Abstract: Objective To expound the application of Bayes analysis in the relationship between Japanese encephalitis (JE) and multiple seasonal autoregressive integrated moving average model (ARIMA) in Hebei province, meanwhile, to evaluate the effect of the multiple seasonal ARIMA model in the prediction of monthly mosquito density and JE prediction. Methods We collected the incidence data of the JE and mosquito population density data. A mathematic model was constructed using SPSS 21.0 and used to predict the situation, discuss the application of Bayes analysis in the relationship between JE and multiple seasonal ARIMA model of total mosquito density. Results ARIMA (0,1, 1)×(0, 1, 1)₁₂ model best fitted the incidence of mosquito density from 2009 to 2016. The incidence of JE disease was correlated with mosquito population densities (r=0.101, P=0.043). Bayes analysis indicated that 63.16% subjects were correctly discriminated among samples of mosquito density and Bayes analysis got a result that the coincidence rate was 100% among the prediction of mosquito density and true ones in JE prediction. Conclusion Bayes analysis verified that the multiple seasonal ARIMA model in the prediction of monthly mosquito density can be used to predict the JE. ARIMA model fits well in the prediction of mosquito density, and applies to the information system of vector monitoring, and to early warn the unusual mosquito density and control mosquito-borne infectious diseases.

Key words: Japanese encephalitis, Mosquito density, Autoregressive integrated moving average model, Bayes analysis

摘要： 目的 利用贝叶斯（Bayes）判别分析方法探讨河北省流行性乙型脑炎（乙脑）发生与蚊密度时间序列预测模型的关系，验证差分自回归移动平均（ARIMA）模型在病媒生物监测信息管理系统中对蚊密度的预测及关联乙脑病例的预警作用。方法 收集河北省2009-2016年乙脑报告病例资料和蚊密度监测资料进行统计分析，采用ARIMA模型进行建模拟合及预测分析；利用Bayes判别分析论证蚊密度预测模型与乙脑的关系。结果 通过ARIMA模型对总蚊密度进行拟合得出最优模型ARIMA（0，1，1）×（0，1，1）₁₂；2009-2016年河北省总蚊密度与乙脑呈正相关（r=0.101，P=0.043）；将Bayes判别分析用于河北省总蚊密度时间序列模型预测值判别2个月后的乙脑发病情况，与实际乙脑发生情况比较符合率为0.631 6，总蚊密度监测值与ARIMA模型的预测值对密度高峰后2个月的乙脑发病状况Bayes判别结果符合率为100%。结论 Bayes判别分析可应用于河北省总蚊密度时间序列模型预测值对乙脑疫情的预警，通过建立模型对蚊密度预测，可以利用病媒生物监测信息管理系统蚊虫监测数据对蚊媒传染病的防控工作提供预警支撑。

关键词: 流行性乙型脑炎, 蚊密度, 差分自回归移动平均模型, 贝叶斯分析