基于三次样条插值的艾滋病治疗模型

An AIDS Therapy Model Based on the Cubic Spline Interpolation

基于数学建模提供的艾滋病治疗方案中的实验数据,依据病人的初始CD4状态,将实验数据分类筛选,采用一维三次样条插值法描绘各类病人服药时间与病情的关系图形,进而由图形确定最佳治疗终止时间;并建立了CD4与时间的函数关系模型,借助于性价比函数进行疗效、价格的综合比较分析,此模型解法对最佳治疗方案的选择提供了有力依据.

Based on the experimental data in AIDS therapeutic regimens provided by The Mathematical Contest in Modeling, we classify and filter the data according to the patients＇ original CD4 state. We describe the relation diagram between dosing time and disease status by using one-dimensional cubic spline interpolation. Thus we can obtain further the optimal cure time from the different therapeutics by the diagram. And the model of the relationship between CD4 and the optimal time is proposed; the price and the curative effect are compared and analyzed synthetically with the aid of the performance price ratio function. The method given in the paper provides forceful foundation for choosing an optimal therapeutic regimen.