A, Sallet G (2014) Aedes, Wolbachia and Dengue. Technical report
dc.relation.referencesKot M (2001) Elements of mathematical ecology. Cambridge University Press, Cambridge
dc.relation.referencesKroese DP, Taimre T, Botev ZI (2011) Handbook of Monte Carlo methods, vol 706.Wiley series in probability and statistics. Wiley, Hoboken
dc.relation.referencesLawson AB (2006) Statistical methods in spatial epidemiology, 2nd edn. Wiley series in probability and statistics. Wiley, Hoboken
dc.relation.referencesLenhart S,Workman JT (2007) Optimal control applied to biological models. Chapman & Hall/CRC, Boca Raton
dc.relation.referencesLiles JN (1965) Effects of mating or association of the sexes on longevity in Aedes aegypti (l.). Mosquito News 25:434–439
dc.relation.referencesLindström J, Kokko H (1998) Sexual reproduction and population dynamics: the role of polygyny and demographic sex differences. Proc R Soc Lond B Biol Sci 265(1395):483–488
dc.relation.referencesManore CA, Hickmann KS, Xu S, Wearing HJ, Hyman JM (2014) Comparing dengue and chikungunya emergence and endemic transmission in A. aegypti and A. albopictus. J Theor Biol 356:174–191
dc.relation.referencesMcGraw EA, O’Neill SL (2013) Beyond insecticides: new thinking on an ancient problem. Nat RevMicrobiol 11(3):181–193. https://doi.org/10.1038/nrmicro2968
dc.relation.referencesMcMeniman C et al (2009) Stable introduction of a life-shortening Wolbachia infection into the mosquito Aedes aegypti. Science 323(5910):141–144
dc.relation.referencesMcMeniman CJ, O’Neill SL (2010) A virulent Wolbachia infection decreases the viability of the dengue vector Aedes aegypti during periods of embryonic quiescence. PLoS Negl Trop Dis 4(7):e748
dc.relation.referencesMoreira LA, Iturbe-Ormaetxe I, Jeffery JA, Lu G, Pyke AT, Hedges LM, Rocha BC, Hall-Mendelin S, Day A, Riegler M et al (2009) A Wolbachia symbiont in Aedes aegypti limits infection with dengue, chikungunya, and plasmodium. Cell 139(7):1268–1278
dc.relation.referencesMoulay D, Aziz-Alaoui MA, Kwon HD (2012) Optimal control of chikungunya disease: larvae reduction, treatment and prevention. Math Biosci Eng 9(2):369–392. https://doi.org/10.3934/mbe.2012.9.369
dc.relation.referencesNdii MZ, Hickson R, Allingham D, Mercer G (2015) Modelling the transmission dynamics of dengue in the presence of Wolbachia. Math Biosci 262:157–166
dc.relation.referencesNguyen T, Le Nguyen H, Nguyen T, Vu S, Tran N, Le T, Vien Q, Bui T, Le H, Kutcher S, Hurst T, Duong T, Jeffery J, Darbro J, Kay H, Iturbe-Ormaetxe I, Popovici J, Montgomery B, Turley A, Zigterman F, Cook H, Cook P, Johnson P, Ryan P, Paton C, Ritchie S, Simmons C, O’Neill S, Hoffmann A (2015) Field evaluation of the establishment potential of wMelPop Wolbachia in Australia and Vietnam for dengue control. Parasit Vectors 8(1):1
dc.relation.referencesOkosun KO, Ouifki R, Marcus N (2011) Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity. Biosystems 106(2):136–145. https://doi.org/10.1016/j.biosystems.2011.07.006
dc.relation.referencesOkosun KO, Rachid O, Marcus N (2013) Optimal control strategies and cost-effectiveness analysis of a malaria model. BioSystems 111(2):83–101. https://doi.org/10.1016/j.biosystems.2012.09.008
dc.relation.referencesPattersonMA, Rao AV (2014) GPOPS-II: AMATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming. ACM Trans Math Softw (TOMS) 41(1):1
dc.relation.referencesPopovici J, MoreiraLA, Poinsignon A, Iturbe-Ormaetxe I,McNaughton D, O’Neill SL (2010) Assessing key safety concerns of a Wolbachia-based strategy to control dengue transmission by Aedes mosquitoes. Memórias do Instituto Oswaldo Cruz 105(8):957–964
dc.relation.referencesRitchie SA, Montgomery BL, Hoffmann AA (2013) Novel estimates of Aedes aegypti (Diptera: Culicidae) population size and adult survival based on Wolbachia releases. J Med Entomol 50(3):624–631
dc.relation.referencesRitchie SA,Townsend M, PatonCJ, CallahanAG, HoffmannAA(2015) Application ofwMelPopWolbachia strain to crash local populations of Aedes aegypti. PLoS Negl Trop Dis 9(7):e0003930
dc.relation.referencesRoberts SM, Shipman JS (1972) Two-point boundary value problems: shooting methods. In: Modern analytic and computational methods in science and mathematics, vol 31. Elsevier, New York
dc.relation.referencesRockwood LL (2015) Introduction to population ecology, 2nd edn. Wiley, Hoboken
dc.relation.referencesRoss PA,EndersbyNM,Yeap HL,HoffmannAA(2014) Larval competition extends developmental time and decreases adult size of wMelPop Wolbachia-infected Aedes aegypti. Am J Trop Med Hyg 91(1):198–
dc.relation.referencesRuang-Areerate T, Kittayapong P (2006)Wolbachia transinfection in Aedes aegypti: a potential gene driver of dengue vectors. Proc Natl Acad Sci 103(33):12534–12539
dc.relation.referencesSchraiber JG, Kaczmarczyk AN, Kwok R, Park M, Silverstein R, Rutaganira FU, Aggarwal T, Schwemmer MA, Hom CL, Grosberg RK et al (2012) Constraints on the use of lifespan-shortening Wolbachia to control dengue fever. J Theor Biol 297:26–32
dc.relation.referencesSepúlveda LS, Vasilieva O (2016) Optimal control approach to dengue reduction and prevention in Cali, Colombia. Math Methods Appl Sci 39(18):5475–5496
dc.relation.referencesSepúlveda-Salcedo LS, Vasilieva O, Martínez-Romero HJ, Arias-Castro JH (2015) Ross-Macdonald: Un modelo para la dinámica del dengue en Cali. Colombia. Revista de Salud Pública 17(5):749–761
dc.relation.referencesSinkins SP (2004) Wolbachia and cytoplasmic incompatibility in mosquitoes. Insect Biochem Mol Biol 34(7):723–729
dc.relation.referencesSinkins SP (2013) Wolbachia and arbovirus inhibition in mosquitoes. Future Microbiol 8(10):1249–1256
dc.relation.referencesSoares-Pinheiro V, Dasso-PinheiroW, Trindade-Bezerra J, TadeiW(2017) Eggs viability of Aedes aegypti Linnaeus (Diptera, Culicidae) under different environmental and storage conditions in Manaus, Amazonas. Brazil. Braz J Biol 77(2):396–401
dc.relation.referencesStyer LM, Minnick SL, Sun AK, Scott TW (2007) Mortality and reproductive dynamics of Aedes aegypti (Diptera: Culicidae) fed human blood. Vector Borne Zoonotic Dis 7(1):86–98
dc.relation.referencesTelschow A, Flor M, Kobayashi Y, Hammerstein P, Werren JH (2007) Wolbachia-induced unidirectional cytoplasmic incompatibility and speciation: mainland-island model. PLoS ONE 2(8):e701
dc.relation.referencesThieme H (2003) Mathematics in population biology. Mathematical biology series. Princeton University Press, Princeton
dc.relation.referencesTurelli M (2010) Cytoplasmic incompatibility in populations with overlapping generations. Evolution 64(1):232–241
dc.relation.referencesTurelli M, HoffmannAA(1991) Rapi d spread of an inherited incompatibility factor inCaliforniaDrosophila. Nature 353(6343):440–442
dc.relation.referencesWalker T, Johnson P, Moreira L, Iturbe-Ormaetxe I, Frentiu F, McMeniman C, Leong Y, Dong Y, Axford J, Kriesner P, Lloyd A, Ritchie S, O’Neill S, Hoffmann A (2011) The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations. Nature 476(7361):450–453
dc.relation.referencesWilliams CR, Johnson P, BallT, Ritchie S (2013) Productivity and population density estimates of the dengue vector mosquito Aedes aegypti (Stegomyia aegypti) in Australia. Med Vet Entomol 27(3):313–322
dc.relation.referencesWoolfit M, Iturbe-Ormaetxe I, Brownlie JC, Walker T, Riegler M, Seleznev A, Popovici J, Rancès E, Wee BA, Pavlides J et al (2013) Genomic evolution of the pathogenicWolbachia strain, wMelPop. Genome Biol Evol 5(11):2189–2204
dc.relation.referencesXi Z, Khoo CC, Dobson SL (2005) Wolbachia establishment and invasion in an Aedes aegypti laboratory population. Science 310(5746):326–328
dc.relation.referencesYamauchi A, Telschow A, Kobayashi Y (2010) Evolution of cytoplasmic sex ratio distorters: Effect of paternal transmission. J Theoret Biol 266(1):79–87
dc.relation.referencesYeap HL, Mee P, Walker T, Weeks AR, O’Neill SL, Johnson P, Ritchie SA, Richardson KM, Doig C, Endersby NM, Hoffmann AA (2011) Dynamics of the “popcorn” Wolbachia infection in outbred Aedes aegypti informs prospects for mosquito vector control. Genetics 187(2):583–595
dc.relation.referencesYeap HL, Axford JK, Popovici J, Endersby NM, Iturbe-Ormaetxe I, Ritchie SA, Hoffmann AA (2014) Assessing quality of life-shortening Wolbachia-infected Aedes aegypti mosquitoes in the field based on capture rates andmorphometric assessments. ParasitesVectors 7(58):1–13. https://doi.org/10.1186/1756-3305-7-58
dc.rights.accessrightsinfo:eu-repo/semantics/openAccesseng
dc.rights.creativecommonsAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)spa
dc.subject.proposalWolbachia-based biocontroleng
dc.subject.proposalWMelPop straineng
dc.subject.proposalAedes aegyptieng
dc.subject.proposalSex-structured modeleng
dc.subject.proposalOptimal controleng
dc.subject.proposalOptimal release policieseng
dc.type.coarhttp://purl.org/coar/resource_type/c_6501eng
dc.type.contentTexteng
dc.type.driverinfo:eu-repo/semantics/articleeng
dc.type.redcolhttp://purl.org/redcol/resource_type/ARTREFeng
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2eng
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85eng
dc.type.versioninfo:eu-repo/semantics/publishedVersioneng


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