Logistic微分方程模型在手足口病疫情预警研究中的应用  

Logistic differential equation model applying in the study of HFMD warning

作　　者：张锡兴[1] 刘如春[1] 谢知[1] 李亚曼[1] 陈水连[1] 赵锦[1] 胡伟红[1] 李叶兰[1] 王智宇[1] 张恒[1] 陈田木[1] 

机构地区：[1]长沙市疾病预防控制中心,湖南长沙410001

出　　处：《中国热带医学》2015年第8期942-946,961,共6页China Tropical Medicine

摘　　要：目的采用Logistic微分方程模型研究手足口病疫情流行特征并确定预警时间。方法收集2008年第17周至2015年第7周长沙市手足口病发病数，分析其流行规律和周期性。根据手足口病流行规律，建立各个周期内的Lo-gistic微分方程模型。利用实际周发病数据计算疫情发展速度参数k和流行周期结束时的累计病例数的理论值N，并根据这些参数求解各个流行周期早期疫情由慢变快的时间点（“疫情加速周”），并计算其标准差，以“疫情加速周”减一个标准差为“建议预警周”。结果长沙市每年均存在两个手足口病流行高峰。夏秋季流行高峰和冬春季流行高峰，对应时间分别为第8～33周，第34周至下一年第7周。可知夏秋季的“疫情加速周”平均值约为第17周（范围：第15～20周），标准差约为2周；冬春季的“疫情加速周”平均值约为第40周（范围：第37～42周），标准差约为2周。夏秋季和冬春季建议预警周分别为第15周和第38周。结论长沙市手足口病季节性和周期性明显。Logistic模型可以很好地刻画手足口病流行规律。采用“痰隋加速周”预警存在滞后现象，提前一个标准差后能够做到提前预警。Objective Logistic differential equation was used to explore the epidemic characteristics and early- warning time of hand foot and mouth disease（HFMD）. Methods The data of HFMD cases were collected from 1Th week 2008 to 7th week 2015 in Changsha city, and its epidemic characteristics and periodicity were analyzed. Logistic differential equation model of each cycle was established according to HFMD epidemic characteristics, The epidemic grow parameter k was calculated by the incident cases of actual weeks, the same as the theoretical cumulative number of cases N of ending epidemic cycles. The inflection point （ ＂epidemic speed week＂ ） that changed from slow to quick at early epidemic period and its standard deviation were calculated according to those parameters. We called the time when＂epidemic speed week＂ minus a standard deviation as＂recommended warning week＂, Results There are two peaks of I-IFMD at each year in Changsha city. One is the peak in summer and autumn corresponding to the 8th- 33th week, the other is the peak in winter and spring corresponding to the time from the 34th week to the 7th week next year. The＂epidemic speed week＂average value of summer and autumn is about the 17th week （ranging the 15th -20th week ） , and the standard deviation is about 2 weeks. The ＂epidemic speed week＂ average value of winter and spring is about the 40th week （ranging the 37th-42th week ） , and the standard deviation is about 2 weeks. So the＂recommended warning week＂of summer and autumn is the 15th week, and that of winter and spring is the 38th week. Gonclusion The seasonal and cyclical of HFMD are obvious in Changsha. Logistic model can be well fitted with HFMD data. Using＂epidemic speed week＂to warn would be lag, and advancing by a standard deviation could get early warning.

关 键 词：手足口病 LOGISTIC方程 数学模型 常微分方程模型 预警 

分 类 号：R512.5[医药卫生—内科学]