海洛因传播系统中若干问题建模与研究

More and more serious heroin and other drugs transmission problems have endangered directly people's health, economic development and social progress, and have become a global disaster. How to effectively control the spread of heroin and other drugs has turned into a challenging that humanity has to face. This project will establish the corresponding mathematical models through analyzing the key factors which affect the spread of heroin, the mathematical models include: age-structured heroin transmission models, heroin models with discrete and continuous diffusion, heroin models with classes age-structure and spatial diffusion at same time, the coupled models for heroin transmission and HIV infection in population, etal. By using the theory of functional analysis, the theory of integral equations and the qualitative and stability theory of differential equations in mathematics, we study the dynamic behavior of these models and perform numerical simulatio, revealing the key factors and laws for heroin transmission and predicting the heroin developing trends, so as to provide theoretical basises for the control and suppression of heroin transmission.

日趋严重的海洛因等毒品泛滥直接危害人民健康，给经济发展和社会进步带来巨大威胁，已成为全球性灾难。如何有效控制海洛因等毒品传播已成为人类面临的具有挑战性的课题。本项目将通过分析影响海洛因传播的关键因素，建立相应的数学模型，包括：年龄结构海洛因传播模型，具有离散扩散和连续空间扩散的海洛因传播模型，同时具有类年龄结构和连续空间扩散海洛因传播模型，海洛因传播和HIV感染耦合系统模型等。运用泛函分析、积分方程、微分方程定性稳定性理论等，研究这些模型的动力学性态并进行数值模拟，揭示影响海洛因传播的关键因素和规律，预测海洛因发展趋势，为控制和抑制海洛因传播提供理论依据。

日趋严重的海洛因等毒品泛滥直接危害人民健康，给经济发展和社会进步带来巨大威胁，已成为全球性灾难。 如何有效控制海洛因等毒品传播已成为人类面临的具有挑战性的课题。本项目通过分析影响海洛因传播的关键因素，建立相应的数学模型，包括：具有空间扩散和治疗年龄结构的海洛因传播模型，具有戒毒年龄和接种疫苗年龄的海洛因传播模型，海洛因与HIV共同感染的模型等。运用泛函分析、积分方程、微分方程定性稳定性理论等，对这些模型的动力学性态进行了分析，给出了模型基本再生数的表达式，讨论了模型无海洛因吸食平衡点和海洛因传播平衡点的存在性、局部渐近稳定性、全局渐近稳定性条件，分析了海洛因传播对HIV感染的影响，并对模型进行了数值模拟，揭示了影响海洛因传播的关键因素及其规律，为控制和抑制海洛因传播提供了理论依据。项目还对疟疾、多菌株、新冠等传染病进行了建模与研究，得到了有价值的结果。项目共发表论文15篇，SCI收录期刊13篇，在德国Springer出版社出版学术著作2部.