传染病传播趋势及医疗费用动态预测研究——基于灰色系统理论与Lee-Carter模型

Research on Transmission Trends of Infectious Diseases and Dynamic Prediction of Medical Costs—Based on Grey System Theory and Lee-Carter Model

摘要: 本文综合运用灰色系统理论与人口统计学模型，构建多维度预测框架，研究了病毒性肝炎、肺结核、梅毒三类重点传染病的流行趋势及其医疗费用增长规律。通过融合GM (1, 1)模型与Lee-Carter模型，跳出单一方法下数据假设的局限，构建一阶线性微分方程，捕捉医疗费用的动态演化规律和传染病的长期趋势以及对时间因子进行外推预测。基于此，本文尝试解析三种传染病的数据预测及预防指标，初步分析了疾病与经济的相关性，为卫生规划提供一种潜在的量化参考工具。

Abstract: This paper comprehensively applies the grey system theory and demographic models, constructs a multi-dimensional prediction framework, and studies the epidemic trends of three key infectious diseases—viral hepatitis, tuberculosis, and syphilis—as well as the laws governing the growth of their medical expenses. By integrating the GM (1, 1) model and the Lee-Carter model, we transcend the constraints imposed by data assumptions under a single method, construct a first-order linear differential equation, capture the dynamic evolution patterns of medical expenses and the long-term trends of infectious diseases, and perform extrapolative forecasting for time factors. Building upon this, this paper attempts to analyze the data prediction and prevention indicators of three infectious diseases, preliminarily examines the correlation between diseases and the economy, and thereby aims to serve as a potential quantitative reference tool for health planning.