An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

• Autor(a) principal: Rocha, J. Leonel
• Data de Publicação: 2013
• Outros Autores: Aleixo, Sandra
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Texto Completo: http://hdl.handle.net/10400.21/2795
• topic: Growth models; Extreme value laws; Beta* (p, q) densities; Bifurcations and chaos; Symbolic dynamics; Topological entropy; Tumour dynamics; Logistic Model; Tumor-Growth; Immunotherapy

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.