大流行期间的大班人数是三重打击

大流行期间的大班人数是三重打击
数学模型可以帮助确定班级规模和配置,以最大程度地减少中断和停课。
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随着大流行和我们对COVID-19的科学知识的继续快速发展,今年秋天在北美制定学校和托儿中心的重新开放计划是一项艰巨的任务。

For students attending in person, there are many questions to consider: How important is the cleaning and disinfecting of surfaces?对于亲自参加的学生,有许多问题需要考虑:表面的清洁和消毒有多重要? Which age of students should use masks, and when?哪个年龄段的学生应该使用口罩?何时使用? What is the best approach to cohorting?最佳的同类群组方法是什么? How large should class sizes be?班级人数应多大?

Knowledge of how COVID-19 spreads has improved since the pandemic started, but as reopening plans were being developed, we recognized a need to investigate outbreak scenarios in schools and childcare centres.自大流行开始以来,对COVID-XNUMX传播方式的了解有所增加,但是随着重新开放计划的制定,我们认识到有必要调查学校和托儿中心的暴发情况。 With our combined background in mathematical modelling, epidemiology, environmental sciences and childhood education, we tackled the question of class sizes.凭借我们在数学建模,流行病学,环境科学和儿童教育方面的综合背景,我们解决了班级规模的问题。

We developed a mathematical model of outbreaks in homes and classrooms.我们开发了家庭和教室中爆发的数学模型。 The model made a very surprising prediction: as class sizes go up, the negative impacts of COVID-19 go up exponentially faster.该模型做出了非常令人惊讶的预测:随着班级人数的增加,COVID-XNUMX的负面影响呈指数级增长。

精细的方法

我们选择了 “基于个人”的模型 where distinct individuals (adults and children) are allowed to interact according to specified rules.允许不同的个人(成人和儿童)根据指定的规则进行互动。 This highly granular approach allows us to see the effects of social groupings and individual characteristics on personal outcomes like missed school days.这种高度精细的方法使我们能够看到社交团体和个人特征对个人成绩(如放学日)的影响。

使用从中获得的年龄和家庭人数信息 加拿大人口普查数据,我们通过儿童教育中心和由一个或多个成人和一个或多个儿童组成的相关家庭来构建人口稀少的社区。 Our model is essentially a simulated virtual world of schools and homes.我们的模型实质上是学校和房屋的模拟虚拟世界。

“ A”代表父母,“ T”代表老师,圆圈是孩子,数字代表孩子的课堂作业。“ A”代表父母,“ T”代表老师,圆圈是孩子,数字代表孩子的课堂作业。 (克里斯·鲍赫), 作者提供


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Children were allocated to classrooms randomly or by grouping siblings together.孩子们被随机分配到教室或通过将兄弟姐妹分组在一起。 We considered childcare centre scenarios with student/educator ratios of 7:3, 8:2 and 15:2.我们考虑了育儿中心方案,学生/教育者比例为8:1、15:1和30:1。 We also considered primary school scenarios with student/educator ratios of XNUMX:XNUMX, XNUMX:XNUMX and XNUMX:XNUMX.我们还考虑了小学情景下的学生/教育者比例为XNUMX:XNUMX、XNUMX:XNUMX和XNUMX:XNUMX。 Students could attend class every day or alternate between in-person instruction one week and online learning the next week.学生可以每天上课,也可以在一周的亲自授课和下一周的在线学习之间进行交替。

影响因素

Then we ran our computer simulation of COVID-19 outbreaks in this setting.然后,我们在这种情况下运行了计算机模拟的COVID-19暴发。 We assumed that when a symptomatic case of COVID-14 appears in a classroom that it would then be closed for XNUMX days.我们假设当有症状的COVID-XNUMX病例出现在教室中时,它将被关闭XNUMX天。

但是,模拟班级人数对疫情的影响是棘手的。

在第一波的大部分时间里学校都关闭了 and so — perhaps unsurprisingly — school-aged children did not account for a significant portion of cases during this period.因此,也许在意料之中的是,在此期间,学龄儿童并未占很大比例。 In addition, children are more likely to be asymptomatic and therefore not reported as having COVID-19.此外,儿童更可能没有症状,因此没有被报告患有COVID-XNUMX。 A host of other factors could influence both the risk and size of outbreaks.其他许多因素也可能影响爆发的风险和规模。

So how can we predict what outbreaks in schools might look like, given that schools have not been open in Ontario since March 2020?既然自XNUMX年XNUMX月以来安大略省的学校都没有开放,那么我们如何预测学校的爆发情况呢? Since we don't know all of the right input values to use, we took an approach of “由于我们不知道要使用的所有正确输入值,因此我们采用了“不确定性分析”,这是科学探究的基石-承认您并不了解一切。

This approach meant that we would change the model inputs and study how those affect the predictions.这种方法意味着我们将更改模型输入,并研究它们如何影响预测。 For example, we distinguished between a “high transmission” assumption, where the virus can spread quickly, and a “low transmission” assumption, where the virus spread is being slowed by the use of masks, disinfection and physical distancing.例如,我们将病毒可以快速传播的“高传播”假设与通过使用口罩,消毒和物理隔离来减慢病毒传播的“低传播”假设区分开。

三重打击

Across all of the permutations used in our uncertainty analysis, we were surprised to find that when class size doubled, the number of cases and student-days lost to closure more than doubled.在不确定性分析中使用的所有排列中,我们惊讶地发现,当班级人数增加一倍时,因关闭而损失的案例数和学生日数增加了一倍以上。 Student-days are calculated by multiplying the number of closure days by the number of students affected, and with each class size doubling, they went up by factors of two to five.学生天数的计算方法是将停课天数乘以受影响的学生数,每增加一班班级,他们的学习天数就会增加XNUMX到XNUMX倍。

对于低传输模型情况,班级规模对COVID-19案例的影响(顶部)和学生损失的教学日(底部)。对于低传输模型情况,班级规模对COVID-19案例的影响(顶部)和学生损失的教学日(底部)。 (克里斯·鲍赫), 作者提供

当我们提高传输速率时,它改变了案例总数,但是在各种班级规模的情况下,因关闭而丢失的案例或学生天数的相对数量并没有太大变化:大班总是比小班相对差,并且大约是二到五倍。

我们将其描述为“三重打击”。 First, when class sizes are larger, the chances are higher that one of the children will test positive.首先,当班级人数较多时,其中一个孩子测试阳性的机会就更大。 Second, when that child does test positive and the class is closed, closure of a larger class affects more children.第二,当那个孩子的测试结果为肯定并且班级关闭时,关闭更大班级会影响更多的孩子。 Third, by the time the case is identified, the student might have been transmitting the virus for several days, or someone else in the class may have been asymptomatic and transmitting for many days.第三,在确定病例之前,该学生可能已经传播了几天病毒,或者班上其他人可能没有症状并且已经传播了很多天。 This third point is crucial — it is increasingly clear that SARS-CoV-2 can be spread by aerosol particles.第三点至关重要-越来越明显的是,SARS-CoV-XNUMX可以被气溶胶颗粒扩散。

其他后果

The worst scenario, by a wide margin, was the 30:1 ratio in the primary school setting.很大程度上,最糟糕的情况是小学背景下的15:1比例。 Switching to a 15:1 ratio with alternating weekly cohorts (XNUMX:XNUMXA) reduced the number of cases and student-days lost to closure by a factor of around four.交替使用每周队列(XNUMX:XNUMXA)的比率为XNUMX:XNUMX,减少的案例数量和因关闭而损失的学生日数减少了大约四倍。 And even though higher student/educator ratios allow more students to get in-person instruction, they also cause more disruptions due to more frequent need to close classrooms when a case is identified.即使更高的学生/教育者比例可以让更多的学生接受面对面的指导,但由于发现病例后需要更频繁地关闭教室,因此也会造成更多的干扰。

In addition, there are likely to be significant psychological, social and mental health consequences for parents and children when schools and childcare centres close.此外,学校和托儿所关闭时,对父母和孩子的心理,社会和心理健康可能会产生重大后果。 And since outbreaks can happen at any time, working parents may need to be pulled from their work with little or no advance notice.而且由于暴发随时可能发生,因此有工作的父母可能需要在很少或没有事先通知的情况下就被迫退出工作。

向前进

Schools and childcare centres have already reopened.学校和托儿中心已经重新开放。 Some districts have been allowed to go with a preferred model that permits smaller class sizes, and this is a step in the right direction.一些地区已被允许采用允许小班授课的首选模式,这是朝正确方向迈出的一步。

There are also many examples of how school districts can reduce class size at minimal cost.还有许多例子说明学区如何以最小的成本减少班级人数。 For instance, kindergarten classes with two teachers could split into two groups, one of which uses the library, gym or spends more time outdoors in activities.例如,有两名老师的幼儿园班可分为两组,其中一组使用图书馆,健身房或在户外活动中花费更多时间。

If widespread school closure occurs again this fall, we suggest that re-reopening plans pay close attention to the aspect of class size.如果今年秋天再次发生普遍的停课,我们建议重新开放计划应密切关注班级规模。 While the risk of outbreaks will never be zero even with small classes, it would be prudent for class sizes to be lower, so these disruptions affect the fewest number of children and families possible.尽管即使是小班授课,疾病暴发的风险也永远不会为零,但降低班级人数是审慎的做法,因此,这些干扰影响了尽可能少的儿童和家庭。 In the meantime, for parents and caregivers, the best thing to do is同时,对于父母和照顾者来说,最好的办法是 进行坦诚而公开的对话 讨论关闭家庭的情况,包括工作和育儿安排。

数学告诉我们,今年秋天许多学校区将关闭学校或教室。谈话

作者简介

应用数学教授Chris Bauch, 滑铁卢大学; Brendon Phillips, Ph.D.布伦登·菲利普斯(Brendon Phillips)博士student, Applied Mathematics,学生,应用数学, 滑铁卢大学; Dillon Thomas Browne,心理学助理教授, 滑铁卢大学以及全球生态变化与可持续性实验室教授兼所长Madhur Anand, 圭尔夫大学

本文重新发表 谈话 根据知识共享许可。 阅读 原创文章.

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