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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/3113545
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