长沙市甲型Ｈ１Ｎ１流感抗体水平趋势数学模型模拟研究

摘要：目的　采用常微分方程（ｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ，ＯＤＥ）模型模拟长沙市甲型Ｈ１Ｎ１流感抗体
水平。方法　根据甲型Ｈ１Ｎ１流感在人群中的传播及抗体消长特点，建立全人群及各年龄组人群抗体水平
变化趋势的ＯＤＥ 模型，利用长沙市人口学资料、以及长沙市人群血清学横断面调查资料拟合模型参数，并
模拟长沙市人群的抗体水平变化趋势、以及抗体水平低于人群最低免疫屏障的具体时间。结果　大流行结
束后疫苗接种者抗体水平高于未接种者，但前者的抗体消失速度高于后者，两者抗体水平分别在２０１０ 年
１２月和２０１３年１月开始接近人群最低免疫屏障。在疫苗接种人群中，抗体消失速度最快的是“≥６０ 岁”
年龄组，最慢的是“０～５岁”年龄组，而“６～１５岁”、“１６～２４岁”、“２５～５９岁”３个年龄组人群抗体水
平消失速度较为接近。在未接种疫苗人群中，抗体消失速度最快的是“６～１５ 岁” 年龄组，其次是“１６～
２４岁”、“０～５岁”、“≥６０岁”年龄组，最慢的是“２５～５９岁” 年龄组。长沙市流感监测数据显示，２０１３
年１月开始甲型Ｈ１Ｎ１流感成为优势毒株，并在１～４月份发生４起甲型Ｈ１Ｎ１流感暴发疫情和１起流感样
病例暴发疫情，这与模型预测结果相似。结论　本研究建立的ＯＤＥ 模型可以较好地模拟长沙市甲型Ｈ１Ｎ１
流感抗体水平变化特点。疫苗接种获得的免疫屏障维持时间比自然感染短。不同年龄组获得免疫屏障水平
不同、消减速度亦不同。
关键词：甲型Ｈ１Ｎ１流感；抗体；常微分方程模型；模拟
中图分类号：Ｒ１８１．２　　文献标识码：Ａ　　文章编号：１００９ ６６３９ （２０１４）０３ ０１７３ ０８

Mathematical model for simulating antibody dynamic change of H1N1influenza A virus in Changsha

Objective To simulate the antibody changing trend of H1N1influenza A virus by using ordinary differential equation（ODE）model in Changsha. Methods An ODE model was established based on the characteristics of H1N1flu transmission and antibody dynamic change Model parameters were fitted according to the demography data and H1N1influenza A serological data obtained from cross-sectional study.The model was used to simulate antibody dynamic change among residents in Changsha. Results After the H1N1flu pandemic,antibody level was higher among vaccinated individuals compared to those unvaccinated,but it quickly dropped to the lowest level in December 2010,while the later happened in January 2013.Individuals aged 60and over had the fastest speed of antibody dropping,while children aged 0-5had the lowest among vaccinated residents.However,among those unvaccinated,individuals aged 6-15had the fastest and those aged 25-59had the lowest speed of antibody dropping.Influenza surveillance data revealed that H1N1influenza A virus was predominant since January 2013and a total of 4H1N1flu outbreaks and 1influenza-like illness outbreak were recorded from January to April 2013,which were concordant with the prediction of ODE model. Conclusions The ODE model established in the study is able to simulate the dynamic change of antibody against H1N1influenza A virus.Active immunity triggered by natural infection lasts longer than that by vaccination and antibody level varies from different age groups as does its dropping speed.