Can we Contain Covid-19 without Locking-down the Economy?
Date Posted:
April 1, 2020
Date Recorded:
April 1, 2020
CBMM Speaker(s):
Amnon Shashua Speaker(s):
Shai Shalev-Shwartz
All Captioned Videos CBMM Special Seminars
Description:
Abstract:
Link to related CBMM Memo: https://bit.ly/2UCMbdl
Presentation Slides (PDF)
Prof. Amnon Shashua: https://www.cs.huji.ac.il/~shashua/ and https://www.mobileye.com/about/management/
Prof. Shai Shalev-Shwartz’s research website: https://www.cs.huji.ac.il/~shais/
TOMASO POGGIO: Welcome, all, to this talk hosted by the Center for Brains, Minds and Machines, together with CSAIL and its director, Daniela Rus I'm Tomaso Poggio, a director of CBMM. This is the first of a regular series of virtual CBMM seminars that we plan to continue for the rest of this semester, every week on Tuesday. The next one, next Tuesday, will be a discussion of stability of over parameterized learning models, which is currently a hot topic in machine learning.
Today's talk is not directly about the science and the engineering of intelligence, which is what CBMM is about. It's about proposing a cure for the pandemics, which is truly better than the disease. And using statistics, machine learning arguments to support it. Let me introduce, briefly, our two speakers.
Amnon Shashua is well-known to CBMM. He's one of the member of our external advisory board committee. In fact, he was supposed to be physically here today for a AC meeting that was later cancelled, and to have a public discussion with David Segal, who is another of our EAC member, on algorithms we can trust. I hope we'll be able to schedule the event for later in the year. Amnon is the CEO and co-founder of Mobileye, an Israeli company that is now part of Intel. Still a professor in the School of Engineering Computer Science at the Hebrew University, where he was the chairman around 2005 or so. In addition to several awards, mostly in computer vision, he was awarded the Dan David Prize in artificial intelligence in 2020, a few months ago, jointly with Demis Hassabis.
Shai Shalev-Shwartz is also a professor at the School of Computer Science and Engineering at Hebrew University of Jerusalem in Israel. He's the CTO of Mobileye and a senior Intel phenom. He's the author, with Shai Ben-David, of one of the best books in machine learning that I know. And without question, one of the smartest theoreticians in machine learning.
So let's welcome both of them. And I give the floor-- well, the screen-- to them. Actually, Amnon will start first.
AMNON SHASHUA: So, both of us are computer scientists, as Tommy mentioned. We work in machine learning, artificial intelligence, autonomous cars. So when you look at the title of this talk, I think the first question that comes to mind, why computer science? The kind of people that you normally hear talking about the disease are epidemiologists. So how come two computer scientists are talking about this topic?
And the reason from our point of view is that the dynamics of this disease-- the duration and the spread-- are very complicated. And there are many, many unknowns still about how to model the dynamics of this disease. Now, computer science has a way to deal with unknowns through taking a worst case. So you take a worst case assumption and then you develop bounds. And if those bounds are tight, it is very, very useful. So this is why computer science can be useful to analyze and look at solutions for how do we contain this-- how do we contain this disease?
Personally, both of us, Shai and myself, have been working in these kinds of settings, of taking a worst case analysis under reasonable assumptions, in our work in autonomous driving, because when you look at the safety of an autonomous car, the safest car is the car that stays in the garage. So you need to balance safety and usefulness. And the way to do that is, again, taking a worse case setting and reasonable assumptions. So we have some experience in dealing with this kind of setting. And we thought, let's apply this to the coronavirus containment strategy.
Without further ado, I will start. If we look at strategies for handling, for containing the spread of the virus, there are three prevalent strategies. One is a full lockdown. For example, Israel right now is in a full lockdown. I think New York City is in a full lockdown. Perhaps, Boston is in a full lockdown. Clearly, a full lockdown is something that can't sustain forever. But as a step along in a greater strategy, it is one tactic that is being employed.
The second containment strategy is what we call precision quarantine, where you isolate positive cases as quickly as possible, you use contact tracing through your smart phones in order to identify all the people that were around the positive cases, and then you quarantine them, self isolate them. And you do that repeatedly until a vaccine is available. Some countries like Singapore have been using this strategy.
The third strategy is herd immunity. You don't wait for a vaccine. You simply let people spread the virus as quickly as possible and then you achieve the herd immunity. Of course, then you'll suffer a high mortality rate, and the health system may not contain the load-- the capacity of the health system would not be sufficient. So we are proposing a combination of those models. I think our proposal is not original. I think the original part is analyzing this proposal, not the proposal itself.
So the proposal is to-- we called this a risk based model, where we divide population into two groups-- high risk group and a low risk group. The high risk group, which is going to be age-related and also pre-existing conditions, like diabetes, obesity, all sorts of pre-existing conditions, the high risk group would be quarantined for a certain period of time. The low risk group, which is the rest of society, would be free to engage in their daily routine until herd immunity is achieved. After herd immunity is achieved, one can then release the high risk group gradually into society. And then we are done with the coronavirus, at least for a reasonable period of time. Could be a year or two until the vaccine is available.
So if we look at this from a pictorial manner, what is this risk based model looks like? So on the left hand side is without any safety measures. Simply let people spread the disease as quickly as possible. So you see that in a very, very short time, the ICU, the number of severe cases, goes way above what the health system can sustain. And this is when you get into an overload of capacity of the health system. And that also increases the mortality rate and could be devastating, also, for the economy, as we see happening in Italy. So this is not something that we want to do.
The middle is what most countries are doing, that flattening the curve. Flattening the curve by doing social distancing, quarantining, kind of spreading the disease as slowly as possible such that the health system is still in capacity. The price that you pay is that it takes a long time until the disease is over.
What we are proposing is the risk based model is the low risk group goes into herd immunity. Because it's a low risk group, we'll show later that we will be able to guarantee that we're not going to exceed the capacity of the health system. The number of critical beds, for example. And then when you achieve herd immunity, then the high risk group is released to society. But because it's released into a self-immuned society, then the spread would be very, very slow. And therefore, we basically flattening the curve in a natural manner for the high risk group.
So this is-- as I said, this proposal is not original. What we want to do is provide tools to decision-makers on how to analyze this kind of risk based model. So if we look at the questions of interest. First is, how do we find the high risk group? As we said before, it's age-related. So we need to find a cutoff of age, say 67 and above. We need to find the cut-off age. And also, what are the pre-existing conditions in this cutoff? And we want to be careful about it not to overfit. So we'll get to that later.
The major question that we want to ask is, can the health system contain the number of severe cases? So severe cases are people that arrive to the ICU units, need critical beds, like a respirator machines. So the more people that need critical beds, the faster the capacity of the health system gets consumed. So how do we guarantee that we have enough critical beds to contain the low risk population, the number of severe cases in the low risk population?
And the first question is, beyond the obvious economical benefits of using this model-- because the low risk population can go into their daily routines and the economy is back on track-- is this model also safer in terms of human lives? In terms of overall mortality? So those are the three questions that we'll answer in this talk.
The last slide that I want to show before we go into the math that Shai will get into is, as I said before, the dynamics of this is too complicated, and we are taking a worst case analysis under reasonable assumptions. So here we are setting the assumptions. So for example, we are upper bounding the time from infection to ICU care as one week. And it's also backed by research.
So the average has been between five to seven days. We're also making an assumption that the probability of a low risk person to be infected and need a critical bed, that probability is fixed. Now, the reason we need to make this assumption, because one can conjecture that if we release the low risk group, we can enter into a viral load situation in which the amount of a viral infection in a very condensed group could create more severe cases than when you have social distancing. So we're making this assumption, because we can release the low risk group under some social distancing guidelines, in order not to create a viral load.
Now, the worst case assumptions we're making, that the infection rate among the low risk group is 100%. Normally, it's not 100%. It could be 60%, it could be 70%. Influenza, I'd say, between 15% to 30%. We're going to make an assumption-- we're going to take the worst case as 100%. Another worst case assumption that we're making is that all the severe cases, the cases that require critical beds, respiratory systems, they all happen simultaneously. That's the worst case assumption. Normally, they'll not happen simultaneously, there'll be some staggering. But we are going to assume that they all happen simultaneously.
So this is the setup. We'll move into the model itself. And then once we go over the model, we'll come back and show some insights we have from the data in Israel to show that the balance that we have developed are really tight and really useful.
SHAI SHALEV-SHWARTZ: All right. So the goal now is to show how to analyze the expected load on the health system, and to make sure that we're not going to overload the health system. From now on, we are focusing on the low risk population, because the idea is that the high risk population will be quarantined for a period of time of two to four weeks, until herd immunity will be achieved for the low risk population.
Notation, we use m as the size of the low risk population. In Israel, for example, it's something like 7 million people. b is the budget of intensive care units that you have in the country. There are several numbers. And maybe in hard times, you can take the largest number by buying more machines and having extra crew members. But this is a parameter that can be set by the government.
What we want to analyze is what is the probability to have a severe case? The probability of a severe case is a probability of a severe case and infected case, because you're not going to be a severe case if you're not infected. And it equals to the probability to be infected times the probability to be a severe case given that you are infected. The probability to be infected is at most 1.
This is one of the worst case assumptions that we have made. And the probability to be severe given that you have been infected we denoted by u. So overall, we need the b, the capacity of the health systems, the number of beds that you have in the ICUs, should be larger than m, the size of the low risk population, times nu, the probability of being severe given that you have been infected.
Now, our next step will be to get an upper bound for nu, because if we would have an upper bound or nu, we will be able to check whether b is equal to n times nu.
So what is nu, again? Nu is the probability to be severe given that you infected. We can estimate it. And now I'm showing an approximation, and later, I will show how we upper bound-- approximation by an upper bound. But roughly, the probability to be severe given that you have been infected is roughly the number of severe cases that we have today over the number of infected cases that we have today. We know k, which is the number of severe to date. The numerator here is something that we know, because we know how many severe cases we have now.
Just a small note, by passing, that in order to be on the safe side, we should be careful about today, because if the pandemic is growing exponentially, maybe there are infected cases today that will become severe just in several days. So today, for the number of severe cases should be from now to the time interval to about one week or something like that. But anyways, this part we know.
What we don't know is the number of people that are infected today. It's not the number of confirmed cases, because it doesn't matter how many confirmed cases. It depends on the policy of the government how to make our own tests. What we care about is the actual number of infected today, both symptomatic and asymptomatic cases. In order to estimate the number of infected people today, we do know by p star, the probability to be infected today. And then, the number of people infected today equals to p star times the size of the population.
So overall, we can estimate nu. This is the parameter that we want, the probability to be severe given that you are infected by k, the number of severe cases today over p star m and which is the number of infected persons to date. Our goal is to prove that the budget of the health system is larger than m times nu, from which we need that b should be larger than k, the number of severe cases today, over p star, the prevalence of infected people today.
So we know k. We know b. Now we need a lower bound on p star. To remind you, p star is the probability to be infected today.
Now, this is a classic trick. If you want to estimate some probability of a [INAUDIBLE], you need to sample niid person from the low-risk population, find how many cases you have, which I denote by s sub n, and then p star is roughly S sub n over n. So if you plug it instead of b star in our formula, what we need to show is that the budget of the health system is greater than the number of severe cases today over the fraction in our sample of random people from the low-risk population of infected people.
So for example, in Israel today we have roughly 15 severe cases in the low-risk population. And we don't know what is b star, but if we estimate based on some side information-- and maybe we'll talk about it later-- by 2% of the populations that have been infected today, what we need is that the budget will be at least 750, and this is something very reasonable for the Israel population.
OK. All of this was based on approximations. Approximations are not enough. So majority of the technical work here is to replace the approximation by bounds that holds with sufficient probability. Because then we can say, with probability of, say, 90% or 95%, we know that a capacity b will be sufficient to maintain the spread of, say, a virus among the low-risk population.
So what do we do? We use tail bounds. We derive concrete bounds on all the relevant parameters based on Bernstein's inequality and another inequality to get some more tight bounds by Zubkov and Serov. Again, it's a probability. It's a tail bound probability of binomial random variables.
So I will not go into the details of the bounds. You can see it in the paper. But let's see what the bottom line. What we need is that the budget will be larger than m times nu. m is the size of the low-risk population, and nu is the probability to be a severe case, given that you are infected.
What we show is that, for a sufficiently large sample size n, and we specify the number n it's a few thousands of people to sample, then with high probability, this m times nu is lower bounded by-- sorry, it should be upper bounded-- it's upper bounded by a little bit less than 2 times k over Sn over n. So the approximations was k over Sn over n, and for the upper bound, we lose roughly a factor of 2.
So overall-- and by the way, you can make the bounds for specific variables even tighter and decrease this factor 1.92. But already now, instead of-- we talked before about 750 beds that you need, then maybe you will have twice this number, something like 1,400 bed, which is something reasonable if the health system is prepared in advance for maintaining this spread.
AMNON SHASHUA: So what I want to go next is some insights from the Israeli data that we have. So we go back to this formula, the capacity, the number of ICU beds is greater or equal than the number of severe cases in the low-risk group. The 1.6 is a bound. This is just bounding k. We'll take p star from indicators because Israel hasn't yet done a random sampling of its population, so we don't have any scientific measure of the p star. We have only a site indications, which I'll mention in a moment.
The site indications that we have is in Iceland. Before the outburst some random sampling were conducted, showing that there were 1% of the sample were positive cases. In Israel, the medical crew was sampled in one of the hospitals in Jerusalem showing 1.8% of the medical staff. Now, it is true that medical staff is a biased population because they are much more exposed to the virus than the normal population, but on the other hand, they are protected. They protect themselves. So we kind of see that one cancels the other, so it is a useful measure, this 1.8%.
Just this morning we have read that in Boston, one of the hospitals in Boston, I think Brigham and Women's, did a similar sampling of their health staff, and 8% were tested positive. So we have reasons to believe that in Israel it's at 2%. But again, it's not scientific. One needs to do sampling in order to get this number right.
But let's assume it's 2%. So we bounded k by 1.6, and again, this 1.6 bound, you can find it in the paper. So if you plug in the numbers-- two days ago we went hospital by hospital, we called every hospital in Israel. We got the number of people who are below 67 without preconditions. And altogether, out of 74 cases, severe cases, 15 of them were in the low-risk group. So k is equal to 15. So if you plug in the numbers, we get that the number of critical bits is bounded by 1,200. So 1,200 means 12 ICU beds for 100,000 of the population.
So if you look at on the left-hand side, this is a list of number of critical beds in every country. For example, in the US, it's 34 critical beds per 100,000 population. Israel is about 6, so very close to the UK. UK is 6.6. Israel is close to the UK, about 6. So for Israel to go from 6 to 12 is not unreasonable. It's something that can be manageable.
So what this means is that Israel, if it prepares right, can prepare itself for a very fast release of the low-risk population. Let the low-risk population as quickly as we want to achieve a herd immunity. And the bounds tells us that the health system can contain, the capacity can be enough to contain the spread in the low-risk population. So what it shows, that the bounds are indeed useful. Of course, before we can do anything, one needs to do a random sampling. Our calculations shows that a sample of 5,000 people would be sufficient in order to get p star at a very high reliability rate.
So if you go to the last slide, and we look at comparing the risk-based model, the model that we're proposing, to the precision quarantine model, there are a number of insights that we can generate here. So on the left-hand side is the risk-based model. We'll have high infection rate among the low-risk group but the low-risk group has very low mortality. On the other hand, in the precision quarantine, we are achieving unified infection rate. It's slow, but it's still unified infection. There is no separation between low risk and high risk.
So we do expect high mortality among the high-risk group, even if they get good care. So we're still in the situation in which the health system is in full capacity because the curve is being flattened using precision quarantine. But since there is no separation between low and high risk, eventually the high-risk population will be infected. Even though it's going to be slow infection, they will be infected, and we know that there is a high mortality among the high-risk group.
So the risk-based model is not only beneficial from an economical standpoint because the low-risk group can go back to their daily routine, and the economy can pick up from where it was a few weeks ago, it's also better for a mortality perspective. So it's not just economical, it's also mortality. When we look at the economical side we're talking about, really, the risk-based model, a minor negative effect on the economy because why quarantine only the high-risk group? It's age-related and-- it's mostly age-related, but also pre-existing the rest of the population.
So for example, in Israel, Israel is about 9 million population. One million are people aged 65 and above. And we assume another one million is pre-existing conditions. So seven million out of nine can go back into their daily work. That will be the low-risk population. On the other hand, in the precision quarantine, there is no guarantee that this is going to end quickly. There could be a second wave. There could be-- it's like controlling a fire, assuming that there's no wind. It's very, very complicated.
For example, in Israel, the society is very heterogeneous. Not every people can be traced using a contact tracing. Some sectors of the society are very densely populated and could be very, very difficult to control. So the precision quarantine may not be that precise. So one could expect a occasional lock-down period. So this could have an extensive negative effect on the economy.
Another advantage of the risk-based model is there is a clear exit point. So a clear exit point says that after the low-risk population have achieved herd immunity, we're basically done with it because the high-risk population can now be released. So it will give us economic stability and also the civilian population will cooperate much more readily, understanding that there is a clear exit point.
With the precision quarantine, there is lack of stability. Nobody knows how long this is going to last, and there is going to be a second wave and third wave. And then when tourists come in, because at some point you need to open the skies, when tourists come, open your borders, tourists come in, there could be a super spreader, and then it all starts again. So the visibility is not clear.
Finally, when you look at the risk-based model, we're talking about a short duration, and the effect on the health system is very, very controlled because it's a very short duration. On the other hand, in the precision quarantine, because it could take a very long time until a vaccine is ready, it could be a devastating effect on the health care system because there are other patients, not only corona-based patients. There are other patients which the care that they would get would not be optimal because the health system would be fully occupied with dealing with the corona patients over a very, very long time.
So this is the end of the talk. Hopefully it wasn't too heavy on the mathematical side. All the mathematics are in the paper, and we urge everyone to go and read it and send us comments. And we're ready for questions, if anyone has questions.
TOMASO POGGIO: I want to thank the speakers. They're mostly, of course, not about mathematics. The first one is about how feasible it is to separate the high-risk group from the low-risk group. In many places, people live in a family, and high-risk group and low-risk people are mixed together. So Amnon or Shai want to answer?
AMNON SHASHUA: It's a very good question. And we don't have a very clear answer. But there is a group at Weitzman Institute headed by Ehud Shapiro, another computer scientist, that have been doing a study on exactly this kind of question-- how to effectively do this separation where people from the low-risk group help people in the high-risk group maintain the quarantine. And we are relying on that study to go and implement such a separation. There are, of course, difficulties in doing the separation, but the alternative is that we are all quarantined. And that is definitely not easy.
TOMASO POGGIO: Thank you. Another question is about the assumption that you're making, which is that there is immunity after infection and that is not a given with unknown pathogen, like COVID-19. So if you want to comment on this.
AMNON SHASHUA: So I think from all what we read, immunity for a certain period of time, I think, is given. The question is, how long that period? Is it six months immunity, is it one year immunity, is it immunity for life? That, I think, is unknown. But that a certain period of time that there is immunity, I think that is well agreed.
And all that we need is to buy time until there is a vaccine. The vaccine is expected in a year and a half from now. And all indications are that this immunity should last at least for that period of time.
SHAI SHALEV-SHWARTZ: It's based on evidence from other coronaviruses. It's a family of viruses. The flu gives you six months, and other members of the corona family gives you usually two years. So it's reasonable to assume that it's something in between.
TOMASO POGGIO: So another comment has to do with the fact that the capacity of the ICU beds should be defined as extra capacity. In other words, you will need some number of the ICU beds in the country for other conditions, not just COVID-19.
AMNON SHASHUA: Well, yes. Yes and no. So let's take the case of Israel. So we came to the bound of 12 ICU beds per 100,000 population, and in Israel, there are six. So the question is, should Israel prepare for 18 or prepare for 12? Since we are talking about a short period of time, so if we allow herd immunity as quickly as possible, that could take only a few weeks.
So in those few weeks, one can embrace and contain, even with 12 ICU beds. If we're talking about a longer spread, then Israel should prepare somewhere between 12 to 18 ICU beds. Yes. But in both cases, it's a reasonable number compared to what Israel has currently.
TOMASO POGGIO: OK. One more question is, did you consider having three groups instead of two, like high risk, medium risk, low risk? Does it make sense?
AMNON SHASHUA: No, we haven't considered. [INAUDIBLE]
SHAI SHALEV-SHWARTZ: We haven't considered. Maybe you have an idea of what to do with the medium group. Because when you have two groups, one of them is out, and one of them is quarantined. If you have a third group the question is, what is the policy with respect to the third group?
TOMASO POGGIO: There was another question, which is, I guess, more of an ethical question, which is what is the mortality in the low-risk population? Is any number greater than zero acceptable?
SHAI SHALEV-SHWARTZ: Yes. So I have two answers. Actually, it's a single answer. But we are not forcing anyone to go out of quarantine in this model. If you're afraid of the coronavirus, and you want to stay quarantined, you are free to do so. OK. So basically, we are giving the choice to the people. Do you want to stay in quarantine or do you want to go out?
Now, if someone will ask me what I will do, then I am for sure will go out. Why? Because according to our calculations, the risk of being severely ill from the coronavirus is about 50% lower than the risk of being hit by a car and being severely injured in a car accident. Now, you can decide that you are not going to use your cars never because you are afraid to be hit by car accidents. If you are willing to do so, then be afraid of the corona. If you are not afraid of car accidents, you shouldn't be afraid of the corona.
AMNON SHASHUA: Just to be more specific, which I mentioned that we saw the number 1,200. The number of severely injured people in car accidents in Israel on an annual basis is 2,300. So we're talking half of that.
TOMASO POGGIO: OK. Next question is whether you have any mechanism to incorporate feedback into the model once it's implemented. I assume so, but have you thought how to correct your estimate?
SHAI SHALEV-SHWARTZ: So, of course. There is a threshold. Are you above b or below b? As we will get more evidence, we will be able to estimate the required amount of beds better and better.
Now, there is a small probability-- it's always the case in statistical analysis-- there is a small probability that you are wrong, you are totally wrong about your estimates. And then, of course, you will know it very, very fast. But this is usually what you do in statistics. You need to make decisions based on reason about levels of confidence.
TOMASO POGGIO: It's a question about how reliably can we assume that the data we have are. And it's not your estimate but the data on which they are based.
SHAI SHALEV-SHWARTZ: So there are two things. There are two types of data. One of them is k. It's what is the number of people which are severely ill and are currently hospitalized in hospitals. I think this number can be known very, very reliably because it's a small number. And what we did is simply went hospital by hospital and double-checked.
The more tricky issue is estimating p star, which is a probability of a person to be infected today. And for this, we need a sampling of the population, [INAUDIBLE] sampling of the population. And then there are many, many tricky questions how you do the sampling and what type of corona tests are you using. Is it PCR or a serologic test and whether there are false positives to these tests. And all of these things should be answered.
To the best of our knowledge right now, if you are performing PCR tests, the ratio for a false positive is negligible. So there is no problem of false positives. There are always issues with sampling bias and the like, but these are the type of things that there is a very clear methodology of how to account for these types of errors. And as long as our estimates are not off by an order of magnitude, then even if there is a small bias here and there, I believe that the health system will be able to manage.
AMNON SHASHUA: But what we have found out that serology tests, the best ones that have a false positive of half a percent, which is not good enough. There was a real-time PCR that have a false positive of 1%. That's not good enough. But lab-based PCR, which takes hours until you get your results, are very, very negligible with false positives. So they should be good enough to do the sampling.
TOMASO POGGIO: There is an interesting comment by Bret Mensch. I don't know about the fact that he says ICU care is likely to be less useful than one image [INAUDIBLE], and it's certainly providing less survival data than the simple availability of supplementary oxygen.
If so, the constraint of not overwhelming the ICU beds may be not really very important. I think I heard the stories from Italy that are consistent with this remark in which extreme procedure, using ventilators and intubation, really did not help in most of the cases.
AMNON SHASHUA: Well, with ICU bed is a proxy for measuring the capacity of the system. The actual bottleneck is not the machines. It is the people that need to attend the machines. This is where you start getting the bottom leg.
So when we say a critical bed unit, it's the critical bed plus all the people that need to support it. So when we come to the bound of 1,200 critical beds, it's 1,200 multiplied by the number of persons, staff members, that you need in order for every critical bed. That is the proxy of the capacity of the health system.
TOMASO POGGIO: So one more from [INAUDIBLE]. Does it make sense, instead of waiting for natural immunity, to just give a shot of coronavirus to the low-risk group?
AMNON SHASHUA: That's an excellent idea. We haven't thought about that.
SHAI SHALEV-SHWARTZ: It is being tested in Israel. But we are not the expert for this. Of course, if there is a scientific evidence that this approach works and is not dangerous, we will offer it. But what we can say from the standpoint of statistics and computer science is that we have evidence on natural infection, and we can give guarantees about it. This is what we can offer. If it works, great.
TOMASO POGGIO: There is one question about Israel, which is, what is your prediction for the number of respirators or ventilators that will be needed at the peak?
AMNON SHASHUA: Well, we just showed the bound of 1,200. So with the data that we have today, we think that 1,200 should be sufficient.
SHAI SHALEV-SHWARTZ: If the high-risk group will be--
AMNON SHASHUA: --will be quarantined. If we do the numbers for the entire population, if we don't quarantine the high-risk group and we let herd immunity of the entire population, it's above 10,000, which is way above what Israel can manage. So you either quarantine the high-risk group or you go to precision quarantine, which we think also is a bad idea.
TOMASO POGGIO: Very good. And with this, I think we should wrap up this webinar. I thank very much the speakers on behalf of the audience. We cannot hear the applause, but I'm sure there will be one. You can imagine it. And I want to thank, again, Amnon and Shai. Wonderful. Thank you.
AMNON SHASHUA: Thank you Tommy and Kris. Thank you.
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