Disparities in cervical cancer mortality rates as determined by the longitudinal hyperbolastic mixed-effects type II model.

Background: The main purpose of this study was to model and analyze the dynamics of cervical cancer mortality rates for African American (Black) and White women residing in 13 states located in the eastern half of the United States of America from 1975 through 2010.

Methods: The cervical cancer mortality rates of the Surveillance, Epidemiology, and End Results (SEER) were used to model and analyze the dynamics of cervical cancer mortality. A longitudinal hyperbolastic mixed-effects type II model was used to model the cervical cancer mortality data and SAS PROC NLMIXED and Mathematica were utilized to perform the computations.

T model of growth and its application in systems of tumor-immune dynamics.

In this paper we introduce a new growth model called T growth model. This model is capable of representing sigmoidal growth as well as biphasic growth. This dual capability is achieved without introducing additional parameters.

A flexible multivariable model for phytoplankton growth.

We introduce a new multivariable model to be used to study the growth dynamics of phytoplankton as a function of both time and the concentration of nutrients. This model is applied to a set of experimental data which describes the rate of growth as a function of these two variables. The form of the model allows easy extension to additional variables.

Clinical and multiple gene expression variables in survival analysis of breast cancer: analysis with the hypertabastic survival model.

Background: We explore the benefits of applying a new proportional hazard model to analyze survival of breast cancer patients. As a parametric model, the hypertabastic survival model offers a closer fit to experimental data than Cox regression, and furthermore provides explicit survival and hazard functions which can be used as additional tools in the survival analysis. In addition, one of our main concerns is utilization of multiple gene expression variables.

Mathematical modeling of stem cell proliferation.

The mathematical models prevalently used to represent stem cell proliferation do not have the level of accuracy that might be desired. The hyperbolastic growth models promise a greater degree of precision in representing data of stem cell proliferation. The hyperbolastic growth model H3 is applied to experimental data in both embryonic stem cells and adult mesenchymal stem cells.

Hyperbolastic modeling of tumor growth with a combined treatment of iodoacetate and dimethylsulphoxide.

Background: An understanding of growth dynamics of tumors is important in understanding progression of cancer and designing appropriate treatment strategies. We perform a comparative study of the hyperbolastic growth models with the Weibull and Gompertz models, which are prevalently used in the field of tumor growth.

Methods: The hyperbolastic growth models H1, H2, and H3 are applied to growth of solid Ehrlich carcinoma under several different treatments.