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.

中文翻译：

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可卡因消费的延迟非线性随机模型：使用真实数据的稳定性分析和仿真

为了描述西班牙可卡因消费的传播动态，本文提出了一种具有分布延迟的随机数学模型。我们研究了条件，以保证通过白噪声过程在随机扰动下达到平衡点概率的稳定性。使用从西班牙国家毒品计划（http://www.pnsd.mscbs.gob.es/）检索的数据将结果应用于可卡因模型消费。从长远来看，所获得的结果对于政策卫生部门可能有用，以改善针对药物消费的策略。