非线性传染率虫媒病毒的传播模型研究  

An Epidemic Model of Arbovirus with Nonlinear Infection Rate

作　　者：陶桂洪[1] 宋贽[1] 惠淑荣[1] 张阚[1] TA0 Gui-hong;SONG Zhi;HUI Shu-rong;ZHANG Kan(College of Science, Shenyang Agricultural University, Shenyang 110161, China)

机构地区：[1]沈阳农业大学理学院,沈阳110161

出　　处：《沈阳农业大学学报》2017年第5期636-640,共5页Journal of Shenyang Agricultural University

基　　金：辽宁省自然基金面上项目(201602660);辽宁省教育厅科学研究项目(LSNYB201609)

摘　　要：虫媒病毒是指通过吸血的节肢动物叮咬敏感的脊椎动物而传播疾病的病毒。寨卡病毒(Zika virus)是一种新发的虫媒病毒,伊蚊是其主要的传播媒介。为研究虫媒病毒的流行规律和发展趋势,建立了虫媒病毒传播模型。为更符合实际情况,模型中的传染率系数选用随时间变化的非线性函数,并利用差分方程模拟病毒的传播规律,采用非线性拟合、最小二乘法等数学方法求出最优参数值。结合新加坡卫生部(MOH)发布的2016年8月28日到9月26日的寨卡病毒累计病例数据为例,说明模型应用,并利用Matlab软件进行数值模拟,给出仿真图。对模型中的可控参数做敏感度分析,发现最大累计病例数对防控措施开始时间呈指数增长规律,得到指数方程为y=aebx,其中a=348.8[95%CI(340.1,357.6)],b=0.2286[95%CI(0.2266,0.2306)]。模型预测如果延迟1d采取防控措施,最大累计病例数会增加70多人,如果延迟14d采取防控措施,最大累计病例数会增加8000多人,说明及时有效的采取防控措施是至关重要的,并针对疫情后期阶段的防控措施给出分析建议。Arbovirus spreads diseases by blood sucking arthropod animal bites vertebrates.Zika virus is a new member of arbovirus,which is carried by aedes mosquito.For the study of transmission rule and trends of arbovirus,the epidemic model of arbovirus was established.The course of the arbovirus outbreaks was modeled via a difference equation that included a smooth transition in the transmission rate after control interventions.By using mathematical methods of nonlinear regression and least squares,the model parameters were fitted to the arbovirus outbreak data to get the best fit parameters.A real data example from Singapore2016(Aug.28-Sep.26;MOH)was used to demonstrate its implementation,and the Matlab software was adopted to numerically simulate for simulation charts.The sensitivity of the final epidemic size to the initial time of interventions was analyzed,and the numerical solutions showed that the final epidemic size growed exponentially fast with the initial time of interventions,which function was y=aebx,with a=348.8[95%CI(340.1,357.6)],b=0.2286[95%CI(0.2266,0.2306)].Moreover,the simulation results revealed that there would have been70more cases if interventions had started one day later,and8000more cases if interventions had started fourteen days later.This conclusion shows that the implementation of control measures timely is crucial.Suggestions on the prevention and control measures in the later stage of the epidemic situation have been given.

关 键 词：虫媒病毒 传播模型 防控措施 差分方程 参数估计 

分 类 号：S476[农业科学—农业昆虫与害虫防治] O175[农业科学—植物保护]