基于脉冲时滞微分方程构建人体内酒精扩散模型  

Construction of Alcohol Diffusion Model in Human Body Based on Pulse Time Delay Differential Equations

作　　者：宋泓庆 宋子琪 李森 SONG Hongqing;SONG Ziqi;LI Sen(School of Science and Chemical Engineering,Changzhou institute of Technology,Changzhou 213032)

机构地区：[1]常州工学院数理与化工学院,江苏常州213032

出　　处：《常州工学院学报》2018年第3期45-48,共4页Journal of Changzhou Institute of Technology

基　　金：常州工学院大学生创新创业训练计划项目(201711055048X)

摘　　要：基于微分方程理论和药物学原理,建立了酒精扩散的微分方程模型。利用非线性最小二乘拟合方法对模型中的参数进行估计,从而得到酒后胃中及体液中酒精含量随时间变化的关系。考虑到实际饮酒过程中酒精的扩散时滞效应,建立了具有脉冲扩散效应的时滞微分方程模型,通过对比已有文献的结果,验证了模型的有效性。最后利用该模型,给出饮酒后人体体液中酒精含量降到标准线下的时间。Based on differential equation theory and the principle of pharmacology,a differential equation model for alcohol diffusion is established. The parameters in the model are estimated by the nonlinear least square fitting method,and the time-varying relationship between alcoholicity in the stomach and body fluid after drinking was obtained. Considering the time delay effect of alcohol in the actual drinking process,a time-delay differential equation model with the effect of pulse diffusion is established,and the validity of the model is verified by comparing the results of the previous literature. Finally,the time of alcoholicity in the body fluid belowthe standard is provided by using this model.

关 键 词：微分方程模型 非线性最小二乘拟合 脉冲微分方程组 酒精扩散 

分 类 号：O175[理学—数学]