It feels like a normal day.

一切一如往常。

It may stay like this for a long time, until one day, a few people you know are sick.

這種情況可能會持續個好幾天，直到某天一些你周遭認識的人都生病了。

And suddenly a few days later, it will seem like everyone is sick, and it will feel like it happened instantly.

再過了幾天，突然間好像所有人也都生病了，感覺一切都是突如其來的。

Everything looks fine, until it isn't fine.

一切看起來都安好，直到狀況失控以前…

This is the paradox of pandemics, and it's why with an outbreak like COVID-19 you hear health officials calling for huge, drastic, and rapid responses in the early days when infection numbers are still relatively small.

這就是「大流行悖論」 ，這也是這次新冠肺炎疫情爆發會看到官方衛生組織開始戲劇性且快速並大動作回應的原因，即使在爆發性傳染的現象尚未發生前。

Some people worry these actions are overreactions.

有些人可能擔心這些都反應過度。

Sports teams playing to empty stadiums, or not playing at all.

例如說運動賽事不開放觀眾入場，甚至說乾脆取消所有賽事。

Canceling huge gatherings and festivals.

或者說取消大型且多人聚集的活動。

Temporarily closing schools and offices.

又或者說短暫性關閉公司與學校。

Telling people to avoid personal contact?

甚至叫大家不要有肢體接觸？

Media sensationalism.

這根本是「媒體轟動效應」。

But this way of thinking fails to appreciate how disease outbreaks work:

但是這種想法是完全忽略了病毒如何開始爆發性地傳播：

It was really never fine to begin with, but we don't notice until it's too late.

雖說病毒的出現本是件壞事，但是在我們意識到的時候為時已晚。

Hey smart people, Joe here.

嘿，各位聰明的觀眾，我是 Joe！

How bad will the coronavirus outbreak get?

你覺得這次新冠肺炎疫情的情況會有多嚴重？

That's what we all want to know, and the answer is in one of these curves.

這正是所有人都想知道的，而答案就藏於接下來的曲線圖。

This is what a rapid global pandemic looks like.

這是一個突發性傳播的瘟疫曲線圖。

Little to nothing to slow the number of new infections means a lot of people sick in a short amount of time.

幾乎沒有方法可以減緩新傳染病的傳播速度，也就是說會造成很多人在短時間內染病。

A slower global pandemic looks like this.

而瘟疫傳播速度比較慢的曲線圖是長這樣。

The rate of new cases is lowered, and they're spread out over a longer period of time.

傳染速度相對較慢的話，受感染人口會分佈在比較長的一段時間。

And which one of these paths we end up on is important because of this line.

而這條線會影響著這次疫情的結果，所以這很重要。

It represents the capacity of our health care system: the number of beds, doctors, respirators, and everything else.

因為這條線代表了我們醫療系統的臨界點：病床、醫療人員和呼吸器等數量，以及其他相關的資源等。

What experts fear is a sudden explosion like this overwhelming this capacity.

現在專家們害怕會有一股爆發性傳染出現，這會完全超過我們醫療系統的負擔。

And what's really interesting here is that even if these two curves represent the same total number of people that eventually get infected, in the rapid outbreak scenario more people will die because there won't be enough hospital beds or ventilators to keep them alive.

有趣的是…雖然這兩個曲線中受感染人數一樣，但在這種突發性增長的情況下會造成更多人死亡，因為在這情況下我們沒有足夠的病房或者說維生器具搶救性命。

This is a strange idea.

這聽起來可能有點奇怪。

That even if the same number of people eventually get sick in the end, even without a vaccine or a cure, taking drastic action before we see things get bad, that will save lives all on its own.

即使在沒有任何疫苗或者說治療方式出現，最後受感染人數也一樣。 我們要在情況惡化以前採取激烈的行動才可以挽救許多不必犧牲的生命。

What we're doing isn't overreacting.

所以我們正在採取的措施並不是反應過度。

It's exactly what the science of epidemics tells us will work.

而是這些作法早已被流行病學證明是有效。

And that's counterintuitive, because our intuition doesn't really "get" exponential growth.

這可能聽起來有點違反直覺，因為我們難以「理解」指數增長的原因。

Instead of thinking about viruses, let's say you have a pond, and on the pond is a single lily pad.

來換個方式想，我們用一個池塘作比喻，而在池塘表面有一片荷葉。

This type of lily pad reproduces once a day, so on day two, you have two lily pads.

這種荷葉每天繁殖一次，所以第二天池塘表面會有兩片荷葉。

On day three, you have four, etc.

第三天會出現四片，以此類推。

If it takes the lily pads 60 days to cover the pond completely, how long will it take for the pond to be covered halfway?

如果要花六十天荷葉才能完全覆蓋池塘表面，那麼要花多久時間荷葉才會覆蓋池塘的一半?

The answer is 59 days.

答案是 59 天。

The area covered doubles from half to the whole pond on the last day.

荷葉覆蓋的區域要從一半變成整個池塘只需要一天。

I bet some of you knew that, though, because you're pretty smart.

我知道有些觀眾早就知道，因為你們都很聰明嘛！

But on what day do the lily pads cover a mere 1 percent of the pond?

那麼你們知道這些荷葉要花多久就可以覆蓋 1% 池塘表面嗎？

Surprisingly, that doesn't happen until day 54.

意外地，答案是 54 天。

The pond is basically empty, until it's very suddenly not empty.

池塘表面基本上看起來很空，直到情況開始失控。

We go from covering less than a percent to covering the whole pond in just the final seven days.

我們從荷葉只覆蓋 1% 的池塘表面直到整個池塘都被覆蓋只花了七天而已！

This is exponential growth and it's how pandemics work.

這就是所謂「指數增長」，這也是傳染病的散播速度與方式。

We multiply today by some constant to get the value for the next day.

我們以今天的感染數量作基數，然後用一個穩定倍數就能推算出明天的受感染人數。

The time doesn't have to be days, but that's helpful to use for something like lily pads—our constant was two—or COVID-19.

其實時間單位不一定是要用天，不過這對於計算荷葉增長速度 (以上所得出的倍數是 2) 或是新冠肺炎比較容易理解。

Starting in mid-February we've seen between 1.1-and-1.4-times more cases each day.

從二月中開始，我們可以看到每天受感染人數的成長速率大概介於 1.1 到 1.4 倍之間。

A number over one tells us every day we're seeing more new cases than the day before.

只要出現第一個病患，就代表我們每天會看到越來越多的新病例。

You can see the number of total cases starts to add up really fast.

而你們可以看到這個病例總數是急速爆增。

Exponential growth can be scary.

這指數增長就是這麼恐怖。

But obviously this can't go on forever and fill the known universe with viruses, for a few reasons.

但當然這不可能永無止境地傳染至整個宇宙都充滿這個病毒。

The virus will either infect everybody, like our lilies filling up the pond, or what actually happens is the virus stops finding people to infect: either by running into people who are already sick, or we isolate people who are sick, or thanks to something like a vaccine spreading resistance in the population.

因為這種病毒會傳染至每一個人，就像佈滿荷葉的池塘表面，換句話說就是病毒不再找新宿主。病毒要嘛是跑到已經患病的人或是隔離病患，又或是有疫苗可以阻止於人群中繼續散播。

But over time the growth rate will naturally slow down, and we end up with a curve for the total number of cases that looks like this.

無論如何，成長率會隨著時間而趨緩，而後最終的曲線圖會看起來會像這樣。

This is called "logistic growth" and we call this curve a sigmoid, which is a weird name, but luckily it starts with "s" which also happens to be the shape of the curve.

這是「邏輯斯生長曲線」，我們稱這為「S 函數」。英文全名聽起來可能很奇怪，不過它的第一個字母代表了曲線的形狀。

While I was working on this, Grant from 3Blue1Brown released a really good video digging into more of the math behind why and how this all changes, and he's definitely my go-to when it comes to math, so I'll put a link down below so you can watch that later.

當我正準備這部影片時，3Blue1Brown 推出了一部非常棒的影片。他用深奧的數學來解釋趨緩現象是如何發生的。而且每當我有數學問題他的影片都是我的參考首選，所以我會在影片下方放上他頻道的連結，大家可以去看喔！

Now, remember that the height of any point on our S curve tells us how many total cases the outbreak has caused as of that day.

大家要知道這條曲線上的每一個點都代表了當天總病例數目。

But if we take the slope at that point, that shows how many new cases that day.

不過我們看看這點上的坡度，這代表當天內的新增人數。

Which makes sense, not many new cases early on, then a whole lot each day, and then not many new cases again as the virus dies out or goes quiet.

這看起來蠻合理的。剛開始沒有什麼確診病例，隨之又新增大量病例，而後期可能沒有那麼多人感染 然後進入高峰期快速成長 然後再過一段時間病毒失去傳染力 這個坡度又開始趨緩

If you've taken calculus and worked out derivatives before, then you may see where I'm going here.

如果你學過微積分且了解什麼是導數的話，那你應該會懂我接下來要說的話。

Plotting the different slopes along our S-shaped curve, we get this.

沿著這條 S 形曲線標出不同的斜率，我們會得到這條紅色線。

This is what health officials are worried could overwhelm our health care system.

而這條曲線就是衛生官員最害怕的，因為這會壓垮我們醫療系統的主要原因。

But luckily, we can make it look like this instead, if we change how our S curve looks.

幸好，我們可以透過改變 S 函數以讓紅色曲線能臨界點。

How we do that is by lowering the constant we multiply by from day to day in our exponential growth.

那要達成這種結果，我們就得降低新案例的成長速度。

The really important thing here is, for a virus that humans have never encountered before, like this one that's causing COVID-19, no one is immune to it.

不過這裡有一個重點是，面對人類從未看過的病毒，例如這次的新型冠狀病毒，沒有人對它有免疫力。

The only way to lower the growth rate, isn't medicine or anything like that, it's to slow down those infections and keep them from happening in the first place.

所以要降低成長速度的方法並不是靠疫苗之類的東西，而是要降低傳染的機會，從開始就要杜絕散播的可能。

A real outbreak plays out like this: You have a bucket of infectious people, I.

爆發性傳染我們可以這樣看：我們有一群帶原者，稱為 I。

And you have a bucket of people who haven't gotten sick yet, S.

然後我們有一群健康的人 S。

The I bucket is tied to the S bucket so that the more full I is, the faster S empties into it.

好比說兩個把 I 與 S 綁在一起，而當 I 水桶越滿，代表 S 水桶清空速度越快。

But people are also getting better all the time.

但別忘了人們也會慢慢康復。

So the I bucket has a hole in it that empties into a bucket R for recovered people at some constant rate.

所以 I 水桶有一個洞可以讓它可以流進 R 水桶，代表著有一個固定速率的人會康復。

So if we can lower how fast S empties into I through some drastic action, I will empty out into R, and we'll stop emptying S.

所以倘若我們可以透過大規模的行動來減緩 S 流進去 I 的速度，那麼 I 裡的水會漸漸流光至 R，而隨後將可以停止把 S 清空至 R 。

If our bucket of infectious people is empty, we starve the virus out.

一旦 I 裡的水都清空至 R，那麼病毒自然就無處可去。

So even if we somehow did nothing else to stop a disease outbreak or pandemic, and the same total number of people get infected in the end, it is so, so important to slow down how many new cases we see every day, to flatten the curve and keep a pandemic from overwhelming health care.

即使我們對於病毒本身已束手無策的，而最後受感染人數仍然會相仿。因此減緩新案例的成長才是至關重要，把曲線拉平以防超出醫療系統的負擔。

In 1918, in the early days of the worst influenza pandemic in history, the city of Philadelphia ignored warnings and held a parade attended by 200,000 people.

在 1918 年曾爆發出一場人類史上最嚴重的大型傳染病，美國費城政府不顧警告依然舉辦了一場 20 萬人的大遊行。

Three days later, every bed in Philadelphia's hospitals was full, and 4,500 people died within a week.

三天後，費城的所有醫院人滿為患，然後接下來一周內有超過 4500 人死亡。

At the same time, St. Louis, two days after detecting the first cases, closed schools, playgrounds, even churches.

在同一段時間，美國聖路易傳出第一宗確診病例後政府立即關閉學校和教堂。

Work shifts were changed.

甚至更改上班時間。

Public gatherings of more than 20 people were banned.

亦禁止舉辦超過 20 人以上的聚會。

And this was the result: a tale of two cities.

而最後兩個城市卻有截然不同的結果。

That's why officials are calling for such drastic action so early on, canceling events and school and everything else, before most of us actually know anyone who's sick.

這就是政府在疫情大規模爆發之前要這麼大動作的原因，在我們知道身邊的人確診之前就先取消各種活動跟關閉學校。

Because with something like this, everything looks fine until it isn't fine, and if we wait until it's our turn to get sick, it's too late.

因為在這種情況下，在狀況惡化前表面都看似平靜。如果我們真的等到所有人都發病時，一切已經不可挽救。

Stay curious.

保持你的好奇心！

And wash your hands.

也記得要勤洗手！

We'll be talking more about that soon.

我們也會在近期推出更多影片。

And as always, a huge thank you to everyone who supports the show on Patreon.

然後我要再次感謝各位在 Patreon 對於我們節目的支持

Your support helps us make videos like this faster than we normally could to get good information out to people who really, really need it.

你們的支持讓我們可以更快製作完這些影片，把不錯的資訊傳播給真正需要的人。

If you'd like to join our community, just check out the link down in the description.

如果各位想要加入我們的社群，請閱讀影片下方的說明。