title: On the therapy effect for a stochastic growth Gompertz-type model.
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.
authors.affiliation: Dipartimento di Scienze Economiche e Statistiche, Università di Salerno, Italy.
authors.forename: Giuseppina
authors.initials: G
authors.lastname: Albano
authors.forename: Virginia
authors.initials: V
authors.lastname: Giorno
authors.forename: Patricia
authors.initials: P
authors.lastname: Román-Román
authors.forename: Francisco
authors.initials: F
authors.lastname: Torres-Ruiz
mesh_terms: D000818:Animals; D008954:Models, Biological; D011157:Population Dynamics; D011817:Rabbits / Q000254:growth & development*; D013269:Stochastic Processes