Inference of a Susceptible-Infectious stochastic model.

We considered a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious (SI) epidemic model in which the transmission intensity function was time-dependent. Such a model was well suited to describe some classes of micro-parasitic infections in which individuals never acquired lasting immunity and over the course of the epidemic everyone eventually became infected. The stochastic process related to the deterministic model was transformable into a nonhomogeneous Wiener process so the probability distribution could be obtained.

Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean.

We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical inference, two procedures to find the maximum likelihood estimates of the unknown parameters are described. One is based on the resolution of the system of the critical points of the likelihood function, and the other is on the maximization of the likelihood function with the simulated annealing algorithm.

Do Chefs Value Health in Their Olive Oil Purchasing Decisions?

Amidst the public's growing preoccupation with healthy eating, both inside and outside the home; an increase in people eating out; and the importance that olive oil has acquired in the markets due to its health benefits, the aim of this study is to find out whether health is also a relevant criterion for chefs in their olive oil purchase decisions. To this end, a survey was conducted of 400 chefs in Spain belonging to the international chefs' association Euro-Toques. The results show that only 2% of the sample consider health to be a relevant criterion in the purchase of olive oils and that the attribute of "health" is not used by restaurants as an element of differentiation by which to position themselves in the market.

Hyperbolastic type-III diffusion process: Obtaining from the generalized Weibull diffusion process.

The modeling of growth phenomena has become a matter of great interest in many different fields of application and research. New stochastic models have been developed, and others have been updated to this end. The present paper introduces a diffusion process whose main characteristic is that its mean function belongs to a wide family of curves derived from the classic Weibull curve.

In search of a consumer-focused food classification system. An experimental heuristic approach to differentiate degrees of quality.

The present paper focuses on the problems that arise in food classification systems (FCSs), especially when the food product type has different levels or grades of quality. Despite the principal function of these systems being to assist the consumer (to inform, clarify and facilitate choice and purchase), they frequently have the opposite effect. Thus, the main aim of the present research involves providing orientations for the design of effective food classification systems.

A hyperbolastic type-I diffusion process: Parameter estimation by means of the firefly algorithm.

A stochastic diffusion process, whose mean function is a hyperbolastic curve of type I, is presented. The main characteristics of the process are studied and the problem of maximum likelihood estimation for the parameters of the process is considered. To this end, the firefly metaheuristic optimization algorithm is applied after bounding the parametric space by a stagewise procedure.

Modeling tumor growth in the presence of a therapy with an effect on rate growth and variability by means of a modified Gompertz diffusion process.

In experimental studies on tumor growth, whenever the time evolution of the relative volume of a tumor in an untreated (control) group can be fitted by a Gompertz diffusion process there is a possibility that an antiproliferative therapy, which modifies the growth rate of the process that fits the treated group, may also affect its variability. The present paper proposes several procedures for the estimation of the time function included in the infinitesimal variance of the new process, as well as the time function affecting the growth rate (which is included in the infinitesimal mean). Also, a hypothesis testing is designed to confirm or refute the need for including such a time-dependent function in the infinitesimal variance.

A stochastic model of cancer growth subject to an intermittent treatment with combined effects: reduction in tumor size and rise in growth rate.

A model of cancer growth based on the Gompertz stochastic process with jumps is proposed to analyze the effect of a therapeutic program that provides intermittent suppression of cancer cells. In this context, a jump represents an application of the therapy that shifts the cancer mass to a return state and it produces an increase in the growth rate of the cancer cells. For the resulting process, consisting in a combination of different Gompertz processes characterized by different growth parameters, the first passage time problem is considered.

Estimating and determining the effect of a therapy on tumor dynamics by means of a modified Gompertz diffusion process.

A modified Gompertz diffusion process is considered to model tumor dynamics. The infinitesimal mean of this process includes non-homogeneous terms describing the effect of therapy treatments able to modify the natural growth rate of the process. Specifically, therapies with an effect on cell growth and/or cell death are assumed to modify the birth and death parameters of the process.

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

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.

Fitting dynamic growth models of biological phenomena from sample observations through Gaussian diffusion processes.

This paper addresses the building of stochastic models that adequately describe dynamic phenomena and, in particular, those that occur in the Biosciences. In this context, the empirical fitting of a Gaussian diffusion process from sample data of a dynamic growth phenomenon is considered. In order to do this, a methodology based on approximations to its mean and variance functions is presented.

Inferring the effect of therapies on tumor growth by using diffusion processes.

Modeling the effect of therapies in cancer animal models remains a challenge. This point may be addressed by considering a diffusion process that models the tumor growth and a modified process that includes, in its infinitesimal mean, a time function modeling the effect of the therapy. In the case of a Gompertz diffusion process, where a control group and one or more treated groups are examined, a methodology to estimate this function has been proposed by Albano et al.

Modelling logistic growth by a new diffusion process: application to biological systems.

The present paper introduces a new diffusion process for the purpose of modelling logistic-type behaviour patterns. Unlike other processes in the same context, this one verifies that its mean function is a logistic curve. In addition, its transition density can be found explicitly, which allows to analyse inference from the discrete sampling of trajectories.

On the therapy effect for a stochastic growth Gompertz-type model.

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.

Inferring the effect of therapy on tumors showing stochastic Gompertzian growth.

The present work deals with a Gompertz-type diffusion process, which includes in the drift term a time-dependent function C(t) representing the effect of a therapy able to modify the dynamics of the underlying process. However, in experimental studies is not immediate to deduce the functional form of C(t) from a treatment protocol. So a statistical approach is proposed in order to estimate this function when a control group and one or more treated groups are observed.

A diffusion process to model generalized von Bertalanffy growth patterns: fitting to real data.

The von Bertalanffy growth curve has been commonly used for modeling animal growth (particularly fish). Both deterministic and stochastic models exist in association with this curve, the latter allowing for the inclusion of fluctuations or disturbances that might exist in the system under consideration which are not always quantifiable or may even be unknown. This curve is mainly used for modeling the length variable whereas a generalized version, including a new parameter b > or = 1, allows for modeling both length and weight for some animal species in both isometric (b = 3) and allometric (b not = 3) situations.