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An extension of Gompertzian growth dynamics: Weibull and Frechet models.
MedLine Citation:
PMID:  23458306     Owner:  NLM     Status:  In-Data-Review    
Abstract/OtherAbstract:
In 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.
Authors:
J Leonel Rocha; Sandra M Aleixo
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Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  Mathematical biosciences and engineering : MBE     Volume:  10     ISSN:  1551-0018     ISO Abbreviation:  Math Biosci Eng     Publication Date:  2013 Apr 
Date Detail:
Created Date:  2013-03-05     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101197794     Medline TA:  Math Biosci Eng     Country:  United States    
Other Details:
Languages:  eng     Pagination:  379-98     Citation Subset:  IM    
Affiliation:
Instituto Superior de Engenharia de Lisboa - ISEL, ADM and CEAUL, Rua Conselheiro Emidio Navarro, 1, 1959-007 Lisboa, Portugal. jrocha@adm.isel.pt.
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