Information measures for the stochastic Gompertz growth model

Stochastic Nonlinear Gompertz Model of Tumour Growth

In this communication, based upon the deterministic Gompertz growth law, a stochastic nonlinear model of tumour growth is proposed to model the conventional size-dependent therapy strategy of tumours. The probability density function of the size of the tumour obeys a nonlinear Fokker-Planck equation which can be solved analytically. It is found that during the cancer treatments the dose intensi...

Statistical Ensemble Theory of Gompertz Growth Model

An ensemble formulation for the Gompertz growth function within the framework of statistical mechanics is presented, where the two growth parameters are assumed to be statistically distributed. The growth can be viewed as a self-referential process, which enables us to use the Bose-Einstein statistics picture. The analytical entropy expression pertain to the law can be obtained in terms of the ...

Multivariate Markov processes for stochastic systems with delays: application to the stochastic Gompertz model with delay.

Using the method of steps, we describe stochastic processes with delays in terms of Markov diffusion processes. Thus, multivariate Langevin equations and Fokker-Planck equations are derived for stochastic delay differential equations. Natural, periodic, and reflective boundary conditions are discussed. Both Ito and Stratonovich calculus are used. In particular, our Fokker-Planck approach recove...

Maximum life span predictions using the Gompertz tumour Growth model

Studies in the evolutionary biology of cancer research require good estimates of the intrinsic growth rate of the tumour coefficient. A Gompertzian model is a classical continuous model useful in describing population dynamics; in particular, it is a very efficient mathematical modelto describe tumour growth in humans and animals. The Gompertz survival model of a tumour growth is the interest o...

Introducing a Relational Network DEA Model with Stochastic Intermediate measures for Portfolio Optimization