On the effect of a therapy able to modify both the growth rates in a Gompertz stochastic model

Giuseppina Albano; Virginia Giorno; Patricia Román-Román; Francisco Torres-Ruiz

doi:10.1016/j.mbs.2013.01.001

On the effect of a therapy able to modify both the growth rates in a Gompertz stochastic model

Math Biosci. 2013 Sep;245(1):12-21. doi: 10.1016/j.mbs.2013.01.001. Epub 2013 Jan 21.

Authors

Giuseppina Albano¹, Virginia Giorno, Patricia Román-Román, Francisco Torres-Ruiz

Affiliation

¹ Dip. di Scienze Economiche e Statistiche, Università di Salerno, Italy. pialbano@unisa.it

PMID: 23347900
DOI: 10.1016/j.mbs.2013.01.001

Abstract

A Gompertz-type diffusion process characterized by the presence of exogenous factors in the drift term is considered. Such a process is able to describe the dynamics of populations in which both the intrinsic rates are modified by means of time-dependent terms. In order to quantify the effect of such terms the evaluation of the relative entropy is made. The first passage time problem through suitable boundaries is studied. Moreover, some simulation results are shown in order to capture the dependence of the involved functions on the parameters. Finally, an application to tumor growth is presented and simulation results are shown.

Keywords: First passage time; Non homogeneous Gompertz process; Relative entropy.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms
Cell Death
Computer Simulation
Humans
Mathematical Concepts
Models, Biological*
Neoplasms / pathology*
Neoplasms / therapy*
Stochastic Processes