拜登在首场总统选举辩论中感染新冠的概率有多高?
作者:邵晓亮 李先庭 来源:微信公众号-暖通空调
作者:邵晓亮 北京科技大学;李先庭 清华大学
1 问题提出
当地时间10月2日,美国总统特朗普通过社交媒体证实自己和夫人梅拉尼娅新冠病毒检测结果呈阳性,并将立即开始隔离。而在9月29日,特朗普与竞争对手拜登举行了一次总统选举电视辩论(图1)。据消息称,该场辩论严格执行防疫标准,场内人员均佩戴口罩并保持社交距离,虽然辩论期间拜登和特朗普没有握手等近距离接触,但两位总统候选人和主持人全程未佩戴口罩,不免让人关注拜登和主持人感染新冠病毒的概率有多高?
图1 电视辩论现场
新冠病毒传播主要的传播方式为飞沫传播和密切接触,近期多项研究表明,新冠病毒可能通过空气(气溶胶)传播,尤其在通风不良的密闭空间中,通过空气传播的风险更高。由于飞沫传播属于近距离传播,而辩论台上候选人和主持人保持有一定距离,且辩论期间没有接触行为,因此,重点考虑通过空气传播新冠病毒的风险。采用经典的气溶胶传播感染概率模型Wells-Riley公式进行分析:
式中:I为感染者人数;q为一个感染者的quanta释放率(quanta/h);p为易感人员的呼吸通风量(m3/h);t为暴露时间(h);Q为通风量(m3/h)。
上述公式基于集总参数假设建立,但实际通风房间空气参数存在非均匀分布,不同气流组织下各位置病毒颗粒浓度被稀释的程度不同,采用稀释倍数(Dilution Ratio, DR)进行描述,即易感者位置处的quanta浓度与感染者呼吸中quanta浓度之比,该值可通过示踪气体分布的模拟获得。基于DR,并考虑感染者和易感者佩戴口罩的效果,式(1)变为:
采用CFD方法建立辩论现场的模型,见图2。假设采用全空气系统,每人新风量为36m3/h,总送风换气次数为6h-1。从现场布局未见在侧墙和空间内有送、回风口,因此假设为常见的顶部送风顶部回风气流分布形式。根据相关资料,现场为特朗普和拜登位置正上方临时安装了送风口(图3)定点送风,用于对两位候选人的通风保护。忽略空调箱中过滤器对病毒的去除效果。假设仅特朗普一人感染新冠病毒,辩论时间为1.5h,现场观众均佩戴口罩,假设口罩的过滤效率为75%。设定感染者呼吸量为0.3m3/h,根据前期研究,选取quanta释放率为14,27和40quanta/h三个水平进行概率分析。
图2 总统选举辩论现场建模
图3 辩论台送风口
3 模拟结果
以CO2作为示踪气体,对污染物分布进行模拟,进而计算概率公式中的关键参数DR,污染分布结果见图4~6。可见,由于场馆为高大空间,整体通风量大,且有新风直接供应,拜登处污染浓度很低;主持人位置的高度相对特朗普处较低,特朗普处上方的送风气流将其呼吸出的病毒颗粒向下向前输送,对主持人形成一定影响,但主持人处浓度仍然较低;观众席离辩论台较远,污染浓度很低。
图4 特朗普和拜登呼吸平面的污染物分布(Y=3.7 m)
图5 主持人呼吸平面的污染物分布(Y=2.6 m)
图6 观众席呼吸平面的污染物分布(Y=1.0 m)
对拜登位置、主持人位置以及观众席位置不同距离处的稀释倍数和感染概率进行计算,结果见图7~9。
图7 拜登和主持人感染概率
图8 观众感染概率(左排,不戴口罩)
图9 观众感染概率(左排,戴口罩)
总体而言,拜登、主持人、观众各位置感染概率均较低。主持人感染概率最高为0.11%~0.31%;拜登处由于有送风气流直接保护,感染概率低于主持人位置,为0.06%~0.16%,其感染概率与远处观众相当;观众距离辩论台较远,与特朗普不同距离处感染概率相差不大,如观众不佩戴口罩,则当释放率分别为14quanta/h,27quanta/h,40quanta/h时,距离特朗普6.8m~14.8m处感染概率分别为0.07%~0.06%,0.13%~0.12%,0.19%~0.18%。因此观众即使不戴口罩,感染概率也很低。实际上所有观众均佩戴口罩,在上述不同quanta取值下,感染概率处于0.02%~0.05%的范围,感染风险非常低。
4 结论
通过上述分析可以看出,虽然拜登和主持人离特朗普相对较近且全程未戴口罩,但由于保持了正常的社交距离,二人感染概率均较低;而观众席由于距离特朗普较远,且全程佩戴口罩,因此感染概率非常低。
上述分析也表明,在室内正常通风情况下,保持合理的社交距离、佩戴口罩对于降低感染概率非常重要。
Assessment of infection probability of Biden during the first US presidential debateXiaoliang Shao1 and Xianting Li21 University of Science and Technology Beijing2 Tsinghua University On October 2, U.S. President Trump confirmed that he and his wife had tested positive for the COVID-19. On September 29, a televised presidential election debate was held between Trump and Biden. The two presidential candidates and the host did not wear masks during the whole process, which caused people to pay attention to the probability of Biden and the host infected with the COVID-19.
Fig. 1 Geometric modelThere is a higher risk of COVID-19 transmission through air (aerosol transmission) in confined spaces. The transmission probability was assessed by using revised Wells-Riley equation considering the non-uniformity of air parameter and mask efficiency. The debate scene was established by CFD method (Fig. 1). Two air supply inlets were temporarily installed just above the positions of Trump and Biden to provide direct air supply. The debate time was 1.5h. The contaminant distributions are shown in Figs. 2 – 4. The infection probabilities are shown in Figs. 5 and 6.
Fig. 2 Contaminant distribution at the respiratory level of Trump and Biden (Y=3.7 m)
Fig. 3 Contaminant distribution at the respiratory level of the host (Y=2.6 m)
Fig. 4 Contaminant distribution at the respiratory level of the audience (Y=1.0 m)
Fig. 5 Infection probability of Biden and host
Fig. 6 Infection probability of audience (left row, wearing mask)
It is shown that the infection probability of Biden, host and audience is low. The infection probability of the host is the highest (0.11% – 0.31%). Due to the direct protection of air supply, the infection probability of Biden is lower than that of the host (0.06% – 0.16%). The audience are far away from the debate platform, and the infection probability at different distances from Trump is similar. In condition that the audience wore masks, the infection probability is in the range of 0.02% – 0.05%, and therefore the risk could be negligible.
来源时间:2020/10/3 发布时间:2020/10/3
旧文章ID:23122