非线性传染率虫媒病毒的传播模型研究
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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 Singapore 2016(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 been 70 more cases if interventions had started one day later, and 8000 more 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.
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 Singapore 2016(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 been 70 more cases if interventions had started one day later, and 8000 more 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.
引文
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[2]朴静子,王晓宏,陈唯军,等.6种虫媒病毒PCR-Mass检测方法的建立[J].沈阳农业大学学报,2012(3):300-305.
[3]张育富,周明浩,刘大鹏,等.江苏沿海地区2005—2013年虫媒传染病流行特征[J].中国公共卫生,2005(1):36-39.
[4]李晓龙,严延生,王环宇,等.Zika病毒:虫媒病毒传染病的新挑战[J].中国人兽共患病学报,2016(9):819-824.
[5]涂文校,马涛,李昱,等.2016年我国内地寨卡病毒的输入和传播风险评估[J].科学通报,2016,61(12):1344-1353.
[6]NAH K,MIZUMOTO K,MIYAMATSU Y,et al.Estimating risks of importation and local transmission of Zika virus infection[J].Peerj,2016(4):e1904.
[7]童珊珊,曾铄寓.登革热数学模型及疫情防控策略分析[J].长江大学学报(自科版),2015,12(31):1-5.
[8]FAUCI A,MORENS D.Zika virus in the Americas-yet another arbovirus threat[J].New England Journal of Medicine,2016,374(7):601-604.
[9]薛定宇,陈阳泉.控制数学问题的MATLAB求解[M].北京:清华大学出版社,2007:157-160.
[10]CHOWELL G,HENGARTNER N,CASTILLO-CHAVEZ C,et al.The basic reproductive number of Ebola and the effects of public health measures:the cases of Congo and Uganda[J].Journal of Theoretical Biology,2004,229(1):119-126.
[11]郑爱华,邹振,施一.寨卡(Zika virus)来袭:地方性流行病毒的全球化[J].科学通报,2016,61(22):2441-2448.
[12]WONG P,LI M,CHONG C,et al.Aedes(stegomyia)albopictus(skuse):A potential vector of zika virus in Singapore[J].Plos Neglected Tropical Diseases,2013,7(8):e2348.
[13]MEANEY-DLEMAN D,HILLS S,WILLIAMS C,et al.Zika virus infection among U.S.pregnant travelers-August 2015-February2016[J].Mmwr Morbidity&Mortality Weekly Report,2016,65(8):211-214.
[14]BOGOCH I,BRADY O,KRAEMER M,et al.Anticipating the international spread of zika virus from Brazil[J].Lancet,2016,387(10016):335-336.