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An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

2013-04Journal article Open access
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dc.contributor.authorRocha, J. Leonel
dc.contributor.authorAleixo, Sandra
dc.date.accessioned2013-10-26T19:19:55Z
dc.date.available2013-10-26T19:19:55Z
dc.date.issued2013-04
dc.description.abstractIn this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.por
dc.identifier.citationROCHA, J. Leonel; AlLEIXO, Sandra M. - An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models. Mathematical Biosciences and Engineering. ISSN 1547-1063. Vol. 10, nr 2 (2013), p. 379-398.por
dc.identifier.issn1547-1063
dc.identifier.other10.3934/mbe.2013.10.379
dc.identifier.urihttp://hdl.handle.net/10400.21/2795
dc.language.isoengpor
dc.peerreviewedyespor
dc.publisherAmer Inst Mathematical Sciencespor
dc.relationPTDC/FEDER
dc.relationStrategic Project - UI 6 - 2011-2012
dc.subjectGrowth modelspor
dc.subjectExtreme value lawspor
dc.subjectBeta* (p, q) densitiespor
dc.subjectBifurcations and chaospor
dc.subjectSymbolic dynamicspor
dc.subjectTopological entropypor
dc.subjectTumour dynamicspor
dc.subjectLogistic Modelpor
dc.subjectTumor-Growthpor
dc.subjectImmunotherapypor
dc.titleAn Extension of Gompertzian Growth Dynamics Weibull and Frechet Modelspor
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleStrategic Project - UI 6 - 2011-2012
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/PEst-OE%2FMAT%2FUI0006%2F2011/PT
oaire.citation.conferencePlaceSpringfieldpor
oaire.citation.endPage398por
oaire.citation.issue2por
oaire.citation.startPage379por
oaire.citation.titleMathematical Biosciences and Engineeringpor
oaire.citation.volume10por
oaire.fundingStream6817 - DCRRNI ID
person.familyNameRocha
person.familyNameAleixo
person.givenNameJ. Leonel
person.givenNameSandra
person.identifier1869126
person.identifier.ciencia-id6A13-4D5A-BABA
person.identifier.orcid0000-0001-8053-6822
person.identifier.orcid0000-0003-1740-8371
person.identifier.scopus-author-id24829973500
person.identifier.scopus-author-id24829443600
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsrestrictedAccesspor
rcaap.typearticlepor
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relation.isAuthorOfPublication.latestForDiscoveryb0ebd0b9-c949-40d7-b8ea-41955a5559f1
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