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[目的]根据艾滋病人服用一段时间后体内CD4与HIV的变化建立数学模型,用于评价药物治疗效果,以及确定最佳停药时间,从而更加有效的控制病情的发展。[方法]用数学软件matlab来实现数据的计算,将服用药物后CD4的值划分为6个疗程求平均值,用matlab中的拟合函数程序包对数据进行3次多项式进行拟合,用求导的方法求出拟合函数达到最大值时对应的疗程数,从而求出最佳停药时间。[结果]高CD4患者在4.7疗程的时候拟合函数达到最大值,低CD4患者在5.2疗程的时候达到最大值,HIV在4.5疗程的时候含量最少。高CD4患者大概在第34周停止用药,而低CD4患者大概在第40周停止用药。[结论]本模型应用于评价药物的疗效,在实际的医学短期预测中还是有一定的作用。推广而来,也可用此模型来拟合和预测一些得不到很多数据的模型。
[Objective] To establish a mathematical model based on the changes of CD4 and HIV in HIV-infected patients over a period of time, to evaluate the effect of drug therapy and to determine the optimal withdrawal time so as to more effectively control the progression of the disease. [Method] Using mathematical software matlab to calculate the data, the value of CD4 after taking drugs is divided into 6 courses for the average, the fitting function package in Matlab for data fitting polynomial 3 times Guide method to find the fitting function to reach the maximum number of corresponding courses, so as to find the best withdrawal time. [Results] In the high-CD4 patients, the fitting function reached the maximum value at the time of 4.7 courses. The patients with low CD4 reached the maximum at 5.2 courses of treatment and the HIV with the least amount of courses at 4.5 courses of treatment. High CD4 patients discontinued treatment at week 34, whereas low CD4 patients discontinue treatment at week 40. [Conclusion] This model can be used to evaluate the curative effect of drugs, and it still plays a certain role in the actual short-term medical prediction. Popularized, this model can also be used to fit and predict some models that do not have much data.