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手足口病传播的数学模型建立与分析
发表时间：2010-06-15 浏览量：2837 下载量：970
| 全部作者： | 包钰，施昀，黄海洋，崔吟歌 |
| 作者单位： | 北京师范大学数学科学学院 |
| 摘 要： | 首先，根据传染病的传播特点，建立关于手足口病人率的常微分方程模型，并对出生率和超过6岁儿童的比率关系分别进行讨论。搜集2008年5月4日至5月11日传染病流行较严重的省份——安徽省比较准确的数据，用Matlab软件进行数值计算，以图形模拟方法求得S-I-R模型中的有关参数。得到手足口病人率比较符合实际数据的变化图，能正确地预测它的发展趋势。并导出手足口病人数关于时间的函数I(t)，利用相轨线理论对结果加以分析并作出预测。然后，建立时间序列的ARIMA模型。根据现有模型，利用时间序列软件EViews对数据进行拟合，得出模型的阶数和参数，对拟合结果进行相关性检验，验证模型的合理性。将拟合数据与原数据进行对比，证明拟合正确。并对未来几天可能的感染人数进行预测。最后根据预报得知，手足口疾病（hand-foot-and-mouth disease,HFMD）大概1个多月后，病情会有大大好转，而现实证明了这一点。 |
| 关 键 词： | 流行病与卫生统计学；手足口病；常微分方程；曲线拟合；时间序列；ARIMA模型 |
| Title： | Establishment and analysis of mathematical model of hand-foot-and-mouth disease |
| Author： | BAO Yu, SHI Yun, HUANG Haiyang, CUI Yinge |
| Organization： | School of Mathematical Sciences, Beijing Normal University |
| Abstract： | Firstly, according to the characteristics of infectious disease, this paper builds ordinary differential equation model of the patient rate of the hand-foot-and-mouth disease and discusses the relation between birth rate and the proportion of children over six years old. The data are from Anhui province where the disease is serious from May fifth to May eleventh in 2008. The research uses the math software Matlab to do numerical calculation and takes advantage of graph fitting to gain the parameter of S-I-R model and to get the changing graph which conforms to the fact and could forecast the trend. The work derives the function I(t) of the number of hand-foot-and-mouth disease patients and makes a prediction. Secondly, ARIMA model of time series is established, and software Eviews is used to fit the data and calculate the degree and the parameter of the ARIMA model. The study tests the correlation to verify rationality of the model. Comparing the fitting data and the original data, the result proves that the fitting is valid and makes the forecast of the disease. Finally, based on the forecast, the condition of hand-foot-and-mouth disease would be better greatly after one month. The facts warrant the conclusion. |
| Key words： | epidemiology and hygienic statistics; hand-foot-and-mouth disease； ordinary differential equation; curve fitting; time series; ARIMA model |
| 发表期数： | 2010年6月第11期 |
| 引用格式： | 包钰，施昀，黄海洋，等. 手足口病传播的数学模型建立与分析[J]. 中国科技论文在线精品论文，2010，3（11）：1157-1163. |
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