It looks like you're new here. If you want to get involved, click one of these buttons!

- All Categories 2.3K
- Chat 499
- Study Groups 18
- Petri Nets 9
- Epidemiology 3
- Leaf Modeling 1
- Review Sections 9
- MIT 2020: Programming with Categories 51
- MIT 2020: Lectures 20
- MIT 2020: Exercises 25
- MIT 2019: Applied Category Theory 339
- MIT 2019: Lectures 79
- MIT 2019: Exercises 149
- MIT 2019: Chat 50
- UCR ACT Seminar 4
- General 67
- Azimuth Code Project 110
- Statistical methods 3
- Drafts 2
- Math Syntax Demos 15
- Wiki - Latest Changes 3
- Strategy 113
- Azimuth Project 1.1K
- - Spam 1
- News and Information 147
- Azimuth Blog 149
- - Conventions and Policies 21
- - Questions 43
- Azimuth Wiki 707

Options

- Coronavirus Policy View 1, Andrius Kulikauskas

Elsewhere, @AndriusKulikauskas wrote:

Hi David and Paul,

I want to suggest here at the Azimuth Project that we might have a significant impact by helping develop and promote mathematical thinking in public policy. Ideas such as "tipping point", "carbon budget", "flattening the curve", can make all the difference. Of course, they can also lead us astray. The idea of "flattening the curve" and references to "the peak", in my mind, often suggest wishful thinking that we just need to slow the pandemic down and it will magically go away. The point of my article is to argue that it won't magically go away and we will have to do massive testing of the population before we can loosen the quarantine. A slogan could be "Wait for the Test".

I machine translated my article and created a page: Coronavirus Policy View 1. My thought is that the Azimuth Project could host many views, possibly contradictory, with the aim of encouraging, developing and promoting mathematical thinking. This would be material for people to use in writing opinions and editorials or simply communicating their own views.

What do you think?

It's an interesting idea.

Some points of form. Since you haven't been around for that long you may not be aware of the following customs that have developed over time (so don't take these as any kind of criticisms).

When proposing group level ideas, it's more fitting to address it to the group at large, rather than directly to e.g. me or to Paul.

As it expresses a view, your page was naturally written in the first person. That's a very different structure than the rest of the wiki, which is in the style of a mini-encyclopedia, oriented towards reference material. We have a structure for accommodating position statements in the wiki, which is to treat them as "virtual" blog articles. Accordingly, I applied the blog category to your article, and formatted the title according to our style convention.

Whenever a new page gets created, we ask people to create a new, dedicated discussion for that page, which has the title of the article in the title of the discussion, and begins with a link to the article. This way, people can be free to create new pages without worrying about asking for permission from the group in advance -- yet on the other hand, by announcing it in a dedicated discussion, it gives it prominence and gives everyone a chance to weigh in on it. For any article other than a blog, others are encouraged to make actively make changes (without asking permission in advance), and then announce their changes on that same discussion. (Of course we're all working together here, so if something isn't clear it may make sense to first discuss it before making the change.)

I have done just this for your article, in this discussion.

If anyone else wants to post other "blogs" with different viewpoints on coronavirus topics, that would be great. At the moment, I don't have any to contribute, simply because my thinking is on other topics at the moment.

My only gut level hesitation about position statements on coronavirus policy is that I wouldn't want things to devolve into ideological arguments e.g. about whether it is more important to save human lives or to open the economy. I.e. to keep things on a fairly scientific / objective basis. Clearly you weren't going in that direction Andrius. It's more a concern about providing food for trolls. Well, we don't have any around here these days, so that's a bit of a theoretical concern. And this doesn't mean that we should avoid topics like the mathematics behind policy -- it's green math! -- but that a vigilance should be kept in the back of our minds, to keep things away from the weeds.

## Comments

Growth is only (approximately) exponential at the beginning of the epidemic. It follows the sigmoidal curve, which looks exponential at the start, moves towards an inflection point (which is the peak of daily infections), and then appears to exponentially approach the asymptotic limit of the maximum number of deaths.

My understanding of the Hubbert linearization is that new cases / total cases is an indicator of how far the epidemic is in its "lifetime" - that it goes down linearly from the outset to the conclusion of the epidemic, where it ends at zero.

So it's not clear to me how new cases / total cases could be used as a comparative measure across countries, when each country is at a different stage of its epidemic relative to the other countries.

`> A simple indicator (new cases / total cases) lets us see what various policies are achieving. Increasingly strict policies make for lower exponential growth, but it still remains exponential. Growth is only (approximately) exponential at the beginning of the epidemic. It follows the sigmoidal curve, which looks exponential at the start, moves towards an inflection point (which is the peak of daily infections), and then appears to exponentially approach the asymptotic limit of the maximum number of deaths. My understanding of the Hubbert linearization is that new cases / total cases is an indicator of how far the epidemic is in its "lifetime" - that it goes down linearly from the outset to the conclusion of the epidemic, where it ends at zero. So it's not clear to me how new cases / total cases could be used as a comparative measure across countries, when each country is at a different stage of its epidemic relative to the other countries.`

David, thank you for setting up this thread and for explaining the customs here.

`David, thank you for setting up this thread and for explaining the customs here.`

David, in response to your comment, I only know to remake the same two points as I did in my article.

It's reckless for us to suppose a model (the sigmoidal curve), as many people do, if we don't first consider the logic. I don't see the logic grounding the presumption that the sigmoidal curve will hold.

The logic I see is that an epidemic will spread through a population and take three possible courses:

Note that currently we are at the very beginning of this pandemic, in the sense that less than 1% of the world's population has gotten sick. The vast, vast majority of the population is not immune to this coronavirus. This means that we are at risk of the worst case scenario.

In a few countries, like South Korea, through aggressive testing, contact tracing and isolation, they have achieved the Best scenario, and basically wiped the virus out.

In most countries what we see now is that different policies have slowed the spread of the virus. But the virus still spreads at a rate proportional to those who are currently contagious. The rate is basically new cases / total cases. And that rate directly reflects the effectiveness of the policies. If you change the policies, the rate will change. Why wouldn't it?

The simple logic behind the sigmoidal curve is that as the population gets sick, the virus runs out of new people, and so it can't grow exponentially any more, and ultimately, it can't grow out all. A more sophisticated way to get a similar curve is if the transmission rate is pushed below 1, then the new cases will drop down. But the latter model only holds conditionally. As soon as the conditions (the quarantine) are changed, it snaps back. It will snap back to exponential growth immediately if our conditions go back to normal.

My concern is that reliance on the sigmoidal model - or the course in other countries - is reckless if we don't sustain the policies, and especially, if we just suppose that the virus dies out on its own. It doesn't and it won't.

The question remains whether the virus will go away. It won't until there's a vaccine or until there is aggressive testing, tracking and isolating. This is a point that responsible parties have been speaking up about and getting heard. So that has put me at ease.

The remaining contribution that my article makes is to note that the indicator (new cases) / (total cases) is a very simple indicator that is much more informative than the typical data given by the WHO and the media. And that this indicator is scientifically relevant as a way to study, across countries, states and regions, what policies are achieving or not.

A conflicting hypothesis, which you may be implying, is that the virus basically takes the same course in each country. That could be examined, for example, to see what the logistic curve (or the bell curve) looks like in each country. But it is immediately obvious that the curve for South Korea is completely different than for the US. So if it's not the virus, then it must be the policy. Or what?

I suppose that a problem I see built into the sigmoidal curve is that it is, like any model, a presumption. It presumes the virus will die out, and then if the virus doesn't die out, then it says, well the conditions changed. Whereas the model for exponential growth presumes exponential growth, and if the rate changes, then it says, well the policy changed. Personally, the latter model seems much more relevant and responsible because it focuses on what's happening now (the rate of growth) rather than some presumptive end in the future (when will this peak, when will this be done). Given the instability of these models, it seems much more pertinent to focus on appreciating what is happening now, what that depends on, what that entails. Is the exponential rate going down? seems to me a much more useful way of thinking than How accurately can we predict the peak? But that's my personal bias, worrying about whether we are doing enough, rather than trying to argue why we can finish with this. Because I look at the underlying logic and conclude that we aren't doing enough until we are actively and completely stomping it out.

It's like looking at a burning house and asking if the flames are going down. And saying, well, the flames are dropping so we don't need any more water.

I am just restating myself. But I may ask, am I understood? Does that help or not? Is there something I'm not understanding?

`David, in response to your comment, I only know to remake the same two points as I did in my article. It's reckless for us to suppose a model (the sigmoidal curve), as many people do, if we don't first consider the logic. I don't see the logic grounding the presumption that the sigmoidal curve will hold. The logic I see is that an epidemic will spread through a population and take three possible courses: <ul><li>Best: It is ruthlessly isolated, has no opportunity to spread, and goes extinct. <li> Worst: It gets everybody sick, and so has no opportunity to spread, and goes extinct. <li> Medium: It finds it difficult to spread and so the transmission rate becomes less than 1 and it dies out. </ul> Note that currently we are at the very beginning of this pandemic, in the sense that less than 1% of the world's population has gotten sick. The vast, vast majority of the population is not immune to this coronavirus. This means that we are at risk of the worst case scenario. In a few countries, like South Korea, through aggressive testing, contact tracing and isolation, they have achieved the Best scenario, and basically wiped the virus out. In most countries what we see now is that different policies have slowed the spread of the virus. But the virus still spreads at a rate proportional to those who are currently contagious. The rate is basically new cases / total cases. And that rate directly reflects the effectiveness of the policies. If you change the policies, the rate will change. Why wouldn't it? The simple logic behind the sigmoidal curve is that as the population gets sick, the virus runs out of new people, and so it can't grow exponentially any more, and ultimately, it can't grow out all. A more sophisticated way to get a similar curve is if the transmission rate is pushed below 1, then the new cases will drop down. But the latter model only holds conditionally. As soon as the conditions (the quarantine) are changed, it snaps back. It will snap back to exponential growth immediately if our conditions go back to normal. My concern is that reliance on the sigmoidal model - or the course in other countries - is reckless if we don't sustain the policies, and especially, if we just suppose that the virus dies out on its own. It doesn't and it won't. The question remains whether the virus will go away. It won't until there's a vaccine or until there is aggressive testing, tracking and isolating. This is a point that responsible parties have been speaking up about and getting heard. So that has put me at ease. The remaining contribution that my article makes is to note that the indicator (new cases) / (total cases) is a very simple indicator that is much more informative than the typical data given by the WHO and the media. And that this indicator is scientifically relevant as a way to study, across countries, states and regions, what policies are achieving or not. A conflicting hypothesis, which you may be implying, is that the virus basically takes the same course in each country. That could be examined, for example, to see what the logistic curve (or the bell curve) looks like in each country. But it is immediately obvious that the curve for South Korea is completely different than for the US. So if it's not the virus, then it must be the policy. Or what? I suppose that a problem I see built into the sigmoidal curve is that it is, like any model, a presumption. It presumes the virus will die out, and then if the virus doesn't die out, then it says, well the conditions changed. Whereas the model for exponential growth presumes exponential growth, and if the rate changes, then it says, well the policy changed. Personally, the latter model seems much more relevant and responsible because it focuses on what's happening now (the rate of growth) rather than some presumptive end in the future (when will this peak, when will this be done). Given the instability of these models, it seems much more pertinent to focus on appreciating what is happening now, what that depends on, what that entails. Is the exponential rate going down? seems to me a much more useful way of thinking than How accurately can we predict the peak? But that's my personal bias, worrying about whether we are doing enough, rather than trying to argue why we can finish with this. Because I look at the underlying logic and conclude that we aren't doing enough until we are actively and completely stomping it out. It's like looking at a burning house and asking if the flames are going down. And saying, well, the flames are dropping so we don't need any more water. I am just restating myself. But I may ask, am I understood? Does that help or not? Is there something I'm not understanding?`

I will add another comment about models and logic.

If I throw a baseball straight up in the air, then it will fall straight down, and the position will be given by a parabola. And that parabola says that the ball will keep gaining speed as it falls, quickly breaking the speed of light, and every other possible limit.

But logic says that the ball will hit the ground first. That was the logical assumption before the model: We are at or near the surface of the Earth.

Here in Lithuania, we have experts who apply models without consideration for their underlying logic. They can predict how many cases there will be next week. And they can explain why their predictions were wrong. But are we kidding ourselves to think that's especially helpful? At best, those are just mathematical interpolations. They aren't giving flesh to the bones of the underlying logic.

Again, the logistic curve, as a model, supposes constant conditions, which is to say, a constant policy. But policy is not at all constant. So then we would have to speak of a family of logistic curves. And whose mind can compare two logistic curves? And what does that logistic curve say more than a bell curve - that it has a start, a middle, an end, and a width? The rest is just interpolation.

It seems much more relevant, simple and helpful to speak of a family of exponential rates. Ordinary people are familiar with interest rates. Each policy brings us down to a particular rate. We have a terrace of rates. If we weaken control, then the rate will go up. So we can only soften policy in ways that don't weaken control. That is my understanding and it will be interesting if I'm wrong but otherwise I think my conclusions stand.

`I will add another comment about models and logic. If I throw a baseball straight up in the air, then it will fall straight down, and the position will be given by a parabola. And that parabola says that the ball will keep gaining speed as it falls, quickly breaking the speed of light, and every other possible limit. But logic says that the ball will hit the ground first. That was the logical assumption before the model: We are at or near the surface of the Earth. Here in Lithuania, we have experts who apply models without consideration for their underlying logic. They can predict how many cases there will be next week. And they can explain why their predictions were wrong. But are we kidding ourselves to think that's especially helpful? At best, those are just mathematical interpolations. They aren't giving flesh to the bones of the underlying logic. Again, the logistic curve, as a model, supposes constant conditions, which is to say, a constant policy. But policy is not at all constant. So then we would have to speak of a family of logistic curves. And whose mind can compare two logistic curves? And what does that logistic curve say more than a bell curve - that it has a start, a middle, an end, and a width? The rest is just interpolation. It seems much more relevant, simple and helpful to speak of a family of exponential rates. Ordinary people are familiar with interest rates. Each policy brings us down to a particular rate. We have a terrace of rates. If we weaken control, then the rate will go up. So we can only soften policy in ways that don't weaken control. That is my understanding and it will be interesting if I'm wrong but otherwise I think my conclusions stand.`

My friend sent me a link to an article in Business Insider: Nobel Prize-winning economist Paul Romer says for the US to return to normal by the summer every person must be tested — at a cost of $100 billion. That would pay for testing every 2 weeks.

`My friend sent me a link to an article in Business Insider: <a href="https://www.yahoo.com/news/nobel-prize-winning-economist-paul-023507777.html">Nobel Prize-winning economist Paul Romer says for the US to return to normal by the summer every person must be tested — at a cost of $100 billion</a>. That would pay for testing every 2 weeks. > The US has been under scrutiny for the slow rollout of its testing. Seven weeks ago, on March 8, for example, South Korea's number of tests per million citizens was roughly 700 times that of the US. South Korea had tested 189,000 people, while America had tested only 1,707. The discrepancy was especially notable since, as Business Insider previously reported, the two countries announced their first coronavirus cases on the same day. > Romer is not alone with his call for mass testing. A "road map" report from Harvard University published April 20 suggested that 20 million people a day needed to be tested by midsummer if the economy was to be remobilized.`

Today I saw this by Bill Gates: The first modern pandemic The scientific advances we need to stop COVID-19. And a shorter version in the Washington Post: The first modern pandemic (short read). He emphasizes the need for massive testing and contact tracing.

`Today I saw this by Bill Gates: [The first modern pandemic The scientific advances we need to stop COVID-19.](https://www.gatesnotes.com/Health/Pandemic-Innovation?WT.mc_id=20200423060000_Pandemic-Innovation_MED-WP_&WT.tsrc=MEDWP) And a shorter version in the Washington Post: [The first modern pandemic (short read)](https://www.gatesnotes.com/Health/Innovation-for-COVID). He emphasizes the need for massive testing and contact tracing.`