In this paper we provide an interval of existence of critical mortality rate parameters A and α and its asymptotic expressions in Gompertz survival model, in the absence of age specific mortality data. c © 2007 Elsevier Ltd. All rights reserved.

Factors determining the diffusion of digital mobile telephony across 200 developed and developing countries in the 1990s are studied with the aid of a Gompertz model. The market size and network effects are found to play more important roles in the developing countries; there is also more need for complementing innovations in, for example, financial and payment systems. Even though the developi...

The growth function of populations is central in biomathematics. The main dogma is the existence of density dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important class of regulatory functions is the θ-logistic, which generalises the logistic equation. Using this model as a motivation, this paper introduces a simple d...

noconstant suppress constant term distribution(exponential) exponential survival distribution distribution(gompertz) Gompertz survival distribution distribution(loglogistic) loglogistic survival distribution distribution(llogistic) synonym for distribution(loglogistic) distribution(weibull) Weibull survival distribution distribution(lognormal) lognormal survival distribution distribution(lnorma...

A two-compartment model of cancer cells population dynamics proposed by Gyllenberg and Webb includes transition rates between proliferating and quiescent cells as non-specified functions of the total population, N. We define the net inter-compartmental transition rate function: Phi(N). We assume that the total cell population follows the Gompertz growth model, as it is most often empirically fo...

We propose a descriptive 2D Hybrid Cellular Automaton model that simulates the growth behavior of a tissue with cancerous cells. We combine a set of hallmarks of cancer (Hanahan and Weinber, 2000) with the effect of acidification of the cell surroundings by the production of acid by tumorous cells and model some aspects of the communication in living tissues. The dynamics of the growth is deter...

The standard linear-quadratic survival model for radiotherapy is used to investigate different schedules of radiation treatment planning to study how these may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al (1977 Br. J. Radiol. 50 681), which was c...

Determining the mathematical dynamics and associated parameter values that should be used to accurately reflect tumor growth continues to be of interest to mathematical modelers, experimentalists and practitioners. However, while there are several competing canonical tumor growth models that are often implemented, how to determine which of the models should be used for which tumor types remains...