酗酒相关问题的建模及研究

项目名称： 酗酒相关问题的建模及研究

项目编号： No.11461041

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 霍海峰

作者单位： 兰州理工大学

项目金额： 36万元

中文摘要： 酗酒是危害人类健康的危险行为之一，本项目基于传染病动力学和生态毒理学建模的基本思想，通过与甘肃省肿瘤医院和兰州理工大学校医院相关医务人员合作，建立若干考虑人群的性别、年龄及迁移，随机因素干扰的确定与随机微分方程酗酒模型，利用动力学分析方法、随机微分方程理论和计算机模拟等方法研究模型的稳定性、分支等动力学问题，进一步利用随机与确定极值原理、随机与确定动态规划等方法，研究酗酒问题的最优控制问题。同时将根据实际数据和现有的统计资料，对所建模型的参数进行调整与优化，使得所建模型更加接近实际，期望人们对酗酒问题从定量的角度有一个更加深入和准确的了解，从而为相关部门控制酗酒提供一定的理论建议。同时丰富和完善相应的数学理论与方法。

中文关键词： 酗酒；时滞；随机扰动；扩散；数学建模

英文摘要： Drinking is one of dangerous behaviours, which are harmful to the health. Cooperating with medical workers of The Tumor Hospital of Gansu Province and The Hospital of Lanzhou University of Technology and based on the basic ideal of epidemic model and ecotoxicology model, we set up several kinds of deterministic and stochastic drinking models which descrip the effects of sex structure, age structure, population diffusion and random factors. With the help of dynamic method, theory of stochastic differential equation and numerical simulation, we will study the stability and bifurcation of these model. Furthermore, by using the methods of deterministic and stochastic maximum principle, deterministic and stochastic dynamic programming, we will study optimal control of drinking problem. We also adjust and optimize parameters of drinking models by using the statistical data and research results, thus the models of drinking comes close to reality. The main objective of this project is to provide some quantitative predictions about drinking, and give some advice for control of drinking. By the studying of this project, we also hope that we can enrich and consummate some method and theory of Mathematics.

英文关键词： Drinking;Delay;Stochastic Perturbation;Diffusion;Mathematical Modelling