数学如何预防麻疹等疾病的爆发
How Math can help prevent outbreaks of measles and other diseases
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2020-01-16 13:02
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The measles vaccine is incredibly effective, yet recurrences and outbreaks abound. Samoa is currently undergoing an outbreak with thousands infected, and in 2019, the United States had the most cases reported since 1992. What can we do about it? In this excerpt from his new book, The Math of Life & Death: 7 Mathematical Principles that Shape Our Lives, mathematical biologist Kit Yates explains how everyone has a part to play in the wider context of public health. Increasing the vaccination rate allows vaccines to prevent deadly illnesses. By understanding the mathematical principles behind disease prevention, the public can better protect themselves from disease.

虽然麻疹疫苗效力强,但麻疹仍大量爆发乃至复发。萨摩亚最近爆发麻疹,上千人感染。而美国2019年的麻疹病例是自1992年来最多的。我们该怎么应对?《生与死的数学》一书中作者数学生物学家基尔叶茨提出了七大关乎我们生活的数学原理。他解释了我们每个人是如何影响公共健康的。疫苗接种率的上升使得疫苗得以有效预防严重疾病。通过了解疾病防预背后的数学原理,公众便能更好地远离疾病。

Sometimes math really is a matter of life and death, particularly when it comes to the outbreak of a deadly disease and the strategies to control it. As well as helping us to understand the unusual features of different disease landscapes, mathematical models of epidemics allow us to peer into the future of disease progression and to take proactive preventive measures, rather than always playing reactive games of catch-up.

有时数学确实关乎生死,尤其是在疾病爆发和防治的问题上。数学不仅能帮助我们了解疾病的特征,还有助于预测疾病的发展进程从而能让我们采取措施预防疾病而不用在病发后再治疗。

Mathematical epidemiology helps us answer a number of perplexing questions that surround childhood diseases such as mumps and rubella.

数学传染病学有助于解决如腮腺炎、风疹等许多多发于儿童的疑难杂症。

The idea that a large population of immune individuals can slow or even halt the spread of a disease, as with the dormant periods between outbreaks of childhood diseases, is a mathematical concept known as herd immunity. Surprisingly, this community effect does not require everyone to be immune to the disease for the whole population to be protected.

有一种说法认为大量免疫个体能减缓甚至阻止疾病的传播,就和儿童疾病爆发有休眠期一样,这是一个数学理念,称为群体免疫。令人意外的是,这种群体效应并不需要每个个体都对疾病免疫。

By reducing the effective reproduction number—the average number of secondary cases produced by a typical case—to less than one, the chain of transmission can be broken and the disease stopped in its tracks. Crucially, herd immunity means that those with immune systems too weak to tolerate vaccination—including the elderly, newborns, pregnant women and people with HIV—can still benefit from the protection of vaccinations.

通过减少有效被传染者数量,即将每个病患传染至的其他人减少至一人以下,疾病传播链便可被打破,而疾病得以停止传播。重要的是,群体免疫意味着像老人、新生儿、孕妇、艾滋病患者这类自身免疫系统弱的人也可受益于疫苗。

Vaccinating only 80 percent of the susceptible population against smallpox was enough, in 1977, to complete one of the greatest accomplishments of our species—to wipe a human disease clean off the face of the Earth. The feat has never been repeated. The debilitating and dangerous implications of smallpox infection alone made it a suitable target for eradication. Its low critical immunization threshold—the minimum proportion of the population that must be immunized in order for the infection to die out—also made it a relatively easy target.

在1977年,人类采取了一个了不起的行动,即消灭天花这一疾病,而达到这一目的,只需对百分之八十的易感人群接种疫苗。此后这一疾病便在未复发,而天花极为危险的传染率使得这一疾病成为首先被消灭的目标。同时其较低的免疫条件——只有一部分人需要接种疫苗便能组织传播——也使得消灭天花成为易于实现的目标。

Many diseases are harder to protect against because they spread more easily. Chicken pox would require 90 percent of the population to be immune before the rest would be effectively protected and the disease wiped out. Measles, by far the most infectious human-to-human disease on Earth would require between 92 percent and 95 percent of the population to be vaccinated. A study that modeled the spread of a 2015 Disneyland measles outbreak suggested vaccination rates among those exposed to the disease may have been as low as 50 percent, way below the threshold required for herd immunity.

许多其他的疾病更易传染,这使得它们更加难以预防。水痘的防治要求百分之九十的易感人群接种疫苗。而麻疹需要百分之九十二至九十五。一项研究模拟了2-15年迪士尼麻疹爆发的情形,研究发现其中易感人群疫苗接种率低于百分之五十,远低于麻疹防治要求的接种率。

Mr. MMR

MMR疫苗

Given the astounding success of the smallpox vaccine in eradicating the formerly deadly disease, why are some vaccination rates for other deadly diseases now falling? One cause of this dangerous trend can be tied to the anti-vaxxer campaign, which has its roots in a now debunked study linking the MMR vaccine to autism.

虽然之前消灭天花的行动取得巨大成功,但为何现在对其他致死疾病的接种率反而下降了呢?导致这一危险趋势的原因之一便是反对疫苗运动,起源是一项错误的研究宣称MMR疫苗会导致自闭症。

As an example, in 1996, England, whose rate of rate of vaccination against measles (through the combined measles, mumps and rubella [MMR] injection) hit a record high at 91.8 percent—close to the critical immunization threshold for eliminating measles. Then, in 1998, something happened that would derail the vaccination process for years.

以1996年英国为例,当时英国借助MMR疫苗(一种同时针对麻疹、腮腺炎和风疹的疫苗)将接种率提升至91.8%,这一数据接近消除麻疹的指标。但在1998年一件事情使得这一进程停滞了好几年。

This public health disaster was caused by what was later found to be a fraudulent study in the well-respected medical journal the Lancet. In the study, lead author Andrew Wakefield proposed a link between the MMR vaccine and autism-spectrum disorders. On the back of his "findings," Wakefield launched his own personal anti-MMR campaign, stating in a press conference, "I can't support the continued use of these three vaccines given in combination until this issue has been resolved." Most of the mainstream media couldn't resist the bait.

这一事件由当年发表在权威医学期刊《柳叶刀》上的一项研究成果导致,这一研究后来经证实是错误的。主要作者安德鲁沃克菲尔德认为MMR疫苗和自闭症存在关联。在这一研究之外,沃克菲尔德自己还开展了反对MMR疫苗运动,他在记者招待会上说,“在这一问题得到解决之前,我始终反对这三种疫苗混用。”大多数主流媒体都报道了他的观点。

While indulging the fears of many fretful parents, the media's coverage of the story typically failed to mention that Wakefield's study was conducted on just 12 children, an extremely small cohort from which to draw meaningful large-scale conclusions. Any coverage that did sound a note of caution about the study was drowned out by the warning sirens emanating from most news outlets. In the 10 years that followed the publication of the infamous Lancet paper, the MMR uptake rate would drop from above 90 percent to below 80 percent. Confirmed cases of measles would increase from 56 in 1998 to over 1300, 10 years later. Cases of mumps, which had been becoming less prevalent throughout the 1990s, suddenly skyrocketed.

媒体一方面煽动家长的焦虑情绪,一方面刻意忽视沃克菲尔德的实验样本仅为12名小孩的事实,这样小的研究样本是远不足以得出普遍性结论的。也有少数对此研究持怀疑态度的报道,但此类声音都被淹没在担忧的声浪中。在接下来的十年中,MMR疫苗接种率由90%多降至不到80%。而麻疹确诊病例由1998年的56例升至10年后的1300例。而在90年代已不再流行的腮腺炎患病人数骤然上升。

In 2004, investigative journalist Brian Deer discovered fraud in Wakefield's work. Among other claims, Deer claimed to have evidence that Wakefield had manipulated the data in his paper to give the false impression of a link to autism. Deer's evidence of Wakefield's scientific fraud and extreme conflicts of interest eventually led to the offending paper's retraction by the Lancet's editors.

在2004年,调查记者布莱恩迪尔发现了沃克菲尔德研究中的漏洞。他向外界表示自己掌握证据证明沃克菲尔德在研究中数据造假并虚构了MMR疫苗与自闭症之间的联系。终于在证据和利益冲突下,《柳叶刀》期刊撤回沃克菲尔德的文章。

In 2010, Wakefield was struck off the medical register by the General Medical Council. In the 20 years since Wakefield's original paper, at least 14 comprehensive studies on hundreds of thousands of children across the world have found no evidence of a link between MMR and autism. Sadly, though, Wakefield's influence lives on.

2010年,沃克菲尔德被医疗委员会除名。在他那篇文章发表后的二十年里至少14项针对大样本的系统研究表明MMR疫苗和自闭症之间毫无关联。而非常遗憾的是,尽管如此,沃克菲尔德的影响始终挥之不去。

Although MMR vaccination in the UK has returned to pre-scare levels, vaccination rates across the developed world as a whole are dropping, and measles cases are increasing. In Europe, 2018 saw more than 60,000 cases of measles, with 72 proving fatal—double the number from the previous year. The United States experienced more measles cases in the first four months of 2019 than in any year for a quarter of a century. The World Health Organization lists what it calls "vaccine hesitancy" as one of 2019's top 10 global health threats. The Washington Post, among other media outlets, attributes the rise of the "anti-vaxxers" directly to Wakefield, describing him as "the founder of the modern anti-vaccination movement." The doctrines of the movement, however, have expanded far beyond Wakefield's now-debunked findings, and anti-vaxxer rhetoric has risen to prominence as a result of support from high-profile celebrities including Jim Carrey, Charlie Sheen and Alicia Silverstone.

虽然英国的疫苗接种率已回升至原来的水平,但在发达国家整体疫苗接种率却下降了,而麻疹病例呈上升趋势。在欧洲,2018年便有超过60000麻疹病例,而其中72例为致死病例,比往年数据翻了一番。而在美国,2019年第一季度麻疹病例达到近二十五年来1顶峰。世界卫生组织将“疫苗恐惧症”列为2019年全球十大健康威胁之一。《华盛顿邮 报》更是将人们对疫苗的排斥直接归因于沃克菲尔德,形容他为“现代抵 制疫苗运动之父”。这一运动的思想现在却已超越了沃克菲尔德那篇满是谎言的文章,受到了包括金凯利、查理辛、艾丽西亚·西尔维斯通等名人的支持而愈演愈烈。

Alongside the rise of the celebrity activist has come the emergence of social media, allowing these personalities to promulgate their views directly to their fans on their own terms. With the erosion of trust in the mainstream media, people are increasingly turning to these echo chambers for reassurance. The rise of these alternative platforms has provided a space for the anti-vaccination movement to grow unthreatened and unchallenged by evidence-based science. Wakefield himself even described the emergence of social media as having "evolved beautifully"—for his purposes, perhaps.

大众传媒帮了这些名人一把,他们可以在媒体上向自己的粉丝大肆宣传自己的观点。随着主流媒体信任的逐渐缺失,大众越来越倾向于从这些社交媒体那里获取信息。日渐壮大的社交媒体使得这一运动不再受到科学的挑战。沃克菲尔德自己甚至称社交平台“美妙地发展”,这一言论或许是出于他个人的目的。

Disease Prevention Is in Your Hands

疾病防御,人人有责

Despite the growing popularity of vaccine hesitancy, the individual decision to get ourselves and our children vaccinated bolsters the herd immunity that keeps whole populations safe. We all have choices to make that affect our likelihood of contracting infectious disease. When we are ill, choices we make affect our likelihood of transmitting disease to others: whether we cancel the much-anticipated get-together with friends; whether we keep our children home from school; whether we cover our mouths when we cough. The crucial decision of whether we vaccinate ourselves and our dependents can only be made ahead of time. It affects our chances not only of catching—but also of transmitting—diseases.

尽管人们对疫苗的恐惧日渐加深,每个人接种疫苗对我们全体大众健康还是有意义的。我们的每一个决定会影响感染疾病的可能性。当我们自己病了的时候,是否取消和朋友的聚会、是否让孩子待在家、咳嗽时是否捂嘴了等等一些选择就回影响疾病传播的可能性。最重要的一点是我们和我们家属是否及时接种了疫苗,而这也是唯一可以提前做好的预防工作。这不仅影响我们患病的几率,更影响我们传播疾病的几率。

Some of these decisions are inexpensive, making their adoption straightforward. It costs nothing to sneeze into a tissue or a handkerchief. Other decisions provide us with more of a dilemma. It is tempting to send the kids to school even if we know it increases the number of potentially infectious contacts they will make. At the heart of all our choices should be an understanding of the risks and consequences.

有些决定随随便便就可以做到,比如打喷嚏时用纸巾或手帕捂住。但其他一些却不这么简单。比如说虽然我们清楚送小孩去学校会增加感染疾病的几率,但我们还是会送孩子去学校。我们在做任何决定时都应该对风险和后果心中有数。

Mathematical epidemiology provides a way to assess and understand these decisions. It suggests strategies to tackle disease outbreaks and the preventive measures we can take to avoid them. In conjunction with reliable scientific evidence, mathematical epidemiology demonstrates that vaccination is a no-brainer. The World Health Organization figures show that vaccines prevent millions of deaths every year and could prevent millions more if we could improve global coverage. They are the best way we have of preventing outbreaks of deadly diseases and the only chance we have of terminating their devastating impacts for good. Not only does it protect you, it protects your family, your friends, your neighbors and your colleagues.

数学传染病学为我们提供了评估决定的途径。为我们提供了疾病预防的方法。借助可靠的科学依据,通过数学传染病学我们得知接种疫苗是毋庸置疑的事情。世界卫生组织的数据显示,疫苗每年能挽救数以百万条生命,全球疫苗接种率的提高能使得更多的人得到救治。这是防止疾病爆发的最好方式,同时也是阻止疾病传播的唯一方式。它不仅保护我们个人,还保护我们的家人、朋友、邻居乃至同事。

→ From The Math of Life and Death by Kit Yates. Copyright © 2019 by Kit Yates. Reprinted by permission of Scribner, an imprint of Simon & Schuster, Inc.

摘自《生与死的数学》,基尔叶茨著,2019年斯克莱布诺出版社再版

Correction 12/26/2019 11:55 p.m.: Updated to clarify that Deer did not set out to expose Wakefield's work as fraudulent, but rather discovered the fraud in the course of his investigation and reported what he found.

2019年12月26日晚11::55修改:迪尔并没有指出沃克菲尔德研究是虚假的,只是发现并提出了其调查过程的漏洞。

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