We consider a diffusion model based on a generalized Gompertz deterministic growth in which carrying capacity depends on the initial size of the population. The drift of the resulting process is then modified by introducing a time-dependent function, called “therapy”, in order to model the effect of an exogenous factor. The transition probability density function and the related moments for the proposed process are obtained. A study of the influence of the therapy on several characteristics of the model is performed. The first-passage-time problem through time-dependent boundaries is also analyzed. Finally, an application to real data concerning a rabbit population subject to particular therapies is presented.
On the therapy effect for a stochastic growth Gompertz-type model
ALBANO, GIUSEPPINA;GIORNO, Virginia;
2012-01-01
Abstract
We consider a diffusion model based on a generalized Gompertz deterministic growth in which carrying capacity depends on the initial size of the population. The drift of the resulting process is then modified by introducing a time-dependent function, called “therapy”, in order to model the effect of an exogenous factor. The transition probability density function and the related moments for the proposed process are obtained. A study of the influence of the therapy on several characteristics of the model is performed. The first-passage-time problem through time-dependent boundaries is also analyzed. Finally, an application to real data concerning a rabbit population subject to particular therapies is presented.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
