疫苗接种后抗体衰减趋势的数学模型建立与应用
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摘要
目的建立数学模型预测乙型肝炎疫苗(HepB)、风疹减毒活疫苗(RV)和麻疹减毒活疫苗(MV)接种后的抗体衰减趋势。方法用曲线拟合的方法,对国产HepB、RV和MV接种后抗体水平(?)随时间(X)的实测数据拟合数学模型,经拟合优度检验,验证模型的可靠性。结果拟合的HepB、RV和MV接种后抗体衰减模型分别为?=165.67exp(-0.019X)、?=269.39e~(-0.3603X)-61.26、?=90.95X~(-0.61),模型决定系数R~2分别为0.98、0.95和1.00,预测误差分别为0.02、0.05、0.003。结论用曲线拟合法拟合HepB、RV和MV接种后抗体衰减趋势的适配性较好。
Objective To develop mathematical models to predict antibody levels after vaccination with hepatitis B vaccine(HepB),rubella attenuated live vaccine(RV), and measles attenuated live vaccine(MV). Methods We used a curve fitting method to develop mathematical models based on actual antibody levels(?) over time(X) after vaccination with domestic HepB, RV, and MV; we determined reliability using the goodness-of-fit test. Results The fitted models for HepB, RV, and MV were ?=165.67 exp(-0.019 X),?=269.39 e~(-0.3603 X)-61.26, and ?=90.95 X~(-0.61), respectively; coefficients of determination(R~2) were 0.98, 0.95, and 1.00, with prediction errors of 0.02, 0.05, and 0.003, respectively. Conclusion Models developed with a curve fitting method reliably predicted antibody levels after vaccination with HepB, RV, and MV.
Objective To develop mathematical models to predict antibody levels after vaccination with hepatitis B vaccine(HepB),rubella attenuated live vaccine(RV), and measles attenuated live vaccine(MV). Methods We used a curve fitting method to develop mathematical models based on actual antibody levels(?) over time(X) after vaccination with domestic HepB, RV, and MV; we determined reliability using the goodness-of-fit test. Results The fitted models for HepB, RV, and MV were ?=165.67 exp(-0.019 X),?=269.39 e~(-0.3603 X)-61.26, and ?=90.95 X~(-0.61), respectively; coefficients of determination(R~2) were 0.98, 0.95, and 1.00, with prediction errors of 0.02, 0.05, and 0.003, respectively. Conclusion Models developed with a curve fitting method reliably predicted antibody levels after vaccination with HepB, RV, and MV.
引文
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[3]孔青.成人不同免疫程序接种乙肝疫苗12年后体液免疫持久性比较研究[D].济南:山东大学,2018.KONG Qing.Antibody persistence of hepatitis B vaccine among adults by dif ferent immunization schedules:a twelve-year comparat ive study[D].Jinan:Shandong University,2018.
[4]黄跃龙,李树民,唐蕊妍,等.国产冻干风疹减毒活疫苗免疫持久性研究[J].中国自然医学杂志,2004,6(2):84-85.HUANG Yuelong,LI Shumin,TANG Ruiyan,et al.Study on the immunity duration of the lyophilized attenuated live rubella vaccine[J].Chinese Journal of Natural Medicine,2004,6(2):84-85.
[5]徐福根,姚怀芳,蒋金香,等.BRDⅡ株风疹减毒活疫苗接种10~11年后的免疫持久性[J].中国计划免疫,1998,4(3):147-150.XU Fugen,YAO Huai fang,J IANG J inxiang,et al.Persistence of antibody 10-11 years af ter vaccination with BRDⅡstrain live attenuated rubella vaccine[J].Chinese Journal of Vaccines and Immunization,1998,4(3):147-150.
[6]王树巧,陈志慧,谢广中,等.麻疹疫苗免疫持久性研究-初免后24-25年追踪观察[J].中国生物制品学杂志,2002,15(1):58-60.WANG Shuqiao,CHEN Zhihui,XIE Guangzhong,et al.Persistence oflive measles vaccine 24-25 years af ter primary immunization[J].Chinese Journal of Biologicals,2002,15(1):58-60.
[7]周洋.肠道病毒71型灭活疫苗免疫持久性及模型预测研究[D].南京:东南大学,2016.ZHOU Yang.The persistence of neutralizing antibodies induced by enterovirus 71 vaccine and predicted by model[D].Nanjing:Southeast University,2016.
[8]倪宗瓒.医学统计学[M].第2版,北京:人民卫生出版社,1995:112-116.NI Zongzan.Medical stat ist ics[M].Second edit ion.Beijing:People's Medical Publishing House,1995:112-116.
[9]孙振球.医学统计学[M].第3版,北京:人民卫生出版社,2013:169-173.SUN Zhenqiu.Medical stat ist ics[M].Third edit ion.Beijing:People's Medical Publishing House,2013:169-173.
[10]罗凤基,董春明,沈永刚,等.指数模型拟合法在乙型肝炎疫苗接种后抗体持久性预测中的应用[J].中华流行病学杂志,2004,25(9):805-807.LUO Fengji,DONG Chunming,SHEN Yonggang,et al.Application of exponent curve model to study the hepatitis B DNA recombinant yeast derived vaccine antibody levels[J].Chinese Journal of Epidemiology,2004,25(9):805-807.