Optimal control for a discrete time influenza model
We formulated a discrete time model in order to study optimal control strategies for a single influenza outbreak. In our model, we divided the population into four classes: susceptible, infectious, treated, and recovered individuals. The total population was divided into subgroups according to activ...
- Autores:
-
González Parra, Paula Andrea
Ceberio, Martine
Lee, Sunmi
Castillo-Chavez, Carlos
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2014
- Institución:
- Universidad Autónoma de Occidente
- Repositorio:
- RED: Repositorio Educativo Digital UAO
- Idioma:
- eng
- OAI Identifier:
- oai:red.uao.edu.co:10614/11551
- Acceso en línea:
- http://hdl.handle.net/10614/11551
- Palabra clave:
- Control óptimo
Gripe
Epidemiología
Influenza
Optimal Control
Epidemiology
Interior-Point methods
- Rights
- openAccess
- License
- Derechos Reservados - Universidad Autónoma de Occidente
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Optimal control for a discrete time influenza model |
| title |
Optimal control for a discrete time influenza model |
| spellingShingle |
Optimal control for a discrete time influenza model Control óptimo Gripe Epidemiología Influenza Optimal Control Epidemiology Interior-Point methods |
| title_short |
Optimal control for a discrete time influenza model |
| title_full |
Optimal control for a discrete time influenza model |
| title_fullStr |
Optimal control for a discrete time influenza model |
| title_full_unstemmed |
Optimal control for a discrete time influenza model |
| title_sort |
Optimal control for a discrete time influenza model |
| dc.creator.fl_str_mv |
González Parra, Paula Andrea Ceberio, Martine Lee, Sunmi Castillo-Chavez, Carlos |
| dc.contributor.author.none.fl_str_mv |
González Parra, Paula Andrea Ceberio, Martine Lee, Sunmi Castillo-Chavez, Carlos |
| dc.subject.spa.fl_str_mv |
Control óptimo |
| topic |
Control óptimo Gripe Epidemiología Influenza Optimal Control Epidemiology Interior-Point methods |
| dc.subject.armarc.spa.fl_str_mv |
Gripe Epidemiología |
| dc.subject.proposal.eng.fl_str_mv |
Influenza Optimal Control Epidemiology |
| dc.subject.proposal.none.fl_str_mv |
Interior-Point methods |
| description |
We formulated a discrete time model in order to study optimal control strategies for a single influenza outbreak. In our model, we divided the population into four classes: susceptible, infectious, treated, and recovered individuals. The total population was divided into subgroups according to activity or susceptibility levels. The goal was to determine how treatment doses should be distributed in each group in order to reduce the final epidemic size. The case of limited resources is considered by including an isoperimetric constraint. We found that the use of antiviral treatment resulted in reductions in the cumulative number of infected individuals. We proposed to solve the problem by using the primal-dual interior-point method that enforces epidemiological constraints explicitly |
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2014 |
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2014 |
| dc.date.accessioned.none.fl_str_mv |
2019-11-20T14:40:53Z |
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2019-11-20T14:40:53Z |
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Artículo de revista |
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Parra P.A.G., Ceberio M., Lee S., Castillo-Chavez C. (2014) Optimal Control for a Discrete Time Influenza Model. In: Castillo L., Cristancho M., Isaza G., Pinzón A., Rodríguez J. (eds) Advances in Computational Biology. Advances in Intelligent Systems and Computing, vol 232. Springer, Cham. https://doi.org/10.1007/978-3-319-01568-2_33 |
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9783319015675 (impreso) 9783319015682 (en línea) |
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http://hdl.handle.net/10614/11551 |
| dc.identifier.doi.spa.fl_str_mv |
10.1007/978-3-319-01568-2_33 |
| identifier_str_mv |
Parra P.A.G., Ceberio M., Lee S., Castillo-Chavez C. (2014) Optimal Control for a Discrete Time Influenza Model. In: Castillo L., Cristancho M., Isaza G., Pinzón A., Rodríguez J. (eds) Advances in Computational Biology. Advances in Intelligent Systems and Computing, vol 232. Springer, Cham. https://doi.org/10.1007/978-3-319-01568-2_33 9783319015675 (impreso) 9783319015682 (en línea) 10.1007/978-3-319-01568-2_33 |
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http://hdl.handle.net/10614/11551 |
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eng |
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eng |
| dc.relation.eng.fl_str_mv |
Castillo L., Cristancho M., Isaza G., Pinzón A., Rodríguez J. (eds) Advances in Computational Biology. Advances in Intelligent Systems and Computing, vol 232. Springer, Cham |
| dc.relation.citationendpage.none.fl_str_mv |
237 |
| dc.relation.citationstartpage.none.fl_str_mv |
231 |
| dc.relation.ispartofbook.spa.fl_str_mv |
Avances en Biología Computacional. Avances en Sistemas Inteligentes y Computación |
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Advances in Computational Biology. Advances in Intelligent Systems and Computing |
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Brauer, F.: Epidemic models with heterogeneous mixing and treatment. Bull. of Math. Bio. 70, 1869–1885 (2008) Brauer, F., Feng, Z., Castillo-Chavez, C.: Discrete Epidemic Models. Math. Biosc. & Eng. 7, 1–15 (2010) Castillo-Chavez, C., Hethcote, H.W.: Epidemiological models with age structure, proportionate mixing, and cross immunity. J. of Math. Bio. 27, 233–258 (1989) Chowell, G., Ammon, C.E., Hengartner, N.W., Hyman, J.M.: Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: Assessing the effects of hypothetical interventions. J. Theor. Biol. 241, 193–204 (2006) Del Valle, S.Y., Hyman, J.M., Hethcote, H.W., Eubank, S.G.: Mixing patterns between age groups in social networks. Social Networks 29, 539–554 (2007) El-Bakry, A.S., Tapia, R.A., Tsuchiya, T., Zhang, Y.: On the formulation and theory of the primal-dual newton interior-point method for nonlinear programming. J. of Optim. Theo. and App. 89(3), 507–541 (1996) González-Parra, P., Lee, S., Velazquez, L., Castillo-Chavez, C.: A note on the use of optimal control on a discrete time model of influenza dynamics. Math. Biosc. & Eng. 8(8), 183–197 (2011) González-Parra, P.: Constraint optimal control for a multi-group discrete time influenza model. PhD. dissertation, The University of Texas at El Paso, El Paso, TX (2012) Herrera-Valdez, M.A., Cruz-Aponte, M., Castillo-Chavez, C.: Multiple outbreaks for the same pandemic: Local transportation and social distancing explain the different “waves” of A-H1N1pdm cases observed in Mxico during 2009. Math. Biosc. & Eng. 8(8), 21–48 (2011) Hethcote, H.W.: An age-structured model for pertussis transmission. Math. Biosc. 145, 89–136 (1997) Lee, S., Chowell, G., Castillo-Chavez, C.: Optimal control for pandemic influenza: the role of limited antiviral treatment and isolation. J. Theor. Biol. 265, 136–150 (2010) Lee, S., Morales, R., Castillo-Chavez, C.: A note on the use of influenza vaccination strategies when supply is limited. Math. Biosc. & Eng. 8(8), 171–182 (2011) Lenhart, S., Workman, J.: Optimal control applied to biological models. Chapman & Hall, CRC Mathematical and Computational Biology series (2007) Nocedal, J., Wright, S.J.: Numerical optimization, 2nd edn. Springer (2006) Rios-Soto, K., Song, B., Castillo-Chavez, C.: Epidemic spread of influenza viruses: The impact of transient populations on disease dynamics. Math. Biosc. & Eng. 8(8), 199–222 (2011) |
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Derechos Reservados - Universidad Autónoma de Occidente |
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González Parra, Paula Andreavirtual::2001-1Ceberio, Martine708c11ae06aeaf13f1263417f6ce4f71Lee, Sunmiab51c6e66c8e2b1bbd8a8c2b44929a99Castillo-Chavez, Carloscdf48edadfb5abd20797e6d0c9763ca6Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí2019-11-20T14:40:53Z2019-11-20T14:40:53Z2014Parra P.A.G., Ceberio M., Lee S., Castillo-Chavez C. (2014) Optimal Control for a Discrete Time Influenza Model. In: Castillo L., Cristancho M., Isaza G., Pinzón A., Rodríguez J. (eds) Advances in Computational Biology. Advances in Intelligent Systems and Computing, vol 232. Springer, Cham. https://doi.org/10.1007/978-3-319-01568-2_339783319015675 (impreso)9783319015682 (en línea)http://hdl.handle.net/10614/1155110.1007/978-3-319-01568-2_33We formulated a discrete time model in order to study optimal control strategies for a single influenza outbreak. In our model, we divided the population into four classes: susceptible, infectious, treated, and recovered individuals. The total population was divided into subgroups according to activity or susceptibility levels. The goal was to determine how treatment doses should be distributed in each group in order to reduce the final epidemic size. The case of limited resources is considered by including an isoperimetric constraint. We found that the use of antiviral treatment resulted in reductions in the cumulative number of infected individuals. We proposed to solve the problem by using the primal-dual interior-point method that enforces epidemiological constraints explicitlyapplication/pdf7 páginasengSpringerCastillo L., Cristancho M., Isaza G., Pinzón A., Rodríguez J. (eds) Advances in Computational Biology. Advances in Intelligent Systems and Computing, vol 232. Springer, Cham237231Avances en Biología Computacional. Avances en Sistemas Inteligentes y ComputaciónAdvances in Computational Biology. Advances in Intelligent Systems and ComputingBrauer, F.: Epidemic models with heterogeneous mixing and treatment. Bull. of Math. Bio. 70, 1869–1885 (2008)Brauer, F., Feng, Z., Castillo-Chavez, C.: Discrete Epidemic Models. Math. Biosc. & Eng. 7, 1–15 (2010)Castillo-Chavez, C., Hethcote, H.W.: Epidemiological models with age structure, proportionate mixing, and cross immunity. J. of Math. Bio. 27, 233–258 (1989)Chowell, G., Ammon, C.E., Hengartner, N.W., Hyman, J.M.: Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: Assessing the effects of hypothetical interventions. J. Theor. Biol. 241, 193–204 (2006)Del Valle, S.Y., Hyman, J.M., Hethcote, H.W., Eubank, S.G.: Mixing patterns between age groups in social networks. Social Networks 29, 539–554 (2007)El-Bakry, A.S., Tapia, R.A., Tsuchiya, T., Zhang, Y.: On the formulation and theory of the primal-dual newton interior-point method for nonlinear programming. J. of Optim. Theo. and App. 89(3), 507–541 (1996)González-Parra, P., Lee, S., Velazquez, L., Castillo-Chavez, C.: A note on the use of optimal control on a discrete time model of influenza dynamics. Math. Biosc. & Eng. 8(8), 183–197 (2011)González-Parra, P.: Constraint optimal control for a multi-group discrete time influenza model. PhD. dissertation, The University of Texas at El Paso, El Paso, TX (2012)Herrera-Valdez, M.A., Cruz-Aponte, M., Castillo-Chavez, C.: Multiple outbreaks for the same pandemic: Local transportation and social distancing explain the different “waves” of A-H1N1pdm cases observed in Mxico during 2009. Math. Biosc. & Eng. 8(8), 21–48 (2011)Hethcote, H.W.: An age-structured model for pertussis transmission. Math. Biosc. 145, 89–136 (1997)Lee, S., Chowell, G., Castillo-Chavez, C.: Optimal control for pandemic influenza: the role of limited antiviral treatment and isolation. J. Theor. Biol. 265, 136–150 (2010)Lee, S., Morales, R., Castillo-Chavez, C.: A note on the use of influenza vaccination strategies when supply is limited. Math. Biosc. & Eng. 8(8), 171–182 (2011)Lenhart, S., Workman, J.: Optimal control applied to biological models. Chapman & Hall, CRC Mathematical and Computational Biology series (2007)Nocedal, J., Wright, S.J.: Numerical optimization, 2nd edn. Springer (2006)Rios-Soto, K., Song, B., Castillo-Chavez, C.: Epidemic spread of influenza viruses: The impact of transient populations on disease dynamics. Math. Biosc. & Eng. 8(8), 199–222 (2011)Derechos 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_abf2Control óptimoGripeEpidemiologíaInfluenzaOptimal ControlEpidemiologyInterior-Point methodsOptimal control for a discrete time influenza modelArtículo 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_970fb48d4fbd8a85Publication8da9707c-13a8-4a6f-995e-283af50e1d65virtual::2001-18da9707c-13a8-4a6f-995e-283af50e1d65virtual::2001-10000-0001-5208-6326virtual::2001-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0001071882virtual::2001-1CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://red.uao.edu.co/bitstreams/0746c326-466b-433e-847c-e7eb4b7b9cb2/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/107337ab-10af-4f05-b7e8-675b2d042777/download20b5ba22b1117f71589c7318baa2c560MD5310614/11551oai:red.uao.edu.co:10614/115512024-03-05 15:49:35.017https://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.coRUwgQVVUT1IgYXV0b3JpemEgYSBsYSBVbml2ZXJzaWRhZCBBdXTDs25vbWEgZGUgT2NjaWRlbnRlLCBkZSBmb3JtYSBpbmRlZmluaWRhLCBwYXJhIHF1ZSBlbiBsb3MgdMOpcm1pbm9zIGVzdGFibGVjaWRvcyBlbiBsYSBMZXkgMjMgZGUgMTk4MiwgbGEgTGV5IDQ0IGRlIDE5OTMsIGxhIERlY2lzacOzbiBhbmRpbmEgMzUxIGRlIDE5OTMsIGVsIERlY3JldG8gNDYwIGRlIDE5OTUgeSBkZW3DoXMgbGV5ZXMgeSBqdXJpc3BydWRlbmNpYSB2aWdlbnRlIGFsIHJlc3BlY3RvLCBoYWdhIHB1YmxpY2FjacOzbiBkZSBlc3RlIGNvbiBmaW5lcyBlZHVjYXRpdm9zLiBQQVJBR1JBRk86IEVzdGEgYXV0b3JpemFjacOzbiBhZGVtw6FzIGRlIHNlciB2w6FsaWRhIHBhcmEgbGFzIGZhY3VsdGFkZXMgeSBkZXJlY2hvcyBkZSB1c28gc29icmUgbGEgb2JyYSBlbiBmb3JtYXRvIG8gc29wb3J0ZSBtYXRlcmlhbCwgdGFtYmnDqW4gcGFyYSBmb3JtYXRvIGRpZ2l0YWwsIGVsZWN0csOzbmljbywgdmlydHVhbCwgcGFyYSB1c29zIGVuIHJlZCwgSW50ZXJuZXQsIGV4dHJhbmV0LCBpbnRyYW5ldCwgYmlibGlvdGVjYSBkaWdpdGFsIHkgZGVtw6FzIHBhcmEgY3VhbHF1aWVyIGZvcm1hdG8gY29ub2NpZG8gbyBwb3IgY29ub2Nlci4gRUwgQVVUT1IsIGV4cHJlc2EgcXVlIGVsIGRvY3VtZW50byAodHJhYmFqbyBkZSBncmFkbywgcGFzYW50w61hLCBjYXNvcyBvIHRlc2lzKSBvYmpldG8gZGUgbGEgcHJlc2VudGUgYXV0b3JpemFjacOzbiBlcyBvcmlnaW5hbCB5IGxhIGVsYWJvcsOzIHNpbiBxdWVicmFudGFyIG5pIHN1cGxhbnRhciBsb3MgZGVyZWNob3MgZGUgYXV0b3IgZGUgdGVyY2Vyb3MsIHkgZGUgdGFsIGZvcm1hLCBlbCBkb2N1bWVudG8gKHRyYWJham8gZGUgZ3JhZG8sIHBhc2FudMOtYSwgY2Fzb3MgbyB0ZXNpcykgZXMgZGUgc3UgZXhjbHVzaXZhIGF1dG9yw61hIHkgdGllbmUgbGEgdGl0dWxhcmlkYWQgc29icmUgw6lzdGUuIFBBUkFHUkFGTzogZW4gY2FzbyBkZSBwcmVzZW50YXJzZSBhbGd1bmEgcmVjbGFtYWNpw7NuIG8gYWNjacOzbiBwb3IgcGFydGUgZGUgdW4gdGVyY2VybywgcmVmZXJlbnRlIGEgbG9zIGRlcmVjaG9zIGRlIGF1dG9yIHNvYnJlIGVsIGRvY3VtZW50byAoVHJhYmFqbyBkZSBncmFkbywgUGFzYW50w61hLCBjYXNvcyBvIHRlc2lzKSBlbiBjdWVzdGnDs24sIEVMIEFVVE9SLCBhc3VtaXLDoSBsYSByZXNwb25zYWJpbGlkYWQgdG90YWwsIHkgc2FsZHLDoSBlbiBkZWZlbnNhIGRlIGxvcyBkZXJlY2hvcyBhcXXDrSBhdXRvcml6YWRvczsgcGFyYSB0b2RvcyBsb3MgZWZlY3RvcywgbGEgVW5pdmVyc2lkYWQgIEF1dMOzbm9tYSBkZSBPY2NpZGVudGUgYWN0w7phIGNvbW8gdW4gdGVyY2VybyBkZSBidWVuYSBmZS4gVG9kYSBwZXJzb25hIHF1ZSBjb25zdWx0ZSB5YSBzZWEgZW4gbGEgYmlibGlvdGVjYSBvIGVuIG1lZGlvIGVsZWN0csOzbmljbyBwb2Ryw6EgY29waWFyIGFwYXJ0ZXMgZGVsIHRleHRvIGNpdGFuZG8gc2llbXByZSBsYSBmdWVudGUsIGVzIGRlY2lyIGVsIHTDrXR1bG8gZGVsIHRyYWJham8geSBlbCBhdXRvci4gRXN0YSBhdXRvcml6YWNpw7NuIG5vIGltcGxpY2EgcmVudW5jaWEgYSBsYSBmYWN1bHRhZCBxdWUgdGllbmUgRUwgQVVUT1IgZGUgcHVibGljYXIgdG90YWwgbyBwYXJjaWFsbWVudGUgbGEgb2JyYS4K |