Suchergebnisse

[EN] 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. ; This work has been supported by the Spanish Ministerio de Economia, Industria y Competitividad (MINECO), the Agencia Estatal de Investigacion (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) grant MTM2017-89664-P. Computations have been carried thanks to the collaboration of Raul San Julian Garces and Elena Lopez Navarro granted by European Union through the Operational Program of the European Regional Development Fund (ERDF)/European Social Fund (ESF) of the Valencian Community 2014-2020, grants GJIDI/2018/A/009 and GJIDI/2018/A/010, respectively ; Burgos-Simon, C.; Cortés, J.; Shaikhet, L.; Villanueva Micó, RJ. (2021). A delayed nonlinear stochastic model for cocaine consumption: Stability analysis and simulation using real data. Discrete and Continuous Dynamical Systems. Series S. 14(4):1233-1244. https://doi.org/10.3934/dcdss.2020356 ; S ; 1233 ; 1244 ; 14 ; 4

[EN] We provide a full stochastic description, via the first probability density function, of the solution of linear-quadratic logistic-type differential equation whose parameters involve both continuous and discrete random variables with arbitrary distributions. For the sake of generality, the initial condition is assumed to be a random variable too. We use the Dirac delta function to unify the treatment of hybrid (discrete-continuous) uncertainty. Under general hypotheses, we also compute the density of time until a certain value (usually representing the population) of the linear-quadratic logistic model is reached. The theoretical results are illustrated by means of several examples, including an application to modelling the number of users of Spotify using real data. We apply the Principle Maximum Entropy to assign plausible distributions to model parameters ; This work has been supported by the Spanish Ministerio de Economa, Industria y Competitividad (MINECO) , the Agencia Estatal de Investigaci on (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) grant MTM201789664P. Computations have been carried thanks to the collaboration of Raul San Julian Garces and Elena Lopez Navarro granted by European Union through the Operational Program of the European Regional Development Fund (ERDF) /European Social Fund (ESF) of the Valencian Community 2014-2020, grants GJIDI/2018/A/009 and GJIDI/2018/A/010, respectively ; Burgos-Simon, C.; Cortés, J.; López-Navarro, E.; Villanueva Micó, RJ. (2021). Probabilistic analysis of linear-quadratic logistic-type models with hybrid uncertainties via probability density functions. AIMS Mathematics. 6(5):4938-4957. https://doi.org/10.3934/math.2021290 ; S ; 4938 ; 4957 ; 6 ; 5 ; R. Goebel, R. G. Sanfelice, A. R. Teel, i>Hybrid Dynamical Systems: Modeling, Stability, and Robustness /i>, Princeton University Press, 2012. ; J. Lunze, F. Lamnabhi-Lagarrigue, i>Handbook of Hybrid Systems Control: Theory, Tools, Applications /i>, ser. Nonlinear Systems and Complexity, ...

[EN] Electronic commerce (EC) has numerous advantages. It allows saving time when we purchase an item, offers the possibility of review without depending on the schedules of traditional stores, access to a wider variety and quantity of articles, in many cases, with lower prices, etc. Based upon mathematical epidemiology tenets strongly related to social behavior able to describe the influence of peers, in this paper we propose an age-group dynamic model with population varying size based on a system of difference equations to study the evolution of the frequent users of EC over time in Spain. Using data from surveys retrieved from the Spanish National Statistics Institute, we use and design computational algorithms to perform a probabilistic estimation of the model parameters that allow the model output to capture the data uncertainty. Then, we will be able to perform a precise prediction with uncertainty. ; This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2017-89664-P and by the European Union through the Operational Program of the European Regional Development Fund (ERDF)/European Social Fund (ESF) of the Valencian Community 2014-2020, grants GJIDI/2018/A/009 and GJIDI/2018/A/010. ; Burgos-Simon, C.; Cortés, J.; Martínez-Rodríguez, D.; Villanueva Micó, RJ. (2019). Computational modelling with uncertainty of frequent users of e-commerce in Spain using an age-group dynamic nonlinear model with varying size population. Advances in Complex Systems. 22(4):1950009-1-1950009-17. https://doi.org/10.1142/S0219525919500097 ; S ; 1950009-1 ; 1950009-17 ; 22 ; 4 ; Bettencourt, L. (1997). Customer voluntary performance: Customers as partners in service delivery. Journal of Retailing, 73(3), 383-406. doi:10.1016/s0022-4359(97)90024-5 ; Brauer, F., & Castillo-Chávez, C. (2001). Mathematical Models in Population Biology and Epidemiology. Texts in Applied Mathematics. doi:10.1007/978-1-4757-3516-1 ; Cortés, J.-C., Lombana, I.-C., & Villanueva, R.-J. (2010). Age-structured ...