扩免后麻疹易感人群累积的数学模型研究

目的：对扩免后麻疹易感人群累积的数学模型进行研究。方法：选择2006-2012年九江市麻疹患者作为研究对象,对所有患者的流行病学特征进行分析,研究扩免后麻疹易感人群累积的数学模型。结果：2006-2012年麻疹的发病率表现为5月份达到最高值222例,之后为4月份的138例,这两个月的例数占总例数的42.40%。2006-2012年,20周的平均发病例数达到最大值为14例,2011年以及2102年由于总病例数很少,所以周分布情况不显著。2006-2012年,麻疹病症的发病人群大多以小于5岁为主要年龄段,发病例数达到424例,占所有患者例数的49.94%。在2009年之前,年龄较大的发病人群占比例较大,年龄在10~20岁组中,麻疹发病例数占总患者例数的22.63%。2006-2012年九江市报告麻疹病例常住人口中,麻疹病例逐年降低,到2012年只有1例。根据计算可得余弦数学模型,y1=0.140＋0.489cos（ti-69.22°）,含第二谐量的三角多项式y2=0.140＋0.489（ti-69.22°）＋0.125cos（2ti-208.7°）,并通过上述模型计算决定系数R21为0.947,R22为0.931。结论：对扩免后的麻疹易感人群累积的数学模型进行研究,用来指导实际工作,避免工作的盲目性。

Mathematical Model Study of after Free Expansion of Measles Susceptible Population Accumulation

Objective：To study mathematical model of after free expansion of measles susceptible population accumulation.Method：From 2006 to 2012 in Jiujiang City of measles patients were as research object, on the epidemiological characteristics of all patients were analyzed, and did the mathematical model after free expansion measles susceptible population accumulation.Result：The incidence rate of measles from 2006 to 2012 showed it reached the highest value of 222 cases, 138 cases after April,accounted for 42.40% in the total number of the number in this two month.From 2006 to 2012,the average incidence cases 20 weeks maximum number of 14 cases,in 2011 and 2102 due to the total number of cases a few weeks,so distribution was not significant.From 2006 to 2012,incidence of measles disease was mostly in less than 5 years as the main age,the number of incident cases to 424 cases,was accounted for 49.94% of all the number of patients.Before 2009,the age of onset of a larger population of large proportion,at the age of 10 years old to 20 years old group, the total number of patients of measles cases number was 22.63%.In 2006 to 2012 in Jiujiang reported measles cases in the resident population, measles cases decreased year by year,to 2012 had 1 cases only.According to the calculation of available cosine mathematical model,y1=0.140＋0.489cos（ti-69.22°）,trigonometric polynomial y2=0.140＋0.489（ti-69.22°）＋0.125cos（2ti-208.7°）,and through the model to calculate the coefficient of determination of R21 0.947,R22 0.931.Conclusion：The research on the mathematical model of the measles free after the expansion of the susceptible population accumulation, use to guide the practical work, to avoid the blindness of the work.