Publicación:
CALIBRATION OF POPULATION GROWTH MATHEMATICAL MODELS BY USING TIME SERIES

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dc.creatorIAN ERWIN HESS DUQUE
dc.creatorANÍBAL CORONEL PÉREZ
dc.creatorSERGIO EDUARDO CONTRERAS ESPINOZA
dc.creatorFRANCISCO EDUARDO NOVOA MUÑOZ
dc.date2019
dc.date.accessioned2025-01-10T15:05:59Z
dc.date.available2025-01-10T15:05:59Z
dc.date.issued2019
dc.description.abstractIN THIS PAPER, WE STUDY THE PROBLEM OF COEFFICIENTS IDENTIFICATION IN POPULATION GROWTH MODELS. WE CONSIDER THAT THE DYNAMICS OF THE POPULATION IS DESCRIBED BY A SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS OF SUSCEPTIBLE-INFECTIVE-RECOVERED (SIR) TYPE, AND WE ASSUME THAT WE HAVE A DISCRETE OBSERVATION OF INFECTIVE POPULATION. WE CONSTRUCT A CONTINUOUS OBSERVATION BY APPLYING TIME SERIES AND AN APPROPRIATE FITTING TO THE DISCRETE OBSERVATION DATA. THE IDENTIFICATION PROBLEM CONSISTS IN THE DETERMINATION OF DIFFERENT PARAMETERS IN THE GOVERNING EQUATIONS SUCH THAT THE INFECTIVE POPULATION OBTAINED AS SOLUTION OF THE SIR SYSTEM IS AS CLOSE AS TO THE OBSERVATION. WE INTRODUCE A REFORMULATION OF THE CALIBRATION PROBLEM AS AN OPTIMIZATION PROBLEM WHERE THE OBJECTIVE FUNCTION AND THE RESTRICTION ARE GIVEN BY THE COMPARISON IN THE L2-NORM OF THEORETICAL SOLUTION OF THE MATHEMATICAL MODEL AND THE OBSERVATION, AND THE SIR SYSTEM GOVERNING THE PHENOMENON, RESPECTIVELY. WE SOLVE NUMERICALLY THE OPTIMIZATION PROBLEM BY APPLYING THE GRADIENT METHOD WHERE THE GRADIENT OF THE COST FUNCTION IS OBTAINED BY INTRODUCING AN ADJOINT STATE. IN ADDITION, WE CONSIDER A NUMERICAL EXAMPLE TO ILLUSTRATE THE APPLICATION OF THE PROPOSED CALIBRATION METHOD.
dc.formatapplication/pdf
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/10414
dc.languagespa
dc.publisherSELECTED CONTRIBUTIONS ON STATISTICS AND DATA SCIENCE IN LATIN AMERICA. FNE 2018.SPRINGER PROCEEDINGS IN MATHEMATICS & STATISTICS
dc.rightsPUBLICADA
dc.titleCALIBRATION OF POPULATION GROWTH MATHEMATICAL MODELS BY USING TIME SERIES
dc.title.alternativeCALIBRACIÓN DE MODELOS MATEMÁTICOS DE CRECIMIENTO DE LA POBLACIÓN MEDIANTE SERIES TEMPORALES
dc.typeCAPÍTULO DE LIBRO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE CIENCIAS BASICAS
ubb.Otra ReparticionDEPARTAMENTO DE ESTADISTICA
ubb.Otra ReparticionDEPARTAMENTO DE ESTADISTICA
ubb.SedeCHILLÁN
ubb.SedeCONCEPCIÓN
ubb.SedeCONCEPCIÓN
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