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ON THE EXISTENCE AND UNIQUENESS OF AN INVERSE PROBLEM IN EPIDEMIOLOGY

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dc.creatorIAN ERWIN HESS DUQUE
dc.creatorANÍBAL CORONEL PÉREZ
dc.creatorLUIS ALBERTO FRIZ ROA
dc.date2021
dc.date.accessioned2025-01-10T15:13:15Z
dc.date.available2025-01-10T15:13:15Z
dc.date.issued2021
dc.description.abstractIN THIS PAPER, WE INTRODUCE THE FUNCTIONAL FRAMEWORK AND THE NECESSARY CONDITIONS FOR THE WELL-POSEDNESS OF AN INVERSE PROBLEM ARISING FROM THE MATHEMATICAL MODELING OF DISEASE TRANSMISSION. THE DIRECT PROBLEM IS GIVEN BY AN INITIAL BOUNDARY VALUE PROBLEM FOR A REACTION-DIFFUSION SYSTEM. THE INVERSE PROBLEM CONSISTS IN THE DETERMINATION OF THE DISEASE AND RECOVERY TRANSMISSION RATES FROM OBSERVED MEASUREMENT OF THE DIRECT PROBLEM SOLUTION AT THE FINAL TIME. THE UNKNOWNS OF THE INVERSE PROBLEM ARE THE COEFFICIENTS OF THE REACTION TERM. WE FORMULATE THE INVERSE PROBLEM AS AN OPTIMIZATION PROBLEM FOR AN APPROPRIATE COST FUNCTIONAL. THEN, THE EXISTENCE OF SOLUTIONS OF THE INVERSE PROBLEM IS DEDUCED BY PROVING THE EXISTENCE OF A MINIMIZER FOR THE COST FUNCTIONAL. MOREOVER, WE ESTABLISH THE UNIQUENESS UP AN ADDITIVE CONSTANT OF THE IDENTIFICATION PROBLEM. THE UNIQUENESS IS A CONSEQUENCE OF THE FIRST ORDER NECESSARY OPTIMALITY CONDITION AND A STABILITY OF THE INVERSE PROBLEM UNKNOWNS WITH RESPECT TO THE OBSERVATIONS.
dc.formatapplication/pdf
dc.identifier.doi10.1080/00036811.2019.1608964
dc.identifier.issn1563-504X
dc.identifier.issn0003-6811
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/10985
dc.languagespa
dc.publisherAPPLICABLE ANALYSIS
dc.relation.uri10.1080/00036811.2019.1608964
dc.rightsPUBLICADA
dc.titleON THE EXISTENCE AND UNIQUENESS OF AN INVERSE PROBLEM IN EPIDEMIOLOGY
dc.title.alternativeSOBRE LA EXISTENCIA Y SINGULARIDAD DE UN PROBLEMA INVERSO EN EPIDEMIOLOGÍA
dc.typeARTÍCULO
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE CIENCIAS BASICAS
ubb.Otra ReparticionDEPARTAMENTO DE CIENCIAS BASICAS
ubb.Otra ReparticionDEPARTAMENTO DE CIENCIAS BASICAS
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