Optimal control of dengue epidemic outbreaks under limited resources
In this paper, we reflect upon control intervention practices habitually exerted by healthcare authorities in tropical areas that suffer from incidental outbreaks of dengue fever, in particular, the city of Cali, Colombia. Such control interventions, principally based on the insecticide spraying, ar...
- Autores:
-
Sepúlveda Salcedo, Lilian Sofía
Vasilieva, Olga
Svinin, Mikhail
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2020
- Institución:
- Universidad Autónoma de Occidente
- Repositorio:
- RED: Repositorio Educativo Digital UAO
- Idioma:
- eng
- OAI Identifier:
- oai:red.uao.edu.co:10614/13298
- Acceso en línea:
- https://hdl.handle.net/10614/13298
- Palabra clave:
- Control vectorial
Denge
Vector control
Dengue outbreaks
Insecticide based vector control
Isoperimetric constraint
Optimal control
Optimization
Ross-Macdonald model
- Rights
- openAccess
- License
- Derechos reservados - Wiley, 2020
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Optimal control of dengue epidemic outbreaks under limited resources |
| title |
Optimal control of dengue epidemic outbreaks under limited resources |
| spellingShingle |
Optimal control of dengue epidemic outbreaks under limited resources Control vectorial Denge Vector control Dengue outbreaks Insecticide based vector control Isoperimetric constraint Optimal control Optimization Ross-Macdonald model |
| title_short |
Optimal control of dengue epidemic outbreaks under limited resources |
| title_full |
Optimal control of dengue epidemic outbreaks under limited resources |
| title_fullStr |
Optimal control of dengue epidemic outbreaks under limited resources |
| title_full_unstemmed |
Optimal control of dengue epidemic outbreaks under limited resources |
| title_sort |
Optimal control of dengue epidemic outbreaks under limited resources |
| dc.creator.fl_str_mv |
Sepúlveda Salcedo, Lilian Sofía Vasilieva, Olga Svinin, Mikhail |
| dc.contributor.author.none.fl_str_mv |
Sepúlveda Salcedo, Lilian Sofía |
| dc.contributor.author.spa.fl_str_mv |
Vasilieva, Olga Svinin, Mikhail |
| dc.subject.armarc.spa.fl_str_mv |
Control vectorial Denge |
| topic |
Control vectorial Denge Vector control Dengue outbreaks Insecticide based vector control Isoperimetric constraint Optimal control Optimization Ross-Macdonald model |
| dc.subject.armarc.eng.fl_str_mv |
Vector control |
| dc.subject.proposal.eng.fl_str_mv |
Dengue outbreaks Insecticide based vector control Isoperimetric constraint Optimal control Optimization Ross-Macdonald model |
| description |
In this paper, we reflect upon control intervention practices habitually exerted by healthcare authorities in tropical areas that suffer from incidental outbreaks of dengue fever, in particular, the city of Cali, Colombia. Such control interventions, principally based on the insecticide spraying, are carried out sporadically in order to overcome an ongoing epidemic or at least to reduce its size. It is worth pointing out that control actions of this type do not usually account for sufficient budget because epidemic outbreaks are difficult to predict. In practical terms, these occasional control interventions are performed by spraying, as quickly as possible, all existing stock of insecticide (regardless of its lethality) and employing all available manpower. The goal of this paper is to design better strategies for insecticide-based control actions, which are capable of preventing more human infections at no additional cost, and to reveal the obsolescence of current vector eradication practices. Our approach relies on dynamic optimization, where the number of averted human infections is maximized under budget constraint and subject to a simple dengue transmission model amended with one control variable that stands for the insecticide spraying. As a result, we obtain structurally robust control intervention policies that demonstrate better performance and higher resilience to possible budget limitations than traditional modus operandi |
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2020 |
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2020-02 |
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2021-09-30T21:04:08Z |
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2021-09-30T21:04:08Z |
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Artículo de revista |
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14679590 |
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https://hdl.handle.net/10614/13298 |
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10.1111/sapm.12295 |
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eng |
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Volumen 144, número 2 (2020) |
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212 |
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2 |
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185 |
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Sepulveda Salcedo, L.S., Vasilieva, O., Svinin M. (2020). Optimal control of dengue epidemic outbreaks under limited resources. Studies in Applied Mathematics. (Vol. 144 (2), pp. 185-212. https://doi.org/10.1111/sapm.12295 |
| dc.relation.ispartofjournal.eng.fl_str_mv |
Studies in Applied Mathematics |
| dc.relation.references.eng.fl_str_mv |
Jansen CC, Beebe NW. The dengue vector Aedes aegypti: what comes next. Microb Infect. 2010; 12(4): 272- 279. Ben-Shachar R, Koelle K. Transmission-clearance trade-offs indicate that dengue virulence evolution depends on epidemiological context. Nat Commun. 2018;9(1):2355 Capeding MR, Tran NH, Hadinegoro SR, et al. Clinical efficacy and safety of a novel tetravalent dengue vaccine in healthy children in Asia: a phase 3, randomised, observer-masked, placebo-controlled trial. Lancet. 2014;384(9951):1358-1365 . Escobar-Morales G, ed. Cali en cifras 2015 [Cali in numbers 2015]. Alcaldía de Santiago de Cali: Departamento Administrativo de Planeación; 2016. Mendez F, Barreto M, Arias J, et al. Human and mosquito infections by dengue viruses during and after epidemics in a dengue-endemic region of Colombia. Am J Trop Med Hyg. 2006; 74(4): 678- 683 Ocampo CB, Wesson DM. Population dynamics of Aedes aegypti from a dengue hyperendemic urban setting in Colombia. Am J Trop Med Hyg. 2004; 71(4): 506- 513. Ocazionez RE, Cortés FM, Villar LA, Gómez SY. Temporal distribution of dengue virus serotypes in Colombian endemic area and dengue incidence: re-introduction of dengue-3 associated to mild febrile illness and primary infection. Mem Inst Oswaldo Cruz. 2006; 101(7): 725- 731 Bortman M. Elaboración de corredores o canales endémicos mediante planillas de cálculo [Establishing endemic corridors or ranges with computer spreadsheets]. Pan Am J Public Health. 1999; 5: 1- 8 Smith DL, Battle KE, Hay SI, Barker CM, Scott TW, McKenzie FE. Ross, Macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens. PLoS Pathog. 2012; 8(4):e1002588 Aron JL, May RM. The population dynamics of malaria. In: RM Anderson, ed. Population Dynamics and Infectious Disease: Theory and Applications. London: Chapman and Hall; 1982: 139- 179. Sepulveda LS, Vasilieva O. Optimal control approach to dengue reduction and prevention in Cali, Colombia. Math Methods Appl Sci. 2016; 39(18): 5475- 5496. Villar LA, Rojas DP, Besada-Lombana S, Sarti E. Epidemiological trends of dengue disease in Colombia (2000-2011): a systematic review. PLoS Neglect Trop Dis. 2015; 9(3):e0003499 Okosun KO, Rachid O, Marcus N. Optimal control strategies and cost-effectiveness analysis of a malaria model. Biosystems. 2013; 111(2): 83- 101 Moulay D, Aziz-Alaoui MA, Kwon HD. Optimal control of chikungunya disease: larvae reduction, treatment and prevention. Math Biosci Eng. 2012; 9(2): 369- 392 Lenhart S, Workman JT. Optimal Control Applied to Biological Models. Boca Raton, FL: Chapman & Hall/CRC; 2007. Fleming W, Rishel R. Deterministic and Stochastic Optimal Control. New York, NY: Springer; 1975 Seierstad A, Sydsaeter K. Optimal Control Theory with Economic Applications. Vol. 24 of Advanced Textbooks in Economics. Amsterdam: Elsevier North-Holland, Inc.; 2002 Rao AV, Benson DA, Darby C, et al. Algorithm 902: GPOPS, a MATLAB software for solving multiple-phase optimal control problems using the Gauss pseudospectral method. ACM Trans Math Softw. 2010; 37(2): 22 Arias JH, Martínez HJ, Sepúlveda LS, Vasilieva O. Estimación de los parámetros de dos modelos para la dinámica del dengue y su vector en Cali, Colombia [Parameter estimation of two mathematical models for the dynamics of dengue and its vector in Cali, Colombia]. Ingeniería y Ciencia. 2018; 14(28): 69- 92 Yang HM, Macoris MLG, Galvani KC, Andrighetti MTM, Wanderley DMV. Assessing the effects of temperature on dengue transmission. Epidemiol Infect. 2009; 137(8): 1179- 1187. Barrios E, Lee S, Vasilieva O. Assessing the effects of daily commuting in two-patch dengue dynamics: a case study of Cali, Colombia. J Theor Biol. 2018; 453: 14- 39 Lasluisa D, Barrios E, Vasilieva O. Optimal strategies for dengue prevention and control during daily commuting between two residential areas. Processes. 2019; 7(4): 197 Sepúlveda-Salcedo LS, Vasilieva O, Martínez-Romero HJ, Arias-Castro JH. Ross-Macdonald: Un modelo para la dinámica del dengue en Cali, Colombia [Ross-Macdonald: a model for the dengue dynamic in Cali, Colombia]. Rev Salud Pública. 2015; 17(5): 749- 761 Bello S, Díaz E, Rojas J, Romero M, Salazar V. Medición del impacto económico del dengue en Colombia: una aproximación a los costos médicos directos en el periodo 2000-2010 [Measuring the economic impact of dengue in Colombia: an approximation to the direct medical costs in 2000-2010]. Biomédica. 2011; 31(Suppl. 3): 3- 315 uaya JA, Shepard DS, Siqueira JB, et al. Cost of dengue cases in eight countries in the Americas and Asia: a prospective study. Am J Trop Med Hyg. 2009; 80(5): 846- 855 Ayala-García J. La salud en Colombia: más cobertura pero menos acceso [Health-care in Colombia: More Coverage but Less Access]. Banco de la Republica de Colombia; 2014. No. 204 |
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Sepúlveda Salcedo, Lilian Sofíavirtual::4684-1Vasilieva, Olga31f6a4db00254953edddbca148e36487Svinin, Mikhailcebfbd9cdab50bbe6233c8c30761320e2021-09-30T21:04:08Z2021-09-30T21:04:08Z2020-0214679590https://hdl.handle.net/10614/1329810.1111/sapm.12295In this paper, we reflect upon control intervention practices habitually exerted by healthcare authorities in tropical areas that suffer from incidental outbreaks of dengue fever, in particular, the city of Cali, Colombia. Such control interventions, principally based on the insecticide spraying, are carried out sporadically in order to overcome an ongoing epidemic or at least to reduce its size. It is worth pointing out that control actions of this type do not usually account for sufficient budget because epidemic outbreaks are difficult to predict. In practical terms, these occasional control interventions are performed by spraying, as quickly as possible, all existing stock of insecticide (regardless of its lethality) and employing all available manpower. The goal of this paper is to design better strategies for insecticide-based control actions, which are capable of preventing more human infections at no additional cost, and to reveal the obsolescence of current vector eradication practices. Our approach relies on dynamic optimization, where the number of averted human infections is maximized under budget constraint and subject to a simple dengue transmission model amended with one control variable that stands for the insecticide spraying. As a result, we obtain structurally robust control intervention policies that demonstrate better performance and higher resilience to possible budget limitations than traditional modus operandi28 páginasapplication/pdfengWileyDerechos reservados - Wiley, 2020https://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 control of dengue epidemic outbreaks under limited resourcesArtículo 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_970fb48d4fbd8a85Control vectorialDengeVector controlDengue outbreaksInsecticide based vector controlIsoperimetric constraintOptimal controlOptimizationRoss-Macdonald modelVolumen 144, número 2 (2020)2122185144Sepulveda Salcedo, L.S., Vasilieva, O., Svinin M. (2020). Optimal control of dengue epidemic outbreaks under limited resources. Studies in Applied Mathematics. (Vol. 144 (2), pp. 185-212. https://doi.org/10.1111/sapm.12295Studies in Applied MathematicsJansen CC, Beebe NW. The dengue vector Aedes aegypti: what comes next. Microb Infect. 2010; 12(4): 272- 279.Ben-Shachar R, Koelle K. Transmission-clearance trade-offs indicate that dengue virulence evolution depends on epidemiological context. Nat Commun. 2018;9(1):2355Capeding MR, Tran NH, Hadinegoro SR, et al. Clinical efficacy and safety of a novel tetravalent dengue vaccine in healthy children in Asia: a phase 3, randomised, observer-masked, placebo-controlled trial. Lancet. 2014;384(9951):1358-1365. Escobar-Morales G, ed. Cali en cifras 2015 [Cali in numbers 2015]. Alcaldía de Santiago de Cali: Departamento Administrativo de Planeación; 2016.Mendez F, Barreto M, Arias J, et al. Human and mosquito infections by dengue viruses during and after epidemics in a dengue-endemic region of Colombia. Am J Trop Med Hyg. 2006; 74(4): 678- 683Ocampo CB, Wesson DM. Population dynamics of Aedes aegypti from a dengue hyperendemic urban setting in Colombia. Am J Trop Med Hyg. 2004; 71(4): 506- 513.Ocazionez RE, Cortés FM, Villar LA, Gómez SY. Temporal distribution of dengue virus serotypes in Colombian endemic area and dengue incidence: re-introduction of dengue-3 associated to mild febrile illness and primary infection. Mem Inst Oswaldo Cruz. 2006; 101(7): 725- 731Bortman M. Elaboración de corredores o canales endémicos mediante planillas de cálculo [Establishing endemic corridors or ranges with computer spreadsheets]. Pan Am J Public Health. 1999; 5: 1- 8Smith DL, Battle KE, Hay SI, Barker CM, Scott TW, McKenzie FE. Ross, Macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens. PLoS Pathog. 2012; 8(4):e1002588Aron JL, May RM. The population dynamics of malaria. In: RM Anderson, ed. Population Dynamics and Infectious Disease: Theory and Applications. London: Chapman and Hall; 1982: 139- 179.Sepulveda LS, Vasilieva O. Optimal control approach to dengue reduction and prevention in Cali, Colombia. Math Methods Appl Sci. 2016; 39(18): 5475- 5496.Villar LA, Rojas DP, Besada-Lombana S, Sarti E. Epidemiological trends of dengue disease in Colombia (2000-2011): a systematic review. PLoS Neglect Trop Dis. 2015; 9(3):e0003499Okosun KO, Rachid O, Marcus N. Optimal control strategies and cost-effectiveness analysis of a malaria model. Biosystems. 2013; 111(2): 83- 101Moulay D, Aziz-Alaoui MA, Kwon HD. Optimal control of chikungunya disease: larvae reduction, treatment and prevention. Math Biosci Eng. 2012; 9(2): 369- 392Lenhart S, Workman JT. Optimal Control Applied to Biological Models. Boca Raton, FL: Chapman & Hall/CRC; 2007.Fleming W, Rishel R. Deterministic and Stochastic Optimal Control. New York, NY: Springer; 1975Seierstad A, Sydsaeter K. Optimal Control Theory with Economic Applications. Vol. 24 of Advanced Textbooks in Economics. Amsterdam: Elsevier North-Holland, Inc.; 2002Rao AV, Benson DA, Darby C, et al. Algorithm 902: GPOPS, a MATLAB software for solving multiple-phase optimal control problems using the Gauss pseudospectral method. ACM Trans Math Softw. 2010; 37(2): 22Arias JH, Martínez HJ, Sepúlveda LS, Vasilieva O. Estimación de los parámetros de dos modelos para la dinámica del dengue y su vector en Cali, Colombia [Parameter estimation of two mathematical models for the dynamics of dengue and its vector in Cali, Colombia]. Ingeniería y Ciencia. 2018; 14(28): 69- 92Yang HM, Macoris MLG, Galvani KC, Andrighetti MTM, Wanderley DMV. Assessing the effects of temperature on dengue transmission. Epidemiol Infect. 2009; 137(8): 1179- 1187.Barrios E, Lee S, Vasilieva O. Assessing the effects of daily commuting in two-patch dengue dynamics: a case study of Cali, Colombia. J Theor Biol. 2018; 453: 14- 39Lasluisa D, Barrios E, Vasilieva O. Optimal strategies for dengue prevention and control during daily commuting between two residential areas. Processes. 2019; 7(4): 197Sepúlveda-Salcedo LS, Vasilieva O, Martínez-Romero HJ, Arias-Castro JH. Ross-Macdonald: Un modelo para la dinámica del dengue en Cali, Colombia [Ross-Macdonald: a model for the dengue dynamic in Cali, Colombia]. Rev Salud Pública. 2015; 17(5): 749- 761Bello S, Díaz E, Rojas J, Romero M, Salazar V. Medición del impacto económico del dengue en Colombia: una aproximación a los costos médicos directos en el periodo 2000-2010 [Measuring the economic impact of dengue in Colombia: an approximation to the direct medical costs in 2000-2010]. Biomédica. 2011; 31(Suppl. 3): 3- 315uaya JA, Shepard DS, Siqueira JB, et al. Cost of dengue cases in eight countries in the Americas and Asia: a prospective study. Am J Trop Med Hyg. 2009; 80(5): 846- 855Ayala-García J. La salud en Colombia: más cobertura pero menos acceso [Health-care in Colombia: More Coverage but Less Access]. Banco de la Republica de Colombia; 2014. No. 204GeneralPublicationaeb47892-e365-4668-9322-a97426768e27virtual::4684-1aeb47892-e365-4668-9322-a97426768e27virtual::4684-1https://scholar.google.com.co/citations?user=u2HFR6AAAAAJ&hl=esvirtual::4684-10000-0002-7052-1851virtual::4684-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000277746virtual::4684-1LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/c7dc2f98-c7a0-4d83-ba43-09459b95825a/download20b5ba22b1117f71589c7318baa2c560MD52ORIGINALOptimal control of dengue epidemic outbreaks under limited resources.pdfOptimal control of dengue epidemic outbreaks under limited resources.pdfTexto archivo completo del artículo de revista, PDFapplication/pdf1618942https://red.uao.edu.co/bitstreams/5a35ec06-8171-4ea4-ac52-4175065a3a4e/download3750551b292bb68a5d243759409a860eMD53TEXTOptimal control of dengue epidemic outbreaks under limited resources.pdf.txtOptimal control of dengue epidemic outbreaks under limited resources.pdf.txtExtracted texttext/plain83229https://red.uao.edu.co/bitstreams/261bba05-b6cf-41b7-aa77-aacf7b56d590/download242d2d72f915f2bba3a49e42492470c4MD54THUMBNAILOptimal control of dengue epidemic outbreaks under limited resources.pdf.jpgOptimal control of dengue epidemic outbreaks under limited resources.pdf.jpgGenerated Thumbnailimage/jpeg13550https://red.uao.edu.co/bitstreams/2e1d2b89-ff24-4191-beb8-41d011f320af/download7d47eb5b6fad802bae0195c3149c245eMD5510614/13298oai:red.uao.edu.co:10614/132982024-03-15 08:58:57.047https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos reservados - Wiley, 2020open.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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 |