传染病动力学模型在水痘疫情预测和防控措施效果评价中的应用
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摘要
传染病仍是全球特别是发展中国家的主要疾病负担。传染病动力学是对传染病进行理论性定量研究的一种重要方法。出于伦理学考虑,传染病传播研究不能采取人群实验的方式开展,研究疾病传播规律及干预措施效果评价,数学模型有其不可替代之处。水痘是由水痘-带状疱疹病毒(VZV)引起的急性呼吸道传染病。水痘传染性强,大部分人在儿童期已感染发病,在小学、幼儿园等集体机构易发生暴发疫情。水痘还不属法定报告传染病,目前仍然缺乏系统完整的疫情监测信息。本研究应用传染病动力学模型的理论和方法,开展水痘疫情预测,并对防控措施效应进行理论评价。
研究目的
1、疫情预测：通过对一起水痘暴发疫情的拟合,对疫情进展情况进行预测；考虑人口动态变化、季节性、带状疱疹发病等复杂因素,对水痘长期流行趋势进行探讨。
2、效果评价：在模型中增加防控因素,对应急接种和病人隔离措施在暴发疫情控制中的效果以及预防接种的长期影响进行理论评价。
3、模型表达：探索易于实施的动力学模型表达形式,方便公共卫生工作人员应用。
材料与方法
1、材料
暴发疫情资料来自2006年浙江省某小学一起水痘疫情的现场调查报告结果。2006年全国水痘疫情信息源于全国疾病报告管理系统的结果分析报道。人群水痘血清抗体水平综合了同期杭州、上海、广东等地的血清学监测报道结果。人口学资料来自于国家统计局公布的2005年全国1%人口抽样调查统计结果。
2、方法
1)在对连续SEIR模型作离散化处理的基础上,考虑水痘潜隐期和传染期的时滞效应建立时滞离散模型。拟合模型可得到理论发病数；加入不同控制措施拟合模型,比较相应的发病人数,评价控制措施效果。利用EXCEL2003软件实现模型表达。
2)应用年龄结构模型开展水痘长期流行趋势预测及预防接种影响评价
在SEIR模型基础上,增加先天免疫者群、带状疱疹感染者群,并将人群分为7个年龄组,设定不同年龄组的传染力调整系数。模型同时考虑人口出生、成长和自然死亡现象等因素,开展水痘长期流行趋势预测；模拟不同预防接种方案长期应用结果,探讨预防接种的效果及其它影响。应用STELLA9软件开展数值模拟。
结果
1、水痘暴发疫情预测及控制措施效果评价
应用时滞离散SEIR模型模拟一小学发生的水痘暴发疫情。该校共有1671名学生,估计期初易感者群为514人。不采取任何控制措施时,绝大部分易感者将染病,理论发病数为504人,罹患率为30.76%。流行过程历时4个月,发病高峰在首例发生后78天,流行过程中可见明显的“代际”现象,代与代之间间隔2周左右。
早期严格隔离病人可使疫情得到有效控制,但由于水痘病人在潜伏期末即有传染性,单纯针对发病者采取措施并不能完全阻断传播。早期高覆盖率的应急接种效果优于同等条件下的严格隔离措施,为有效控制疫情,建议应急接种接种率达90%以上。
2、水痘长期流行趋势预测及预防接种影响评价
长期(80年)模拟结果显示,前五年水痘发病率有较大波动,之后稳定维持在8.3‰左右。带状疱疹年发病率一直稳定,为2.2%o左右。分年龄组看,4岁～组发病率远高于其他各组,模拟末期年发病率达65%o。
模拟对新进入1岁～组的儿童持续接种时,可见随着时间推移预防效果逐渐显现,10年后趋于稳定。预防效果与接种率正相关,接种率为10%、30%、50%、70%和90%时,可使水痘年发病率相应降低11%、34%、57%、78%和92%。相同的接种率,针对低龄儿童接种能取得更大的收益。当接种率为90%时,接种7岁～组、4岁～组与1岁～组可使水痘年发病率分别降低82%、90%和92%。
接种率的提高,可引起疫苗突破病例比例相应增加。预防接种还可引起水痘平均染病年龄增大,不过同时可见大年龄组人群水痘发病数相应减少。
敏感性分析显示,带状疱疹患者传染性存在与否对水痘的流行规律影响很大。不考虑带状疱疹患者传染性时,水痘发病呈现周期性现象,流行高峰间隔6-8年出现；考虑了带状疱疹患者传染性,各年间流行强度稳定。带状疱疹患者传染性存在与否对水痘疫苗的接种效果影响更大。不考虑带状疱疹患者传染性时,按90%的接种率对1岁～组儿童持续接种,3年后即无新病例发生(模型不考虑外来传染源流入)；而将带状疱疹患者作为传染源时,维持同样高的接种率,水痘将仍以较低的水平(年发病率约为0.7/‰)持续存在。
结论
应用时滞离散SEIR模型模拟水痘暴发疫情,以模型得到的理论发病数,可作为现场控制措施效果评价的参照。早期实施严格的病人隔离措施和高覆盖率的应急接种效果均恳定,但在相同条件下,应急接种效果更好。应用年龄结构模型预测水痘长期流行趋势,发现水痘发病缺乏周期性现象,各年间水痘发病率维持在8.3‰左右。水痘疫苗主要体现了对受种者个体的保护作用,未发现明显的群体保护效应。由于VZV能在人体内长期潜伏并能重新激活导致传播,短期内不大可能通过水痘疫苗的广泛接种消除水痘。
本研究的理论和实际意义有：通过对模拟得到理论发病数与现场发病数的比较,为暴发疫情现场控制措施效果评价提供一种思路；对各种模拟的应急控制措施效果的定量比较,为选择有效的现场控制措施提供参照；在当前缺乏系统完整的疫情信息条件下,综合分析模拟的结果,实现水痘流行趋势的预测、影响疫情重要因素的识别和水痘疫苗公共卫生价值的评判,可为今后水痘-带状疱疹感染的流行病学现场研究提供参考。
Infectious diseases are still regarded as the main burdens around the world, especially in developing countries. Epidemic dynamics is an important quantitative analysis method to study on infectious diseases. In consideration of ethics, study on transmission of the infectious diseases can't conduct in population experiment way. So, mathematical modeling plays an irreplaceable role to study the characteristic of spreading and effect evaluation of intervention measures.
Varicella is an acute and highly contagious respiratory disease caused by varicella-zoster virus (VZV). Most people have been infected VZV in childhood, and it frequently leads to outbreak in primary school or kindergarten. Varicella is not notifiable disease and still lacks of systematic and complete epidemic data in China. In the present work, we apply epidemic dynamics modeling theory and method to forecast the epidemic trend and to evaluate the effect of intervention measures.
Objectives
1. Epidemic trend forecasting:by fitting an outbreak event, to predict the future course of the epidemic; and considering more complicated factors such as population change, seasonal characteristics and herpes zoster prevalence, to discuss the long term epidemic trend.
2. Effect of intervention measures evaluating:by adding the intervention measures in the model, to evaluate the hypothetical effects of cases isolation, emergent vaccination in outbreak and the long term impact of immunization program.
3. Model expressing:to explore how to implement the model easily by public health workers.
Materials and Methods
1. Materials
The varicella outbreak data from a field research report which took place in a primary school in Zhejiang province in 2006. The national-wide varicella epidemic data from an analysis report that derived from National Diseases Reporting System. The population levels of VZV antibody resulted from combining the serum test reports in Hangzhou, Shanghai and Guangzhou in the same period. And, the demographic data based on 1% national population sampling survey in 2005 which public informed by National Bureau of Statistics of China.
2. Methods
1) A discrete time delay SEIR model for varicella outbreak prevalence forecasting and control measures effect evaluating
The model was discretized on a SEIR continuous model. The time delay effect of latent period and infectious period was took into account as well. The number of expected cases could be obtained by fitting the model; and the control measures effect could be evaluated by comparing the different number of cases in a given scenario. The model was carried out in EXCEL2003.
2) An age-structured model for long term varicella trend forecasting and immunization impact evaluating
Adding maternal immunity class and herpes zoster infected class in the SEIR model, and dividing the whole population into 7 age groups that with different force of infect coefficient to forecast the long term varicella trend. In addition, the model included influence factors such as birth, aging and naturally death in the population. The vaccine effect and other impacts were discussed by comparing the long term results of different immunization program. The numeric simulation was executed by STELLA9.
Results
1. Varicella outbreak prevalence forecasting and control measures effect evaluating A discrete time delay SEIR model was used to fit a varicella outbreak which took place in a primary school. The total number of students was 1671, and the estimated number of the susceptible was 514 in the initial stage of the outbreak. In the scenario that without any control measures, most of the susceptible will be infected, and the number of expected cases is 504 with an attack rate of 30.76%. The course of the epidemic lasts for 4 months and the peak epidemic time is 78 days after the onset of index case. 'Generation'phenomenon has been observed in the course of the epidemic with the interval of two weeks. With the perfect cases isolation in the early stage of an outbreak, epidemic spreading can be disrupted effectively. However, as with the communicability in the late stage of incubation period, VZV spreading can't be blocked utterly under the intervention only focussing on the patients. The effect of emergent vaccination with high coverage rate in the early stage is better than the perfect cases isolation under the same conditions. For reasons of controlling the outbreak effectively, it's suggested that the coverage rate should reach to 90%.
2. Long term varicella epidemic trend forecasting and immunization impact evaluating The long term (80 years) simulation results indicate that varicella incidence is fluctuated dramatically in the first 5 years, and then keep steadily in the later course with the incidence rate around 8.3%o per year. Herpes zoster incidence keeps steadily all the time with the incidence rate around 2.2%o per year. By comparison, the incidence of 4-age group is much higher than others'with the incidence rate up to 65%o per year in the late of simulation period. With the routine immunization program only inoculating the one year old children, the vaccine effect will emerge gradually and keep stable 10 years later. The effect has the positive relationship with the coverage rate. When the coverage rate is 10%,30%,50%, 70% or 90%, the yearly varicella incidence rate is dropped 11%,34%,57%,78% and 92%, respectively. Under the same coverage rate, inoculating younger children will gain more benefits. When the coverage rate is 90%, inoculating 7-,4-, or 1-year old age group, the yearly varicella incidence rate is dropped 82%,90%, and 92%, respectively. With the higher coverage rate of vaccine, the proportion of breakthrough cases will increase correspondingly. Immunization program will increase the average age of varicella infection, nevertheless, the varicella cases in elder groups are reduced as well. Sensitivity analysis indicates that whether the herpes zoster cases have the ability to spread the virus will have great influence on varicella epidemic trend. Ignoring the communicability of herpes zoster cases, the varicella epidemic turns out to have cyclicity phenomenon, and the interval of epidemic peaks is about 6-8 years. While taking into account its communicability, the varicella epidemic intensity will keep stable in whole course. Furthermore, the communicability of herpes zoster cases has greater influence on the vaccine effect. Ignoring its communicability, and inoculating the one year old children with the coverage rate of 90%, the varicella will die out after three years (the model ignoring the immigration of infection source). While taking into account its communicability, the varicella will exist persistently with the lower level incidence (the incident rate was around 0.7%o per year) under the same coverage rate.
Conclusion
A discrete time delay SEIR model was used to fit a varicella outbreak event. The number of expected cases can be regarded as the reference to evaluate the control measures effect. Both the effects of perfect cases isolation and emergent vaccination with high coverage rate in the initial stage of an outbreak are soundly. An age-structured model was used to forecast long term varicella trend. The results indicate that varicella epidemic doesn't have the cyclical phenomenon, and the incidence rate is around 8.3%o per year. It is suggested that the vaccine lacks of herd protection or it can only protect the individual who has been inoculated. Because VZV can establish in a latent form in the dorsal root ganglia after primary infection and will be reactivated after dozens years, varicella is unlikely to be eliminated by mass vaccination in short term.
The theoretical and practical meanings of present work may list as follows:It provides one way to evaluate the effect of control measures in an outbreak event by comparing the number of expected cases with the number of actual cases. It's available to give advice to choose the effective field control measures by quantitatively comparing the effect of theoretical emergency measures. Even the lack of systemic and complete epidemic data nowadays, by comprehensive analyzing the simulation results, it's feasible to implement the long term varicella epidemic trend forecasting, the influence factors identifying and the public health utility of varicella vaccine judging. Besides, the conclusion of this work may offer helpful reference for further field research on VZV infection.
研究目的
1、疫情预测：通过对一起水痘暴发疫情的拟合,对疫情进展情况进行预测；考虑人口动态变化、季节性、带状疱疹发病等复杂因素,对水痘长期流行趋势进行探讨。
2、效果评价：在模型中增加防控因素,对应急接种和病人隔离措施在暴发疫情控制中的效果以及预防接种的长期影响进行理论评价。
3、模型表达：探索易于实施的动力学模型表达形式,方便公共卫生工作人员应用。
材料与方法
1、材料
暴发疫情资料来自2006年浙江省某小学一起水痘疫情的现场调查报告结果。2006年全国水痘疫情信息源于全国疾病报告管理系统的结果分析报道。人群水痘血清抗体水平综合了同期杭州、上海、广东等地的血清学监测报道结果。人口学资料来自于国家统计局公布的2005年全国1%人口抽样调查统计结果。
2、方法
1)在对连续SEIR模型作离散化处理的基础上,考虑水痘潜隐期和传染期的时滞效应建立时滞离散模型。拟合模型可得到理论发病数；加入不同控制措施拟合模型,比较相应的发病人数,评价控制措施效果。利用EXCEL2003软件实现模型表达。
2)应用年龄结构模型开展水痘长期流行趋势预测及预防接种影响评价
在SEIR模型基础上,增加先天免疫者群、带状疱疹感染者群,并将人群分为7个年龄组,设定不同年龄组的传染力调整系数。模型同时考虑人口出生、成长和自然死亡现象等因素,开展水痘长期流行趋势预测；模拟不同预防接种方案长期应用结果,探讨预防接种的效果及其它影响。应用STELLA9软件开展数值模拟。
结果
1、水痘暴发疫情预测及控制措施效果评价
应用时滞离散SEIR模型模拟一小学发生的水痘暴发疫情。该校共有1671名学生,估计期初易感者群为514人。不采取任何控制措施时,绝大部分易感者将染病,理论发病数为504人,罹患率为30.76%。流行过程历时4个月,发病高峰在首例发生后78天,流行过程中可见明显的“代际”现象,代与代之间间隔2周左右。
早期严格隔离病人可使疫情得到有效控制,但由于水痘病人在潜伏期末即有传染性,单纯针对发病者采取措施并不能完全阻断传播。早期高覆盖率的应急接种效果优于同等条件下的严格隔离措施,为有效控制疫情,建议应急接种接种率达90%以上。
2、水痘长期流行趋势预测及预防接种影响评价
长期(80年)模拟结果显示,前五年水痘发病率有较大波动,之后稳定维持在8.3‰左右。带状疱疹年发病率一直稳定,为2.2%o左右。分年龄组看,4岁～组发病率远高于其他各组,模拟末期年发病率达65%o。
模拟对新进入1岁～组的儿童持续接种时,可见随着时间推移预防效果逐渐显现,10年后趋于稳定。预防效果与接种率正相关,接种率为10%、30%、50%、70%和90%时,可使水痘年发病率相应降低11%、34%、57%、78%和92%。相同的接种率,针对低龄儿童接种能取得更大的收益。当接种率为90%时,接种7岁～组、4岁～组与1岁～组可使水痘年发病率分别降低82%、90%和92%。
接种率的提高,可引起疫苗突破病例比例相应增加。预防接种还可引起水痘平均染病年龄增大,不过同时可见大年龄组人群水痘发病数相应减少。
敏感性分析显示,带状疱疹患者传染性存在与否对水痘的流行规律影响很大。不考虑带状疱疹患者传染性时,水痘发病呈现周期性现象,流行高峰间隔6-8年出现；考虑了带状疱疹患者传染性,各年间流行强度稳定。带状疱疹患者传染性存在与否对水痘疫苗的接种效果影响更大。不考虑带状疱疹患者传染性时,按90%的接种率对1岁～组儿童持续接种,3年后即无新病例发生(模型不考虑外来传染源流入)；而将带状疱疹患者作为传染源时,维持同样高的接种率,水痘将仍以较低的水平(年发病率约为0.7/‰)持续存在。
结论
应用时滞离散SEIR模型模拟水痘暴发疫情,以模型得到的理论发病数,可作为现场控制措施效果评价的参照。早期实施严格的病人隔离措施和高覆盖率的应急接种效果均恳定,但在相同条件下,应急接种效果更好。应用年龄结构模型预测水痘长期流行趋势,发现水痘发病缺乏周期性现象,各年间水痘发病率维持在8.3‰左右。水痘疫苗主要体现了对受种者个体的保护作用,未发现明显的群体保护效应。由于VZV能在人体内长期潜伏并能重新激活导致传播,短期内不大可能通过水痘疫苗的广泛接种消除水痘。
本研究的理论和实际意义有：通过对模拟得到理论发病数与现场发病数的比较,为暴发疫情现场控制措施效果评价提供一种思路；对各种模拟的应急控制措施效果的定量比较,为选择有效的现场控制措施提供参照；在当前缺乏系统完整的疫情信息条件下,综合分析模拟的结果,实现水痘流行趋势的预测、影响疫情重要因素的识别和水痘疫苗公共卫生价值的评判,可为今后水痘-带状疱疹感染的流行病学现场研究提供参考。
Infectious diseases are still regarded as the main burdens around the world, especially in developing countries. Epidemic dynamics is an important quantitative analysis method to study on infectious diseases. In consideration of ethics, study on transmission of the infectious diseases can't conduct in population experiment way. So, mathematical modeling plays an irreplaceable role to study the characteristic of spreading and effect evaluation of intervention measures.
Varicella is an acute and highly contagious respiratory disease caused by varicella-zoster virus (VZV). Most people have been infected VZV in childhood, and it frequently leads to outbreak in primary school or kindergarten. Varicella is not notifiable disease and still lacks of systematic and complete epidemic data in China. In the present work, we apply epidemic dynamics modeling theory and method to forecast the epidemic trend and to evaluate the effect of intervention measures.
Objectives
1. Epidemic trend forecasting:by fitting an outbreak event, to predict the future course of the epidemic; and considering more complicated factors such as population change, seasonal characteristics and herpes zoster prevalence, to discuss the long term epidemic trend.
2. Effect of intervention measures evaluating:by adding the intervention measures in the model, to evaluate the hypothetical effects of cases isolation, emergent vaccination in outbreak and the long term impact of immunization program.
3. Model expressing:to explore how to implement the model easily by public health workers.
Materials and Methods
1. Materials
The varicella outbreak data from a field research report which took place in a primary school in Zhejiang province in 2006. The national-wide varicella epidemic data from an analysis report that derived from National Diseases Reporting System. The population levels of VZV antibody resulted from combining the serum test reports in Hangzhou, Shanghai and Guangzhou in the same period. And, the demographic data based on 1% national population sampling survey in 2005 which public informed by National Bureau of Statistics of China.
2. Methods
1) A discrete time delay SEIR model for varicella outbreak prevalence forecasting and control measures effect evaluating
The model was discretized on a SEIR continuous model. The time delay effect of latent period and infectious period was took into account as well. The number of expected cases could be obtained by fitting the model; and the control measures effect could be evaluated by comparing the different number of cases in a given scenario. The model was carried out in EXCEL2003.
2) An age-structured model for long term varicella trend forecasting and immunization impact evaluating
Adding maternal immunity class and herpes zoster infected class in the SEIR model, and dividing the whole population into 7 age groups that with different force of infect coefficient to forecast the long term varicella trend. In addition, the model included influence factors such as birth, aging and naturally death in the population. The vaccine effect and other impacts were discussed by comparing the long term results of different immunization program. The numeric simulation was executed by STELLA9.
Results
1. Varicella outbreak prevalence forecasting and control measures effect evaluating A discrete time delay SEIR model was used to fit a varicella outbreak which took place in a primary school. The total number of students was 1671, and the estimated number of the susceptible was 514 in the initial stage of the outbreak. In the scenario that without any control measures, most of the susceptible will be infected, and the number of expected cases is 504 with an attack rate of 30.76%. The course of the epidemic lasts for 4 months and the peak epidemic time is 78 days after the onset of index case. 'Generation'phenomenon has been observed in the course of the epidemic with the interval of two weeks. With the perfect cases isolation in the early stage of an outbreak, epidemic spreading can be disrupted effectively. However, as with the communicability in the late stage of incubation period, VZV spreading can't be blocked utterly under the intervention only focussing on the patients. The effect of emergent vaccination with high coverage rate in the early stage is better than the perfect cases isolation under the same conditions. For reasons of controlling the outbreak effectively, it's suggested that the coverage rate should reach to 90%.
2. Long term varicella epidemic trend forecasting and immunization impact evaluating The long term (80 years) simulation results indicate that varicella incidence is fluctuated dramatically in the first 5 years, and then keep steadily in the later course with the incidence rate around 8.3%o per year. Herpes zoster incidence keeps steadily all the time with the incidence rate around 2.2%o per year. By comparison, the incidence of 4-age group is much higher than others'with the incidence rate up to 65%o per year in the late of simulation period. With the routine immunization program only inoculating the one year old children, the vaccine effect will emerge gradually and keep stable 10 years later. The effect has the positive relationship with the coverage rate. When the coverage rate is 10%,30%,50%, 70% or 90%, the yearly varicella incidence rate is dropped 11%,34%,57%,78% and 92%, respectively. Under the same coverage rate, inoculating younger children will gain more benefits. When the coverage rate is 90%, inoculating 7-,4-, or 1-year old age group, the yearly varicella incidence rate is dropped 82%,90%, and 92%, respectively. With the higher coverage rate of vaccine, the proportion of breakthrough cases will increase correspondingly. Immunization program will increase the average age of varicella infection, nevertheless, the varicella cases in elder groups are reduced as well. Sensitivity analysis indicates that whether the herpes zoster cases have the ability to spread the virus will have great influence on varicella epidemic trend. Ignoring the communicability of herpes zoster cases, the varicella epidemic turns out to have cyclicity phenomenon, and the interval of epidemic peaks is about 6-8 years. While taking into account its communicability, the varicella epidemic intensity will keep stable in whole course. Furthermore, the communicability of herpes zoster cases has greater influence on the vaccine effect. Ignoring its communicability, and inoculating the one year old children with the coverage rate of 90%, the varicella will die out after three years (the model ignoring the immigration of infection source). While taking into account its communicability, the varicella will exist persistently with the lower level incidence (the incident rate was around 0.7%o per year) under the same coverage rate.
Conclusion
A discrete time delay SEIR model was used to fit a varicella outbreak event. The number of expected cases can be regarded as the reference to evaluate the control measures effect. Both the effects of perfect cases isolation and emergent vaccination with high coverage rate in the initial stage of an outbreak are soundly. An age-structured model was used to forecast long term varicella trend. The results indicate that varicella epidemic doesn't have the cyclical phenomenon, and the incidence rate is around 8.3%o per year. It is suggested that the vaccine lacks of herd protection or it can only protect the individual who has been inoculated. Because VZV can establish in a latent form in the dorsal root ganglia after primary infection and will be reactivated after dozens years, varicella is unlikely to be eliminated by mass vaccination in short term.
The theoretical and practical meanings of present work may list as follows:It provides one way to evaluate the effect of control measures in an outbreak event by comparing the number of expected cases with the number of actual cases. It's available to give advice to choose the effective field control measures by quantitatively comparing the effect of theoretical emergency measures. Even the lack of systemic and complete epidemic data nowadays, by comprehensive analyzing the simulation results, it's feasible to implement the long term varicella epidemic trend forecasting, the influence factors identifying and the public health utility of varicella vaccine judging. Besides, the conclusion of this work may offer helpful reference for further field research on VZV infection.
引文
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