宁夏彭阳县包虫病传播动力学建模及分析  

Modeling and Analysis of the Transmission Dynamics of Echinococcosis in Pengyang County,Ningxia

作　　者：崔倩倩 CUI Qianqian(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China)

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021

出　　处：《应用数学》2023年第2期277-289,共13页Mathematica Applicata

基　　金：国家自然科学基金(12001305);宁夏高等学校自然科学项目(NGY2020005);宁夏自然科学基金项目(2020AAC03060)。

摘　　要：包虫病是严重影响人类身体健康和社会经济发展的人畜共患病.彭阳县是宁夏回族自治区包虫病比较严重的地区,基于彭阳县囊型包虫病的传播机理,本文建立了包虫病在人,羊,犬及环境中传播的数学模型,预测彭阳县包虫病流行趋势并评估防控措施对疾病传播的影响.理论结果表明包虫病的流行与否取决于基本再生数R0.当R0<1时,无病平衡点全局渐近稳定即包虫病趋向灭绝;而当R0>1时,地方病平衡点全局渐近稳定即包虫病持久存在.依据彭阳县2011-2018年包虫病的监测指标及宁夏统计年鉴,得到彭阳县包虫病的基本再生数R0=0.63<1,说明彭阳县最终将消灭包虫病.最后,通过数值模拟及基本再生数的敏感性和不确定性分析,得到犬驱虫较羊免疫更能影响包虫病的传播,另外羊屠宰情况也是影响疾病传播的关键因素,这为彭阳县相关部门制定包虫病防控策略提供一定的理论依据.Echinococcosis is a zoonotic disease that seriously affects human health and social and economic development.Pengyang County is one of the areas where echinococcosis is more severe in Ningxia Hui Autonomous Region.To predict the epidemic trend and evaluate the influence of control strategies of echinococcosis in Pengyang,a mathematical mode based on the echinococcosis transmission among human,sheep,dogs and environment was established.The theoretical results show that the transmission of echinococcosis depends on the basic reproduction number R0.When R0<1,the diseasefree equilibrium is global asymptotically stable which means that the disease dies out.When R0>1,the endemic equilibrium is global asymptotically stable which means that the disease persists.According to the surveillance indicators of echinococcosis in Pengyang from 2011 to 2018 and Ningxia Statistical Yearbook,the basic reproduction number of Pengyang is R0=0:63<1.That is to say,the echinococcosis in Pengyang will die out in the further.Finally,numerical simulation was performed and the sensitivity and uncertainty of basic regeneration number were analyzed.The results showed that dog deworming is more affected the transmission of echinococcosis than sheep immunization.Furthermore,sheep slaughter is a key factor in echinococcosis transmission.

关 键 词：传染病动力学模型 包虫病 全局渐近稳定性 控制策略 

分 类 号：O175[理学—数学]