A delayed nonlinear stochastic model for cocaine consumption: Stability analysis and simulation using real data

Abstract

[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