文档介绍：
离散传染病模型下我国百日咳流行趋势的
预测
崔倩倩1,张强2*
5
10
(1. 石河子大学理学院, 石河子 832000;
2. 石河子大学理学院, 新疆石河子 832000)
摘要:通过建立一类离散 EIR 传染病模型来研究百日咳的传播,讨论了模型平衡点的存在
性,得到基本再生数即决定疾病灭绝与否的阈值的具体表达形式,其次研究了基本再生数对
模型参数的依赖性。最后,通过对 1990-2009 年百日咳数据分析,拟合模型的参数,并通过
数值模拟预测百日咳在我国的传播规律,拟合结果和实际数据吻合的很好,并说明降低接触
率将会有效地控制百日咳的传播.
关键词:应用数学,百日咳,离散传染病模型,基本再生数,稳定性
中图分类号:O175
15
A discrete epidemic model for Pertussis trends forecast in
China
CUI Qianqian, ZHANG Qiang
(College of science, Shihezi University, Shihezi 832000)
20
25
Abstract: A discrete EIR epidemic model was formulated to investigate the transmission of
pertussis and the existence of equilibrium for this model was studied. The expressions of the basic
reproductive number for this model to use as a threshold to determine the extinct of the model
have been gave. The dependence of the basic reproductive number on the parameters has been
discussed. Finally, the parameters of the model have been estimated on the basis of statistical data
from 1990 to 2009 and numerical simulations have been carried out to describe the transmission
process for pertussis in China. The simulation results data matches the statistical data well and
indicate that a lower contact are crucial to control of pertussis.
Key words: applied mathematics pertussis, discrete epidemic model, basic reproductive number,
stability
30
0 引言
百日咳(Pertussis)是一种通过呼吸道传播的细菌感染性疾病, 传染