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科学美国人60秒:感染人数指数型增加

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Exponential Infection Increases Are Deadly Serious

指数型感染人数增加

Here in New York the coronavirus cases are exploding—we’re on the steep part of the curve. Now, you’ve probably heard about the basic reproduction number, R0. or R-naught. And that’s basically how many people an infected person goes on to infect themselves. The other night, I happened to see a tweet that showed just how big a difference there is over 10 cycles of transmission between a basic reproduction number of 1.3 and a basic reproduction number of 3. The different was astounding. The 1.3 after 10 cycles infected on average 14 other people total. The basic reproduction number of 3.0 led to 59.000.

在纽约,冠状病毒病例呈爆炸式增长——我们处在曲线的急剧上升部分。现在,你可能听说过基本再生数字R0.基本上就是被感染者感染自己的人数。前几天晚上,我碰巧看到一条推文,显示了在基本再生数在1.3和 3之间,有超过10个传播周期的巨大差异。这种差异令人震惊。1.3在10个周期后平均共感染14人。3.0的基本复制数为5.9万。

Looking at those numbers was startling. So I got a calculator out. And I’m going to repeat this exercise that I did with the calculator. And you can do it, too. It’s even a little bit fun. And it’s kind of amazing. So I’ve got two calculators, because I’m going to do the two different basic reproduction numbers, the R-naughts, together. And it’s kind of amazing.

看到这些数字令人吃惊。我拿出计算器。我要重复一下曾经用计算器做过的练习。你也可以这么做。甚至还有点好玩。也很神奇。我有两个计算器,因为我要把两个不同的基本再生数,,放在一起。这很神奇。

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Okay, so the calculator on my left—I’m going to assume 1.3 as the basic reproduction number. Each person infects 1.3 other people on average. The calculator on the right—I’m going to do 2.5—just to pick a number and because that looks like it may be fairly close to what the coronavirus number is.

左边的计算器假设1.3是基本再生数。平均每人感染1.3人。右边的计算器,我选用数字2.5.因为它比较接近新型冠状肺炎。

So we’ll start with one person (1) on each side. We multiply by 1.3 on the left to get 1.3. obviously. We multiply by 2.5 on the right to get, not surprisingly, 2.5. For cycle two, we multiply the one on the left by 1.3 again, and we get 1.69. On the right, we take 2.5. and we multiply it by 2.5. and we get 6.25. So that’s two rounds.

我们从每边1个人开始。左边乘以1.3.得到1.3.右边乘以2.5.得到2.5.对于第二周期,左边的再乘以1.3.得到1.69.右边是2.5.然后乘以2.5.得到6.25.这是两轮计算的结果。

Let’s do it again. On the left, for the third round, multiplying by 1.3. we now have 2.197. On the right, multiplying by 2.5. we’re up to 15.625.

让我们继续。左边,第三轮,乘以1.3.得到2.197.右边乘以2.5.得到15.625.

So let’s do the fourth round here. On the left, we multiply by 1.3. and we’re up to 2.86 people.

们来做第四轮。左边乘以1.3.得到2.86人。

On the right, we multiply by 2.5—we’re up to 39.1.

右边,乘以2.5.得到39.1.

On the left, 1.3 is our number—we’re up to 3.7. On the right, 2.5 is our number—we’re up to 97.7.

在左边,1.3是我们的数字——我们上升到3.7.右边是2.5.得到的结果是97.7.

Another round: 1.3. we multiply by, and we get 4.8 on the left. When we multiply our number on the right by 2.5. we’re up to 244.

再一轮,我们乘以1.3.左边得到4.8.当我们把右边的数乘以2.5.得到244.

Let’s do it again. We’re going to multiply by 1.3. and we’re now up to 6.3 people on the left. We multiply our right figure of 244.1 by 2.5. and now we’re up to 610 people.

让我们再做一次。左边乘以1.3.得到6.3人。右边我们用244乘以2.5.现在我们有610个人感染。

Let’s do another round. Multiply by 1.3 on the left—we now have 8.2 people infected. Multiply the right number, 610.4. times 2.5—we’re up to 1.525.9. But we’re not done; we’re going to go through this and take rounds.

我们再来一轮。左边乘以1.3.现在感染了8.2.右边用610.4.乘以2.5.得到1525.9.但我们还没有结束;我们要仔细检查一下,轮流检查。

One more on the left by 1.3—we’re up to 10.6 people. On the right, multiply by 2.5: 3.814.7.

左边再多一个1.3——我们有10.6个人感染。右边,乘以2.5.得到3814.7人。

Let’s do it again: 1.3 on the left—13.8. 2.5 on the right brings us up to 9.537.

That’s why it’s so important to cut the number of people each individual can infect with the policies of social distancing.

我们再做一次,左边乘以1.3.得到 13.8感染。右边乘以2.5.得到9537人感染。这就是为何通过社会疏远政策保持人与人之间的距离如此重要。

Exponential Infection Increases Are Deadly Serious

Here in New York the coronavirus cases are exploding—we’re on the steep part of the curve. Now, you’ve probably heard about the basic reproduction number, R0. or R-naught. And that’s basically how many people an infected person goes on to infect themselves. The other night, I happened to see a tweet that showed just how big a difference there is over 10 cycles of transmission between a basic reproduction number of 1.3 and a basic reproduction number of 3. The different was astounding. The 1.3 after 10 cycles infected on average 14 other people total. The basic reproduction number of 3.0 led to 59.000.

Looking at those numbers was startling. So I got a calculator out. And I’m going to repeat this exercise that I did with the calculator. And you can do it, too. It’s even a little bit fun. And it’s kind of amazing. So I’ve got two calculators, because I’m going to do the two different basic reproduction numbers, the R-naughts, together. And it’s kind of amazing.

Okay, so the calculator on my left—I’m going to assume 1.3 as the basic reproduction number. Each person infects 1.3 other people on average. The calculator on the right—I’m going to do 2.5—just to pick a number and because that looks like it may be fairly close to what the coronavirus number is.

So we’ll start with one person (1) on each side. We multiply by 1.3 on the left to get 1.3. obviously. We multiply by 2.5 on the right to get, not surprisingly, 2.5. For cycle two, we multiply the one on the left by 1.3 again, and we get 1.69. On the right, we take 2.5. and we multiply it by 2.5. and we get 6.25. So that’s two rounds.

Let’s do it again. On the left, for the third round, multiplying by 1.3. we now have 2.197. On the right, multiplying by 2.5. we’re up to 15.625.

So let’s do the fourth round here. On the left, we multiply by 1.3. and we’re up to 2.86 people.

On the right, we multiply by 2.5—we’re up to 39.1.

On the left, 1.3 is our number—we’re up to 3.7. On the right, 2.5 is our number—we’re up to 97.7.

Another round: 1.3. we multiply by, and we get 4.8 on the left. When we multiply our number on the right by 2.5. we’re up to 244.

Let’s do it again. We’re going to multiply by 1.3. and we’re now up to 6.3 people on the left. We multiply our right figure of 244.1 by 2.5. and now we’re up to 610 people.

Let’s do another round. Multiply by 1.3 on the left—we now have 8.2 people infected. Multiply the right number, 610.4. times 2.5—we’re up to 1.525.9. But we’re not done; we’re going to go through this and take rounds.

One more on the left by 1.3—we’re up to 10.6 people. On the right, multiply by 2.5: 3.814.7.

Let’s do it again: 1.3 on the left—13.8. 2.5 on the right brings us up to 9.537.

That’s why it’s so important to cut the number of people each individual can infect with the policies of social distancing.


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