 Okay. We are live now. So welcome everyone. So welcome to this series of Latin American webinars on physics. Today we have a super interesting seminar. We have a very special one, because it's not about highly physics or as the particles of physics. So we have a very special webinar that I told you. It will be about the modeling COVID-19 on the fly by Professor Roberto Cankel. So Roberto is from the University, from the University of Sao Paulo in Brazil. And so thank you very much Roberto for being here with us and sharing all your expertise. So thank you for this kind invitation. Thank you for watching me actually. So I know the community of the usual attended seminars are very high energy and astroparticle physics. But this will be a low energy down to earth seminar. So just to make, just to introduce myself, I work on what people usually call complex systems or whatever. Nonlinear dynamics with multiple agents and so on and so on and so on. And I work with applications and biological systems and mainly in epidemiology and ecology. So that's the thing I do. I'm over the last 10 or 15 years. Before that I used to be a more theoretical guy. Now I'm more applied theory. So very good. So I will share my screen so that you see my presentation. Let me see. There's always a share screen. Okay, screen share. And here we go. So this seminar will be about modeling coronavirus epidemics, COVID-19 on the fly. On the fly means just as it is happening. And this is very different from doing theoretical work. It is something completely crazy. So the main thing, let's see how all of this works. So say you are at the beginning of an epidemic. And this is an epidemic. It's a new emergent disease. What does it mean? It's a disease that no one is immune. Everybody is susceptible of getting this disease, in the case of COVID-19. But anyway, it would be the same for any emergent disease. So that's in the jargon in epidemiologists that a new emergent disease. So every epidemic of a new disease starts with an exponential growth. So that means that you have a completely susceptible population. Everybody is, let's say, able to catch the disease. I mean, to be infected. And there's a certain number of secondary cases given a primary case. And this number at the beginning of the epidemics is usually constant. So at the very beginning of an epidemic, you could say, OK, I want to model epidemics. And I will talk about that in the second part. So you will want to write down, for instance, equations or models that will explain you all the epidemic curve. The epidemic curve is the number of people that are infected over the time, like this one. So nice. You would like to explain all the epidemic curve. But when you are at the very beginning of the epidemic, you just don't see the epidemic curve. You just see some cases. And this is well approximated by an exponential. So no need of big models at this point. It's very simple. Just an exponential. So what can we do with that? So if you try to take a big model and just fit the model with the first point of your epidemic, you will get an enormous amount of uncertainty. There's no point of doing that at this point of time. So the thing is, at the very beginning, what are the problems that a modular would face? The first thing is that the data is very noisy. Noisy means you don't know, for instance, the date of the first case. You would say, well, OK, I go to the newspaper and say that the first case was they, I don't know, 20-something of February in Brazil at 25 of February, I think. So that's the first case. But is it the relevant case? Because the first cases are all of them important. Somebody coming from abroad bringing the disease. If this person didn't multiply, didn't transmit, it is the first case, but it's irrelevant for the epidemic, actually. So the first uncertainty you have is you don't know the first case. When did your epidemic start? Unknown exact date. More or less, you know it, but so you don't know when the epidemic actually started because of this phenomenon of when really the replication of cases started. So at the first moment, what you try to do is just to characterize what is happening. And you can do this by calculating two numbers. One is the doubling time, which means how long does it take to double the number of cases? So if you have an exponential growth, the doubling time is constant. I mean, constant over time. It's just a geometric series. And so you could try to calculate that and give a characterization of this part. This is the initial part of the... And then another interesting number is the effective reproductive number. It's the number of secondary cases given a primary case, which you can calculate from the doubling time plus some other characteristics of the disease, which I won't go into detail. These are the first things that you can do. And so that's what you do. You go on and doubling time is easy to calculate. Just put it on an exponential logarithmic plot. You got a line and you discover that... And you discover that the number of cases more or less doubles every two and a half or three days. That's everywhere. More or less everywhere in the world except for very special cases like Korea or Taiwan. And so that's the easy part. You see that obviously the points don't lie exactly on a line. You have to do some fitting. You can do this, you'd say least squares or whatever. You can do that better. There are people from statistics that will do this in a very sophisticated way, supposing that you have a personal process behind of this and so on. You can do this in many ways. And you can fit the best line and you can get the even arrow bars and whatever. And then you can also say, okay, we are at the beginning of the epidemic. And the number of people that are infected is very, very small compared to the total population. So we will be for some time at least in the exponential phase. So I can extend this into the future and I can make projections which will be valid for say a week or 10 days or something like that. So you can do this and you actually do it. So the doubling time is important when you are at the very beginning of the epidemic. It's characterized epidemic. So for COVID it's two and a half days or three days more or less. There are lots of uncertainties, but more or less it's like that. So this is the doubling time at the beginning of the epidemic. This has been true for Europe, US, Brazil and so on, Argentina and whatever. So that's more or less characteristic of the COVID-19. And you can also calculate the reproductive number which is the number of secondary infections created by a primary infection. And in Brazil this is a line between two and three. And more or less everywhere in the world and in China it's like 2.7 or something. So this is the characterization of the epidemic at the very first stages. So a way of keeping track of the epidemic at the beginning of the epidemic would be just calculating the doubling time like locally. I have today and I use the last let's say it's five days or seven days and I calculate the doubling time. So I go on and there and so if I'm a really exponential phase this doubling time doesn't depend on time. I mean it's constant, but well there are many in most countries there are isolation measures. People are staying at home and so on. So you expect that the doubling time increases means that the epidemic is going slower and slower. So you can do this and you can follow the doubling time over the time. So here you have an example of what this means. This has been made like a month ago which was March 18. Brazil was only these two points at that time. But imagine that there are countries that are clearly doing something which is Korea in this case which means that the doubling time started somewhere like two or three here. And it increases and I mean I don't know here it's a logarithmic thing but 30 days or something so it's very slow evolution of this case. So that's good. On the other hand you have this country here which is Thailand which is doing very bad. So the doubling time is decreasing means that the pace of the epidemic is speeding up. So that's a way to compare things you usually put today and then you look for some days ago and look how this behaves. So you expect that once you introduce policies like social distancing or contact tracing or whatever things that you do to have the epidemic slowing down you expect to see this on an upload like that with a doubling time that's increasing. This would be a very effective way of keeping track. I'm not talking about modeling at this point. I'm just talking about how to keep track of what is happening. So if this is happening you look at that. So what could go wrong with this? It seems perfect. There are so many things that can go wrong and that's when you as a theoretical physics you at a certain point you want to give up. I can cope with that kind of thing and what kind of thing is. So you don't know the number of cases. At the very beginning you have a certain number of cases being notified every day. Every day there's something that it's in the website of your counter and saying that the number of cases is X. That's it. You go on, you do your doubling time analysis and you keep on tracking and everything and you say okay yeah yeah everything's nice. So but what happens is that when the number of cases increases you hit barriers and the main barriers. So one barrier is what people call sub notification. Sub notification means not not define. Not keeping track of cases that are potentially positive. So in Brazil this means from March 20 Brazil is only testing people that are in severe cases. So mild cases are not even tested. So these people don't leave a trace on the statistic. Nothing. Anything. There's nothing there. So this is sub sub notification. You only have the severe cases but okay. Then you say okay I have to severe cases like let me follow the severe crazy let me keep track of the severe cases. So, in order to do that, you know, no, you have to know how many severe cases you have, but then you hit a barrier which is a hard barrier that you have unlimited testing capability. Which means that you have a limited number of tests that you can perform per day. So which which means what aren't there sufficient testing tests. Well sometimes you have the test but you don't have the people to perform the test. And then after the people you need machines and you need all the things in the labs and so on. So, there's a maximum ability to perform tests. You cannot perform more than a certain point. So at the very beginning this is not a problem, because you have a constant flux of people of tests going going into the your system your system is not overflow and you get a constant output. But now you have a certain bottleneck here, and a lot of people a lot of tests coming here and through your bottleneck you have only a constant number of outputs. That's a problem. That's a real problem. So you don't know how many people are sick. Okay, so you're doubling time. That doesn't mean you don't know anymore. And then still, once you say okay I have now I hired more people like I bought more tests and everything. And still is a lag between the results of the tests and typing them into the database. So this is really down down to real world things and and you have to cope with that. If you want to do something relevant for the for informing people that take decisions. Okay, so and all these legs between for instance legs between having the result and typing them into the system are not constant. Maybe just on Sunday people don't work. They don't have anything on on Sunday, maybe a better take a moving average or whatever so you need a lot of statistical machinery to cope with this kind of problem. And so, most importantly is if a lab can only test a certain fixed number of cases. It means that the number of confirmed cases of COVID-19 or whatever you're talking about but take COVID-19 the number of confirmed cases will not increase exponentially it will increase linearly if I can only put out say 100 tests per day. And I have a proportion of certain number say 80% is positive COVID I will get 80 positive tests of COVID-19 per day which is linear increase. However, the epidemic is actually probably increasing still exponentially so there's no relation between confirmed cases and actual actual number of cases because you have a bottleneck with your. With your testing apparatus. So that's, that's really, really, really the end of the war. Okay, so you cannot the thing which seems so so nice that's keeping track of the state of the epidemic if, if our measures of our isolation policies are doing okay or not. Just keeping track of the doubling time doesn't work like that. And I know that this is really problematic because we have a site we have a we have a website. So, when I say we there's a, it's a bunch of people that work together. And, and we had this doubling times and, and at the very beginning and looking at that and lots of journalists or whatever. Asking us how is the thing going on so on and a certain point. We saw an enormous increase in the doubling time as if the epidemics were just going well, I mean, if the effects of the isolation measures were super super super strong. And just look at that and well, it's not true. It's just because we are not testing enough. So the bottleneck of having a number of tests, very important, and, and spoils your analysis. So, very big problem. So what can you do in this case. So depends, depends. The first thing is what data you have access. So if you have access to honor to the data that is usually made public by most of the government, which is the number of confirmed cases per day, you cannot do much. But just just a minute. But sometimes you can be lucky enough or you can be smart enough to get access to more detailed data. So if you get access to more detailed data, not only the number of confirmed case. But you can try to do the now casting of cases. So now casting of cases is the following. I had, I had need to have access to a full data of cases, which are suspected cases. I know, when is the data of the first symptom. I know the day the test has been performing. How long does it take to have the result of the test. How long does it take to have the test on the database and so on. I have a statistics of that. I can use the present situation and using the knowledge that there are set of number of people that are a number of tests that are being performed and so on. I can project from this from the past to the present and estimate the number of cases I have right now. So to do this, you need more specific data as the public data means that you have to work with authority. And this is very difficult. This is, well depends on the country and depends on your position and whatever. So in Brazil, my group and the people that have been working with me, we have access only to the municipality of Sao Paulo, not the state Sao Paulo, not not to speak of Brazil, the country. But we have access to data of the municipality of Sao Paulo. You have a spreadsheet where you have each line as a case and this data has been anonymous. They just took out a name and then the occasion of the person. But it has all the dates of all occurrences like first symptoms, the person went to the doctor, the person got tested and so on and so on. And so you can do some now casting of data. So now the casting of data means this. You see, that's what it's in Portuguese, but I think you will understand it. So that's the absurd number of cases here, which is actually looking like it's leveling. It's not increasing very much. But here you have the now casting of the day. How many cases we have right now? Well, with some simple model, you can hear in the case we have a logistic model, but you can have access to financial model and so on. So that's not the worst case scenario. It's a relatively mild scenario, which is adjusting a logistic curve here, which is an S-shaped curve and to the observed data. So you can do some projection for some days here. And you could do it with other models instead of the logistic, you could have some exponential model and it would give you the worst case scenario. So doing now casting allows you to have a better view of what is actually happening. And you are not being, I mean, dumped. You are not being fooled by the fact that the number of observed cases is like becoming constant. It's becoming constant because you don't have the necessary number of tests. But knowing what is coming on in line for your test, maybe you can get a better estimate of what is happening right now. You see there are error bars. All of this is a lot of statistics. It's Bayesian statistics and so on and a lot of things behind that. So now casting of days is the way to keep track of what is happening right now. And just to know the situation, right? We are not talking about models at this point. So next, okay, looking ahead, now you say, okay, you have the now casting and you have an idea of how many cases you have. So what will happen next? So models in epidemiology are all of them based on all of them, maybe 90% of them are based on dividing the population into classes, susceptible individuals, infected individuals, recovered individuals, exposed individuals, hospitalized people, infected but not infectious, infectious but not symptomatic, whatever you want, lots of possibilities. So, and you have fluxes between these classes, which will be connected to contact rates between the classes. So I'm not writing down the equation for that and it's no point here to analyze equations. So you divide the populations and so what kind of models do people in epidemiology work with? So what I like most is differential equation is deterministic equations for the number of people in each class, susceptible, infected, recovered or whatever other classes you have in your model. So this is a nice way to do the things. Then you could also do stochastic dynamics, suppose you have a marker process and you go on and you have like reactions, okay, and you do stochastic dynamics and you could also do individual based modeling. Individual based modeling means that you have individuals that can be in any of these classes and then they do something, they may move around, they may interact or whatever depends on the model. And then you see how the epidemic spreads in the population. So, what we are working on right now is it's the Brazilian version of what it's called COMO model, COMO is construction of models, which is based at the University of Oxford, and which has all these classes. I don't want you to, I mean, I don't expect you to now to look at all the classes you have infected with no symptoms, mild symptoms, hospitalized and then lots of things can happen if you need hospitalization, maybe you'll find a bed for you, but maybe you don't find, maybe you need an ICU, but you have an ICU or don't you have an ICU and so on. And there are probabilities of all from going from one class to the other classes, if you want rates or probabilities, if you want, and then you get, at a certain point you get uninfected or dead. And most people now take for granted that most models take that immunity is there, you are immune after having the symptom. So this is a big model, and this generates this kind of kind of a plot. So don't pay too much attention on the numbers because this is a preliminary results, this has been done doing, I mean, this is the result of two days ago, so it's not still something at the level of being published and so on. But the important thing about models is, and this is very, very different from what you have usually in, what you have usually in, with systems and physics, models are not made to make really precise predictions. Because why? Why? Because uncertainties are enormous. As I told you, you don't know even your initial condition, which is the number of infected people, you don't know this, you have to estimate this and you have an enormous error bars, and you know, these error bars go on multiplying and so on, and it's a hell, and there are a lot of parameters and so on. So what do you do with the models? So what you do with the models is to build scenarios, and what's the scenario? You have a baseline scenario, which means that you don't do anything. Just let the epidemic go on, epidemic go on. What will happen? Like in Brazil it would be like almost two million of people dead. But then you know that even the most crazy government in the world will not do anything. I mean, even crazy people would do something. So there are interventions, and you can model the interventions in your model and see how effective they will be. So say intervention, just making people wash their hands a lot of time. This has a very small effect, but you can try to quantify this into a model. Then you say, OK, isolation, OK, voluntary isolation, or mandatory isolation, then you say quarantine, or lockdown, full lockdown. So you can trace scenarios and try to see what will happen according to the assumptions you made and for how long you do this and this, and so on and so on. So I don't have results for Brazil at this point. I'm working on that actually, but I think one of the only groups that work on that and so these results are not final, but there are results for other groups in the war. And this is a paper from yesterday. So it's just an idea how this thing is evolving a month ago as eternity. So this is a paper from a Harvard group from Mark Lipzig, which is one of the leading at the emergency ward. So, and he was looking at scenarios, not for the new future like one month or two, but what will be the issue of this, all of this, and so there are two main factors which are completely anonymous in order to make more long time scenarios. One factor is, is this seasonal or not? No idea. Is it depending on temperature? We don't know. If you look at the archives, there's a specific archive for this kind of thing, which is not the archive, it's called math archive, and there's a section of epidemiology, which has a lot of paper, more than 10 papers per day on COVID. And there are people saying, yeah, temperature has effect and other people say, temperature has no effect. So we don't know the seasonal behavior of the epidemic of this disease. And the second thing, we don't know anything about immunity. Is immunity going to be long term? So we know something about immunity, which means that if you're at COVID now, you don't have it next day. But how long will this last? Can I have a lifetime immunity, lifelong immunity? A lifetime immunity will be nice, but maybe you have a veining immunity, immunity over some time. So impossible to know. So you have to build up scenarios and try to figure out what is happening, and then as the epidemic progresses, you will get more and more results. But maybe we'll select which scenario you are. So here, just as an example, this paper appeared yesterday in Science. So this is a long term thing, you see, until the year 2025, five years. What happens is, so this is taking into account, you have seasonality. So this is with US data, and it's usually assumed for temporary climate. So you have strong seasonality, and in winter you have more infections than in the summer, which may not be the case in many of our countries, not in America. So this has to be adapted. But what you see is, here are several, there's a big model, differential equation model. And you see that if you have immunity for 40 weeks, which is a very short time, it's not even one year. You will have recurrent epidemic, just like flu, which is really a problem, a real problem. If you have longer time epidemic, for instance, if you have 104 weeks immunity, you will have biannual. Outbreaks every two years. And obviously, if you have complete immunity sometimes, at a certain point, the thing will go away. And this scenario here is something intermediate, where you have small outbreaks all the time. So with seasonality and final duration of immunity, you can have several scenarios, but the main thing is you expect this to come back unless you have lifetime immunity. So bad news. Obviously, if there's a vaccine, then everything changes. We hope to have a vaccine actually, because there's no reason that we should be very pessimistic for a vaccine. But in the absence of a vaccine, you see the human having partial immunity and not lifelong immunity will bring back the epidemic. Now I think that these are the same people have studied. Yes. Okay, let's see there's no seasonality just to make the things easier and let's do one time interventions. It's a long time scenario. It's an intermediate time scenario. What happens is we only have one time intervention, which is, is the temptations of many of governments and, and, and, well, in Latin America, and not only there, so you say, okay, enough with enough with interventions. It should be okay. So what you see here in blue is the time of interventions we have. And, and the many curves you see is the fact of intervention so no intervention and how effective the interventions are. So you see that the only optimistic case is to maintain an intervention for all time. It's obviously not possible. In this case, if the intervention is strong enough you have a curve here with a very small mortality that these are mortality curve here. So you see the secondary peaks here in this cases. In all cases you have secondary ways. Okay. And one time interventions are really not enough to do the job. What are our best, I mean, best hopes, it's, it's vaccination, which can happen. And well, and something which is not shown here in this, in this thing is to have a long time testing and isolation, which would be more or less corresponding to this case here. Okay. So then the ventures doesn't mean necessarily that you are at home all the time for the rest of your life. The ventures can be very effective. Also, if people are tested intensively test everybody like that, and isolate people that the tests that test the positive, and everybody that has been in contact with these people over the last week. For instance, this would generate a curve of low mortality like the one that we see here. So this result from the Harvard group is means that just short time interventions will generate second wave and that's it. You need long time interventions and this can be of several kinds. I'm not saying you need to stay at home forever, but you need to have some way of having having interventions over the time and the one way of having interventions. Testing a large majority of the population and isolate people that test the positive. So that's it. And just so there are a lot of people that have been working on several aspects. So you see the number of names here is impossible to read. There are people from physics from biology from computation and medicine and working and we have we have an initiative. It's called the COVID 19 Brazil observatory. And so these people are doing a lot of things which I didn't mention everything that people are doing. And so that's it. And so thank you. Thank you for your attention. Thank you very much Roberto for the super nice talk. Are there problems? Yeah, the virus is a problem at the moment. I do have one question. Problems that are a lot of problems. Yeah, problems we do have Nicholas. Thank you for your webinar. I have a question that maybe you can comment without going into many technicalities, but I was wondering like, how should we read those error bars? Like, more or less like, for me that I'm not an expert modeling or something. What type of things are keeping into account whenever you have these error bars when you present something. Two things. Two things. Two main things. First, your parameters are not precise. Okay, you have a model as parameters and activity and time to time of recovery and so on. All of this is our probability distributions not not not really constant. So this generates the four error bars probability distribution. Second and more difficult than just just looking for the sensitivity to your parameters is the fact that you don't know your state your initial state is unknown. And that that's a problem. That's a problem you don't know your initial state so if you if you go for a problem for things with differential equations or even other other kind of models. So you have two sources. One, you don't know the parameters. Second, you don't know the initial state. I mean, it's not that you don't know anything about it. You know, but you have a probability distribution for your initial state also. So, you have, you have this two sources are of of errors. They are a problem. And that's why it's so this is a little bit like meteorology. Okay, you want to it's it's not it's not a. It's not a key it exists in that system with time dependent precision and with time dependency being whatever you want. And, and the problem is, at a certain point you make prediction with error bars that says that you could have a say 1000 or a million of people infected, which means nothing, nothing. This is not informative for any, any people, any person in it at the government or trying to take a decision and the person wants to know, will I have a lot of people dead or not. If I say you have 10 people that they say okay, that's normal. You say I have a million people that it's very important for this person. And if your model just says between 10 and one million in the model says nothing. I don't have questions. I actually have one. If you, Robert, if you could go back to your slide. Okay. Share screen. Okay. Go back where maybe to slide back. I think slide 12. I don't know the number of the that one. So, in your first scenario, the, the one course point to 40 weeks. There's a case where the number of cases increases with time. I mean, it's like the black or red Corb. Yes, there, there are, there are cases that can increase again because there's a replenishment of susceptibles due to the birth of people. That are given birth. Okay, that's like the worst case scenario, right? This is the scenario. Yeah, that's, I don't think I mean this, this is a little bit the frightening scenario in the sense that this is pretty much like, like, like influenza like like flu. It's, it's not that it's different in the sense that you had, you don't have long time immunity because because the, the, the, the virus has such a high, high mutation rate that you everybody actually does not have immunity for more than one year. So then you get this kind of scenario. Okay, so this would be the flu scenario like a thing for, for COVID but you know, COVID is 20 or 30 times more deadly than, than flu, which would be a disaster. But I mean, I'm not saying that this is necessarily the only scenario. I mean, this is one possible scenario but not necessarily the one that will happen. And we, but, but we are really in the dark about immunity. Nobody knows because we have this epidemic for three months. So people don't know if the people will continue to be immune or not. No idea. No idea though. Okay, thanks. So there's a question from public, I think from Diego Restrepo. So he's asking in practice how well your models have been predicting the evolution of the epidemic in Brazil. So that's a point that we, we have not completed the work that that's why I didn't show you the full things. Okay. This kind of model. I didn't show you the full results. Because, you know, with this kind of model with this in certainties and parameters and initial conditions so fitting model is difficult. So it's easy to say my, my model is a good model because my predictions are consistent with the, with, with what to observe it because of the error bars, but well this is, your error bars are very, very, very large and anything is consistent. So, we're still working on that on it's not our models and I mean, all models are more like that, more or less like that. Okay. And so we don't have the results at this point. And then you have to ask yourself for which locality are you doing the model because we are now working for the municipality of some power. So the first results of the model are pretty okay. But let's see because I mean we can set the model to what is known now but let's see what the predictions will be confirmed or not. So we need some months and months are true to know if the predictions will be confirmed and so on. And this is for the specific case of the municipality of some public why why not why not apply this to anywhere, because if you apply it on into the confirmed case, which is the public data, which you have for anywhere in Brazil or any state in Brazil, this will give you nothing because the confirmed cases are not the representative of the number of actual cases so you need the now casting procedure in order to initialize your model. So and we only have this first citizen Tom. Okay, thanks. Another question from the audience, this time from Omar Suarez is asking how our environment and the environmental variables included in the simulation of these models. So they are not included explicitly. But you know when you do the fitting variables like the transmissibility of the disease or the transmissibility could depend on the environment. Okay. And so, but transmissibility is fitted, because you don't have the absolute value of that. So you are fitting the environmental variable in this case. Now, for the model that I showed from the Harvard School, from Harvard Medical School, the last model. They assume seasonality, which is an environmental bear. But I mean, that's like, like the scenario like, let's say it's seasonal. Nobody knows because we didn't have even one season. Okay. You cannot know with certainty you can try to infer from other diseases. Like there are all other kinds of coronavirus and they're called beta coronaviruses, which circulated and around and so on, which has some seasonality, not very strong. So but just this coronavirus will it be seasonal or not. No way to know. No way to know because you don't have any not even one season you have three months. For three months that that's it. So you don't know the effect of the environment. Yeah. Maybe last question. So, first of all, very nice to talk is very explaining how how to model and all the difficulties that has, in fact, to try to make any prediction on the in this case, but I was wondering in the because this is a stuff that most of the government are using like an excuse to why not to make a full down, because it's in that if everybody make a lockdown, the, the, all these epidemics should pass quite fast, let's say, just like a nightly speaking. But most of the government, they all the time they use the excuse that is the because of the economical impact. Is that a way or is it a way to to try to include in the model this economic impact of to have these people out of the community because government they just based on no it's the economy so all the people has to go outside and we don't have to get infected because the economy has to continue. This is the kind of the version of many point that you gave was like this month until the Prime Minister got infected kind of they were pushing to to here in Chile sometime there is a mix opinion for the government making like with like a blind test to make politician politics to try to So, yeah. There are attempts to include economical variables into epidemiological models. It's not trivial and we have been discussing this with this consortium this co mold. And that's more variables and more unknown parameters. Yeah, I know. But what for sure. If you are at the start of an exponential growth. If you do anything. You get a million of people dead in Brazil in some, some, some weeks so so that whatever the economic car is. You have to, I mean, you have to take action. Now, serious debate, which is not obviously the case of Brazil because you know, situations. But seriously, but for instance in Europe like in Germany or follow model as the German situation is about obviously how do we get out of this thing. Okay, so the population will still be susceptible because we are in home we didn't have the infection. I'm still susceptible and I think just lose out the all I mean just lose the the the the interventions I go how I go on the streets and so on. The buyers will say okay nice new, new people for me. Okay, so we'll be a mess and will be just really bad. Okay, so how how should we go out of the thing. Well, the favorite policies that I've been discussed it is like the Korean way the Korean way is you just test people. But I mean this means intensive testing, lots of tests, putting up a system of testing people. It's a kind of very intensive thing. And then you have and then also issuing immunity cars like I mean if you have had that you have been tested, you will have mark on your on your car. Okay, positive, negative, positive, you are immune and so on, which would then decide what what kind of activities you would be allowed to do and so on. But it's, you know, this is this is a very complicated thing. It's not an easy thing to do to put up. And in countries like Brazil, this is seems seems crazy because you know, what the time being in Brazil if you want that we are in a soft lockdown and like in some problems, Rio de Janeiro and other cities. It's a soft thing because you are not you're not you can go out, you can do whatever you want actually. Okay, but the commerce is closed so maybe you don't go out because there's nothing to do outside but you can go out. Now, in such a situation, there has been no attempt to build a way of getting out of this situation so we are stuck with the situation. We are stuck and economically this is obviously very, very, very difficult situation. But you have to build a way of getting out without having a super epidemic, because if you just say now, okay, it's over. You go out, you have an epidemic, you have again a million of people there. So that's the situation. Yeah, it's complicated. No, it's very complicated. No, please go ahead. One more question because since in my case, I live in a small city from respect with the capital of Chile that is where most of the cases are but we do have cases here locally. You know, how this, this mobilization in terms of the points that when you were presenting the different models, sIR model and so on, should be also made locally in each city, I guess, no, not because sometimes I can take the whole country like all the population is mixed together, kind of. So, yes. Actually, collaboration with some of those people that were on my list on the at the end, arguing network theory and not with the airplanes but with roads. So, to assess vulnerability of cities because maybe you are a small city which is not connected to anything, then you are not very vulnerable. If you're connected to a lot of things you are more vulnerable. So, using network theory, network metrics can be a way to access vulnerability. The second layer of analysis is which is how many hostile bad you have. So, maybe you are in a place that it's likely to be to take some time for have the epidemic. But maybe you don't have bad. So then there's the second layer of vulnerability says okay you're in that situation. There are these two things and one thing is this is the spread distribution of the spacious distribution through the road and two movement of people in a certain region so we have made this kind of analysis for the status and power and for the north eastern part of Brazil. So, you'll see the hubs and so on and where are the next cities that you're expecting to have the epidemic and so on. You can get others and all of that you can do this. And then you have the second layer of okay. There will be a certain city, but okay this city has a lot of bad. So, you don't expect to have an overwhelming problem there, but could be also the contrary. For instance, in the St. Paulo State we have discovered that some cities are very far apart from the capital, and which have no cases at all at this moment of time. Well, if nobody does anything or there should be cases because, well, some, unless you just shut down the, I mean, completely the transportation system. And then there will be a case and the case will be transmitted. It's highly effective. And then then you look at this places and I say okay but this places can be a problem because even if it will take time to get the epidemic there. It will have very bad, very high, very strong consequences because there are no, no hospital. Okay, thanks. Let me take a very last question. This one comes from Mario. He's asking about vaccination and whether they're treated as immunity in the model. I didn't understand whether there are treated as immunity in the people that got immune to the virus in the model. So, in the model we are working for, Brazil immunity is lifelong, but obviously the model is meant to model the next months. So if you want to go for a long time, thank you have to have something like the Harvard model, then you can say okay, I don't know immunity. Okay, so it is completely open, the natural immunity of people. How long will it take? Okay, then I have a vaccine. Okay, if I have a vaccine like the ones that we have for the child disease and so on, then you are okay, then you are immune and that's fine, that's problem solved. But maybe you have a vaccine with a certain percentage of effectiveness and maybe immunity conferred by the vaccine is not lifelong. So, if you look, if you talk about, for instance, vaccines today are miscellaneous. You know, you have to go to vaccination for your kids and then they don't happen. The disease never in their life. It's fabulous. But this is also a result of many years of research from going from something which has an effectivity of say 60%, 70% and gives you immunity over five years to something which actually has a very good coverage and lifelong immunity. So there's this research to be done. It's kind of not the kind of research that we do because there's this research in microbiology and in biology. But this is likely to take time. And it's not that there will not be a vaccine. Maybe there's a vaccine next year. What kind of vaccine? We have a vaccine, lifelong immunity. How long will the immunity be built? So you will have to have tests and you know, in order to access, just to make an assessment of how long is the immunity conferred by a vaccine. And you have to follow a cohort of people over a lot of years. And why are you doing this? You are completely in the black and you don't know. Unknown. And that's the way it is. And it's not only for COVID, obviously. Okay, thank you very much, Roberto. Welcome and thank you for the opportunity to talk to you. And so one more thing. So next week we will not have a webinar, but in two weeks time we'll have a look at it in early talking, maybe about action physics, I think. So we're, we're back to, to, to hire this piece. But okay. Thank you very much, Roberto. We can create a day. Thank you for the, I mean, for the, for the same. Thank you. All the audience and for the invitation. Thank you very much. Goodbye. Bye. Hasta la vista.