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In this paper, we study a stochastic system of differential equations with nonlocal discrete diffusion. For two types of noises, we study the existence of either positive or probability solutions. Also, we analyze the asymptotic behavior of solutions in the long term, showing that under suitable assumptions they tend to a neighborhood of the unique deterministic fixed point. Finally, we perform numerical simulations and discuss the application of the results to life tables for mortality in Spain. [ABSTRACT FROM AUTHOR]

In this paper we propose a stochastic mathematical model with distributed delay in order to describe the transmission dynamics of cocaine consumption in Spain. We investigate conditions to guarantee the stability in probability of the equilibrium points under stochastic perturbations via the white noise processes. The results are applied to the model cocaine consumption using data retrieved from the Spanish Drug National Plan, http://www.pnsd.mscbs.gob.es/. The obtained results may be useful for policy health authorities in order to improve the strategies against the drug consumption in the long-run. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the dynamics of the transmission of respiratory syncytial virus (RSV) in the population using stochastic models. The stochastic models are developed introducing stochastic perturbations on the demographic parameter as well as on the transmission rate of the RSV. Numerical simulations of the deterministic and stochastic models are performed in order to understand the effect of fluctuating birth rate and transmission rate of the RSV on the population dynamics. The numerical solutions of stochastic models are calculated using Euler-Maruyama and Milstein schemes, and confidence intervals for stochastic solutions are given using Monte-Carlo method. Analysis of the numerical results reveals that perturbations on the transmission rate are more decisive in the dynamics of RSV than perturbations on demographic parameters. In addition, the stochastic models show the advantage of reproducing more effectively the noisy RSV hospitalization data. It is concluded that these stochastic models are a viable option to provide a realistic modeling of the RSV dynamics on the population. [Copyright &y& Elsevier]

The article proposes a bivariate stochastic Gompertz diffusion model for the statistical aspects and application to the joint modeling of the Gross Domestic Product and carbon dioxide emissions in Spain. The authors establish the probabilistic characteristics of the mathematical model, such as the bivariate transition density, the bidimensional moment functions, the conditioned trend functions and in particular, the correlation function between each of the components of the Gompertz diffusion model. The implementation is carried out on the basis of annual observations of the variables over the period of 1986 to 2003, according to the authors.

The aim of this work is the study of a new stochastic diffusion model with a cubic-type drift coefficient. The model is considered as the solution of an Ito stochastic differential equation. Using the Ito's stochastic calculus and properties of the Kummer function, the trend functions and steady-state distribution for the process are obtained. Statistical estimation and corresponding computational methodology are established. Finally, the model is applied to modelling and prediction of the global CO2 emission in Spain [ABSTRACT FROM AUTHOR]