 Good morning to the other people from all around the world. I'll let me start by sharing my screen and OK. No, let me share. Let's go to the presentation. So this is actually the second part, models of disease and ecology. And as you may remember, today is devoted to the general topic of macro parasites, brief introduction to the basics. And then I will illustrate our work on schistosomiasis in Senegal. So you may remember this slide where I introduced micro and macro parasites, the difference in terms of modeling and the micro parasites with respect to micro are characterized by lifetime, which is comparable to their host's lifetime. So their dynamics cannot be neglected. Also, of course, they are larger macro parasites. So you can actually count them in a way in many cases. So you can look at the load of the parasites inside each host and count the number of parasites. Now, the life cycles I am going to consider, well, the one of the left is the simple cycle. For instance, the roundworm or nematode, and you see that that pig is ingesting the eggs. And then the eggs will develop inside the pig. And then they will become adult. And they would reduce more eggs. And then these eggs will be defecated in the environment. And then the infection goes on that way with another pig eating the eggs, and so on and so on. On the right, you have a more complex life cycle, which is actually also the life cycle of schistosomiasis, which I am going to speak later on. Because in that case, you have two hosts. So you have the human host, or in this case, the cattle. And in that case, there is a stage called the circarial stage. And this stage will penetrate, in general, the skin of the host. So we'll get inside the host and then, again, the adults will develop inside the host. And then they will reproduce inside the host, the main host, I mean, in a way. And then the eggs will be produced. These eggs will actually hatch and produce another stage with a called myrazidium. And this myrazidium will actually infect another host, a snail, in this case, in the case of fasciolopsis booski. And so then there are other stages inside the snails. And then finally, the snails will release the myrazidia and the circaria. And then the cycle will go on. But without the snails, the disease cannot establish. And on the other hand, without the cattle, without the human host, the disease cannot establish a snail either. So they are necessary. Both hosts are necessary. And we will first start, obviously, from the simple life cycle. And then we will proceed to the more complex life cycle. So first of all, I told you that in macroparasitics, in many cases, you can count them. And here you see, for example, for instance, the perch. And this is a tapeworm inside the perch. And you can count the burden. So some of the perches have zero parasites, some have one parasite, some have two parasites, and so on and so on. OK. Now, you can do the same with a completely different parasite. In this case, it is a fly, a stinging fly. And these are the reindeer. And of course, in this case, the number of parasites roast is much larger. And so, well, what you do, you do a histogram. And again, you see that there is some reindeer without any parasite. And then, OK, you bin the number of parasites in your histogram. Here is instead a starling. And in that case, it is a nematode. And also, it is a nematode for the frogs. And you see that the histogram of the parasite burden, it's quite different. So I mean, the shape, the kind of shape. And in some cases, you see, for instance, typically in the case of frog, what we call an over-despiration with a few holes carrying a lot of parasites and many holes without any parasite. OK, so that typical structure of the word in many cases. So it would be nice to find a way to statistically describe this burden. And well, the first thing you might think about is, for instance, a simple binomial distribution, where are the number of parasites and you P is the probability of having a parasite, hosting a parasite. And well, the binomial distribution is correct by under what we call under-despiration. Because if we consider the mean and the variance, then the variance is smaller than the mean, smaller or equal. It is equal to the mean when you go to the limit for the number of trials going to infinity and the probability of hosting the parasite going to zero, so that n times p converges to a constant. And then you have a Poisson distribution. In the Poisson distribution, the mean is equal to the variance. But actually, in many cases, you don't have variance equal to the mean, but you have variance which is larger than the mean. That's why usually the most appropriate distribution is the negative binomial. It is more flexible. Of course, you have one more parameter with respect to the binomial, or if you like, and the Poisson distribution. And it is this parameter k, which is a parameter of clumping. And the smaller is k, and the larger the over-despiration. Because in fact, you can prove that the variance is equal to the mean plus the square of the mean divided by this parameter k. So you see that if this parameter is very large, practically you have Poisson distribution with variance equal to the mean. Then with k equal to 5, you have an aggregated distribution. And you may remember that, for instance, well, I say, this one is kind of aggregated, k equal to 1, in this case. And well, for instance, k is more than 1. You have a highly aggregated distribution. So it is very popular, let's say, to use a negative binomial distribution as a flexible distribution with just two parameters. If you adjust these two parameters, you can reasonably fit the parasite load. And that would be useful for the simple model I am going to show to you. So it is a simple model where you have a simple cycle where you have the host number or the host density, if you like, number, for instance, of pigs per square kilometer or number of deer per square kilometer. And p is the allowed parasite number or density, if you like. Of course, the parasite burden, what I once called is p divided by h in the average. So total number of parasites divided by total number of hosts. And that will give you the average burden. But actually, each host might have a different, might host a different number of parasites, 0, 1, 2, 3, et cetera. So now let me also introduce the number of free living stages, for instance, larvae or eggs, if you like. And then we can write down two differential equations, one for the host and one for the parasite. And then the one for the host will be the birth rate minus the death rate times the host. No disease. But if there is a disease, then what happens? Well, let's first suppose that if you carry a lot of parasites, your mortality is larger. So let me call alpha the additional mortality goes by one parasite. So if you carry i parasite, there is an extra mortality alpha i. Now, if you consider the whole population and you consider the distribution, pi probability that one host carries i parasites, you see that this is actually the average mortality. And then you multiply by h. And then you have the dynamics for the host. As for the parasites, well, each host might ingest a certain number of larvae. Then the parasite will have their own, let's say, intrinsic natural death rate. But there's another thing. Any time a host dies, also all the parasites that are carried by the host will also die. And so you have to consider more mu plus some alpha i pi. And that it should be included in this equation. Now, notice that here you multiply by i pi. Because whenever a host dies, all the i parasites that are hosted by that host will also die. OK, so that's the equation. Now, OK, we can now calculate the parasite load. Well, pi divided by h is the mean. And then you may note that if you develop this term now, it involves also the mean of the square of the i square. Well, so you may remember that this is the square of the mean plus the variance. Now, if we assume negative binomial, then the square of the mean plus variance can actually derive from the formula that I showed to you before. And so it turns out that it is p divided by h plus k plus 1 divided by k. k, remember, is the clumping parameter. And when the clumping parameter is low, then there is a lot of over-expulsion. Time p squared divided by h squared. So to make it short, you can get Anderson and May's model provided you also introduce a static equation for the larvae where if there are many adult parasites, they will produce a lot of larvae. But on the other hand, if there are a lot of hosts around, they will ingest the larvae. And therefore, the number of larvae in the environment will be lower. Actually, you can find this kind of static relationship. If you also add another differential equation for the larvae dynamics, then you assume that the larvae dynamics is so fast that in practice, you can use the slow, fast approach, and then, OK, you get a static relationship for the larvae. Now, if you plug everything in, you get a celebrated Anderson and May's model, which is, in practice, a simple system of two differential equations, h and p, which is closed under the hypothesis that the larvae describe this relationship and that the distribution of the parasite burden actually follows a negative binomial distribution. Now, if you study the system of differential equation as usual, for instance, by drawing the eyes of clients or linearizing whatever you want, then you find out that, again, you can define a basic reproduction number. And in a way, the recipe is always the same. So 1 divided by m plus mu plus alpha, this is the residence time in the infectious stage. And this actually is the number of, say, parasites that are ingested in unit time, OK? Now, as usual, r naught equal to 1 marks a transcritical bifurcation, because these green eyes of client can be shaped in this way. And this is, of course, the case of r naught larger than 1. So there is an endemic equilibrium, which is stable. But then, of course, you can also be shaped in this way, that eyes of client. In that case, r naught is smaller than 1. So, again, we see a simple transcritical bifurcation with r naught equal to 1 marking the boundary when you switch. You have a bifurcation at r naught equal to 1. Now, what is interesting that you might now say, well, that is true if the parasites are going to affect the mortality of their hosts. That is a very interesting study. And maybe you remember that I introduced that show the red grouse to you at the very beginning of part 1. And my good friends, Andy Dobson and Pete Hudson, now, they observe that actually the red grouse have an oscillatory behavior. There's an oscillatory behavior. OK. And they carry these intestinal paracetricostroendular stainless. Now, how is it possible? How is it possible to describe such a behavior? Because in this case, you do not get any permanent oscillation. Now, what they observe, actually, is that the parasites do not affect so much the mortality. They affect the fertility, the reproductive success of the red grouse. So let me now introduce that kind of hypothesis. And you see that in this case, mortality is not affected by the parasites, but it is the fertility new, which is actually decreased. And the larger the number of parasites that one host carries and the larger the decrease in fertility. And then, of course, the parasite will die from their own mortality, but they will also die when the host dies. And the host dies with mortality in the mu, which is the interesting mortality. Now, if you go to these equations, these equations actually appear, in a way, simpler with respect to the previous one. Notice that here you don't have to assume any negative binomial. OK. You still have to assume that the larvae are described by the static relationship. When you study this very simple system of equation, what you get is something like that. And again, you know, this is an isocline. And this is the other locus with the other isoclines. And fine. OK. Now, the expression for or not is this one. Now, you don't have alpha, which was the mortality in use by the parasites and the host. What is interesting, if you look at the number of hosts at the equilibrium, OK. Now, if R0 is larger than 1, you have anyway an intersection. Of course, R0 might be smaller than 1. If R0 is smaller than 1, this isocline is actually placed here. So you don't have any intersection, any intersection. So you don't have a known trivial equilibrium. So R0 less than 1. And you have only the disease-free equilibrium. As usual, and R0 equal to 1, there is a transcritical bifurcation. When these H stars are exactly equal to K, then you have transcritical bifurcation. But what is interesting, that if H star is actually smaller, much smaller than K, and you can actually prove that, that when it is smaller than K divided by 2, you have a HOPF bifurcation. So this equilibrium is no longer asymptotically stable. It becomes unstable and surrounded by a limit cycle. So you see here what I told you that you can have HOPF bifurcation in this case. Now, note that K, the carrying capacity of the density of the host, as usual, is influencing R0. So the more dense the population, the larger the carrying capacity and the larger R0. So you can make R0 larger than 1. And you have an endemic disease. Pick it up, OK. So the epidemics can, reasonable, easily establish when the population is very high. Think of cattle raising or pig raising in a farm. And so they are there. So of course, it's easy to get a disease there. But if you look at the H star, H does not depend carry capacity. So R0 can be larger than 1. But it very much depends on the parasite fertility. So for increasing parasite fertility, you see H star is decreasing. And therefore, you have first a transcritica and then a HOPF bifurcation. OK. Now, it's time to go to Schistosomiasis. No, first, let me stop and ask whether there are questions regarding this introduction. So there are currently no questions in the chat. But if anyone, yes, there is a question by Alfonso, please. Alfonso. Yeah. Hello. My question is related with the if there are ecological explanation behind the fact that the parasite burden is distributed like a negative binomial variable. Well, no. I would say that, well, as far as I know, maybe I'm wrong. It's mostly an empirical remark that the negative. We know that in most cases, you have this over-despiration. And so the negative binomial is, let's say, the simplest distribution that can describe over-despiration. Well, let's say that in a way like the story of the super spreaders that like the people that are super spreading the same way you might have supercharged, supercharged hosts, well, it also depends on your immune system, of course. Because when you count the parasites, the adult parasite that you count. And there are ways. Either you sacrifice the host and go and see how many parasites it is carrying, OK, or you purge, if it is an intestine parasite, you purge. So clearly, the adult also depends on the reaction of your immune system. So if your immune system is very, very active, so you might ingest a lot out of eggs, but the immune system is actually recognizing that there is something going wrong and it's react. And well, we know that the immune system in the different individuals is pointing in a very different way. So I don't know whether this is an explanation. I would say that anyway, it's mostly an empirical observation. You have many different cases like the one I showed to you at the very beginning, OK? And you say, well, can I find something which is so flexible as to describe all these possible cases? In fact, you see that you go from K equal to 6 to K equal to 1 to K equal to 0.35 to K equal to 0.38. And so with a negative randomity in describing all this variation of OK, I hope I answered your question. Yes, I think that this I have another question and it's related with the we are going to talk about another models that account for different stages in the life cycle of the parasite more explicitly or? Yes. Because why is this? OK, you mean that? No, I mean, schistosomiasis is even more complex. So I'm starting from the simple life cycle, this one on the right, on the left. And then now we are proceeding to the actual life cycle of schistosomiasis where you have two different hosts. OK, and then you can have even more complex parasite life cycles with three hosts. And well, OK, I think that Professor Rinaldo, for instance, might speak of proliferative kidney disease in his lecture, where the life cycle is even a bit more complex. OK. Thank you. Oh, OK, so can I proceed to schistosomiasis then? I think yes. Yes, there are no other questions. Yeah, please go ahead. So schistosomiasis is actually affecting many parts of the world, mainly sub-Saharan Africa, a little bit in the Middle East and Far East and South America. It affects more than 700 million people, more than seven countries, at least potentially because they live in endemic areas. More than 200 million people are affected worldwide. And every year there are several tens of thousands of deaths that might be ascribed to schistosomiasis. And 90% of global infections are found in sub-Saharan Africa. Now, sorry, before going into that, now let me first of all show the schistosomia life cycle. And it is very similar to the one I showed to you for fascialopsis. Well, considering humans and then humans are actually infected because they simply contact infested water infected with sulcaria. So the sulcaria can actually penetrate through the skin. And then the adult parasites will develop inside humans. OK. And they mate, actually, so you have male and female, so you need a pair of actually parasites. And these will actually produce schistosome X. And the schistosome X will develop into myrosedia. This myrosedia will infect snails of different genera, bionfolaria, bulinus, oncomilania. So oncomilania is typical of schistosomiasis in the Far East. And also the schistosomia is a little bit different. So you have schistosomia, Japanese schistosomia, monsonia, et cetera, schistosomia, matomium. And the humans mainly will suffer urogenital or intestinal problems. Usually it is not deadly disease per se, but anyway it can contribute to lethality very strongly. You can be infected several times. It's not that if you get the disease that you will not get the disease again. You can get the disease. So you can get infected and re-infected. The treatment is simple, but for poor countries, although it is simple, it might be expensive. And in practice, you have to take a very future project one time. Now we have mainly started the problem of schistosomiasis in Senegal and Burkina Faso. We started that a few years ago with the Tiva Professor Rinaldo and also with our friends in Stanford and then other French people working in Senegal. I will mainly talk of Senegal today. So first of all, let me show the local model that you can make. And then we will proceed to consider a more complicated model where you have networks of nodes. And first of all, what's important that here you have the mixture of the two approaches. You can recognize the negative binomial approach of being the mortality due to the parasites carried by the hosts. But now you couple that with the snails. And in the case of the snails, you can treat that as a microparasitic disease. So you divide the snails into susceptible snails, exposed snails. So these are infected, but not yet infectious. And infectious snails. And so then you come out with a five differential equation where you have a number of human hosts, a number of adult parasites, the density of susceptible snails, the density of exposed snails, and the density of infectious snails. Now, I'm sorry. And then again, you can make an approximation that we made, the approximation we made in this paper, that the number of sarcaria, that's a sarcaria of very fast dynamics, can suppose that the number of sarcaria is simply proportional to the number of infectious snails. And the same for myrocedia, that myrocedia is simply proportional to the number of adult parasites. And if you do a bifurcation diagram, OK, you find out that, after all, what you can get is something which is very similar to what I showed to you. But for the case in which the parasite was affecting the reproductive success. In this case, no, the parasite is actually affecting the mortality of humans. But in this case, and this is more complicated case with the schistosomiasis model, then you have transcritical bifurcation and house bifurcation. You can study that in a two-parameter space with human infection rate and the snail infection rate with two parameters. So in this case, you do the bifurcation study with pet to both parameters. And again, you get a transcritical bifurcation. So increase the human infection rate and increase the infection rate and go through it, transcritical bifurcation. You further increase both infection rates and then you have hop bifurcation with this kind of limits. But the most interesting case is when you consider now a more realistic, well, actually, this is partially realistic, meaning that the value of the parameter would tune on the Senegal and Burkina Faso case. But the most challenging case came out for us in Senegal when this challenge D4D by Orange and Sonatal data for development was launched. And in this case, Orange is the mobile phone provider, mobile phone connection provider. And they put anonymized data on phone calls available to scientists and asked them, OK, choose a problem of social importance that you might want to solve using our data. And then we decided to use those data for developing a model for schistosomiasis in Senegal. You see the schistosomiasis. You can find the urogenic schistosomiasis a little bit all over Senegal. And especially in the areas, especially in the rural areas, clearly you're more subject to schistosomiasis when you live close to water. So agricultural areas, you're more exposed to schistosomiasis. Now, so when you consider the network structure of the model, what do you need? Well, you need a high-resolution population density. That's available by a geographical information systems. Then a human mobility flux system that has been made available in a way by starting the phone calls in year 2013. Then people living in rural settings and rivers. These are mostly ephemeral rivers. And then, of course, the data on the prevalence of urogenic schistosomiasis. Now, first of all, we had to study human mobility from cell phone data. So it's big data. There are about 9 million solatile mobile phone users. And well, at the beginning, we're not given 9 million, actually 9 million users, but a smaller sample. And then because we were winning the challenge for health, actually, later on, they provided us with 9 million, really 9 million mobile phone users. Not to name, of course, they are anonymized and they're collected from one year. And so, of course, by algorithm, you can actually deduct mobility in a way. I don't go into the details. You can find the details in the pen and paper. But it's not very much used. Well, of course, now remember one thing. These are mobile. These are not smartphone in general. So they don't have GPS, global positioning system. But you know in a way the position of the people by knowing the antenna to which they are connected in a certain moment. Now, these are the results of study mobility. So, for instance, it's very clear there are two big festivals where the Senegalese go to two cities. Oh, I'm sorry. The Grama Gal de Tuba and the Cazula Job. And indeed, the very precise period. OK. And so you can really find them easily. So, for instance, this is mobility from San Luis, a region that we have started, which we have to hear. And of course, most of the people stay home within region mobility. But then, OK, they can move to other departments. And here you see the Gamut of Tiva 1, Cazula Job, and the Grama Gal de Tuba. OK. So we are rather confident that we can find mobility in this way. Now, if you look at the model, it is similar to the local model I showed to you. But it's even more complicated because now we are also modeling Cercaria and Myrosidia in each location I. And not only that, but the host in location I can, they are also divided into a host carrying zero parasite, a certain number of parasites, the maximum number of parasites. So actually, it's more complicated with host having zero parasite and then being infected and getting one more parasite and so on and so on. And then, OK, the core, in a way, I'm sorry, the core, of course, is the human mobility matrix because the disease is spread by people moving and people moving. And therefore, they can have adult parasite and then release the Myrosidia somewhere else where they go. Or they go somewhere else, get infected in the place where they do not leave usually and then come back and infect their home place. So OK, so it's complicated now because the force of infection and the rate of freshwater contamination will depend on that matrix Q. And so you have Qij and Qji. I go to j or coming back from j and going to i. So exporting or importing the disease. So you can now round that model. Of course, part of the parameters are actually known in a way, measured. And some of these parameters have to be estimated. And so here are the results of calibrations performed against the reported prevalence in each region. And here is, in a way, the fit. These are the prevalence data. These are the prevalence calculated by the model. Of course, it worked perfectly to stay on the 45 degrees line. Anyway, it's a reasonably good fit. Now, you can do a sensitivity analysis with respect to the mobility of people. By mobile people, we mean the percentage of people that might move away from their own region. Of course, most of the people stay in their own region. One of the 14 regions in which you can divide Senegal, administrative region. And you see that the prevalence corresponding to the mobility that we estimated is actually more or less at the minimum. And then the average parasite burden is about seven parasites per human. That's the average parasite burden. Now, when you have a model like that, then you can say, well, what can I do? Can I prevent the disease in some way? And there are different intervention strategies that you can think of. So first of all, you might have so-called wash strategies, water, sanitation, and hygiene. OK. And then information, education, and communication strategies. So you say, children, please be aware. Don't go play in that river in that canal because that canal might be infested by snails. Snails will release a carriander. Carriander can penetrate your skin. Or if you go there, wear boots. For instance, it's difficult to think that children wear boots and gloves. But anyway. OK. And then you can distinguish between what we call untargeted strategies. So you try to ameliorate sanitation everywhere in Senegal. Or you can have targeted strategies that might be prevalent, targeted, where the prevalence is larger than you put more sanitation or risk targeted. So for instance, this stat is the rural and water risk cars there, maybe, or depending on that. And you see that for wash strategies, it is better to have targeted strategies. While for information, education, and communication were rather intuitive, untargeted strategies. Those strategies that are aimed at informing people all over the Senegal, in a way, are better in terms of reducing the average and the maximum prevalence. Now give me five more minutes to say that then we have also started with people, friends at Stanford, who carry a program on the region of San Luis. Which is located here near the Senegal River, north of the part of Senegal, at the border with Mauritania. And that we are carrying on that program. It's also going to be financed by Politecnico de Milano. And there are a lot of people who are actually collaborating on a tool which also spent a period with us in Politecnico, that went back to, and then master students. And then, for instance, Gilles Rivaud, the epidemiologist, who's actually doing the work in Senegal, in the Indian law, and the mine, and so on. Oh, OK. OK, so by the way, that is Professor Kanzangrandi in Senegal. He's wearing gloves and boots, of course. And this is Lameen, I think, I'm not sure. OK, they are wearing boots and gloves, because it'd be very dangerous if you go there, because you see the small snails, these are the small snails that are releasing the sulcaria. Now, in this case, we went more in detail, because you see there are villages. OK, the triangles. Phone antennas, they're not all located in villages. Some of them are located in between the villages. And then the sample points, and then the water point, the water points. So we developed a more complicated model where you have several connection matrices, because you have some matrices describing the probability that the snails, the sulcaria, or a mericidium moves between any two water points using the ideological network, which you didn't use for the whole Senegal, actually. The antenna to antenna mobility matrix, then another metric is describing the village to antenna movement. Well, not really movement, but you see you have to decide that that village is actually connected to that antenna or another antenna. And then another metric is describing the proximity of water points to antennas. OK, so it's complicated. So we introduce all that. And then we, so this model now includes several transportation mechanisms. And we found a reasonably good agreement with prevalence data in people. Unfortunately, prevalence can be very high all over, especially along the Duse Lake and also the Canala and then the river. It can mean in some places the children might have, the 80% of the children might have blood in their urine. So it's really a big problem in rural areas. And I hope that in this way we have small contributed to the fight against schistosomiasis. And well, I think that's the end of my time. But of course, if there are questions I'm willing to answer. And of course, I would like to answer your questions. Yes, so there is indeed a question from the chat. How do you account for the infection occurring somewhere else, but reported in the patient home? For instance, infection happening in San Luis, but reported in the car? No, the infection that are reported, the infection, of course, are reported at home. Because these are actually where we remember the so-called sanitary department. And these are the regions. So of course, usually you get sick at home. I mean, if you travel, then OK, if I make that approximation. So you report home, but then if you go to the, of course, you can get what you see. You are, each host stays in a location, I, which is the home. And the home actually, how do you find the home of a phone user? Well, usually most of the time, the phone calls at evening most frequent phone calls at evening are usually attributed to home. So you can say one of those nine million users, that the home is this one. And then usually he or she gets sick at home. OK, that's how they're attributed to home. But they can get the infection somewhere else. So they might go somewhere else, be infested by Sarcaria, somewhere else, as they come home. And well, usually they release MiraSidia in their own water body or sewer system. OK, so that's the approximation. Yes, there is a partially related question, which is in the last part, how do you account for underreporting, underreporting in prevalence data? Well, OK, the data on prevalence were directly collected by Gilry Buu. OK, so it was called by Gile and Lamin. Gile and Lamin were actually conducting their own, at least in St. Louis, they conducted their own campaign looking at prevalence. So the prevalence I have shown to you, this one is actually the prevalence that we're measuring through. We are rather, well, hopefully underreporting is not high, but this one is in the region. Any other questions? Yes. There is no other question in the chat. If anyone has any question, please raise hand with the tool. You are, I'm sure, now familiar with. OK, I don't think there is any other question. Oh. Everything is very clear or very obscure. There is another question about how, I try to interpret it, is how did you infer mobility from the phone record? OK, well, first of all, as I told you, OK, now there are very, very many algorithms around. You would reduce mobility from phone calls. Now, of course, if these were smartphones and the GPS were on the global positioning system, that would be an way easy to like. In this case, unfortunately, that you don't have orders to use a smartphone, but you can use a normal or an M, maybe you have a smartphone, but you don't switch on the GPS, the global positioning system, because you don't want to be located in any minute of your life. So in this case, it is the antennas that we know. So we know that one of the users at a certain precise moment was connected to a certain antenna. And of course, the density of the antenna is not the same all over Senegal and not all over Italy or over France or everywhere, because of course, there are more antennas in urban settings and fewer antennas in a rural setting. So for instance, if you go to San Luis, these are the location of the antennas. So you see that sometimes they are close to a village and sometimes they're not even close to a village. Also, it might be possible that there are many antennas at the border with Mauritania. That probably because they are trying to not have people connected to antennas in Mauritania or something like that. Anyway, so first of all, there's a problem that you have to attribute antennas to villages, for instance. OK, you can do that by usual algorithms that are also used by hydrologists where they have to reconstruct, for instance, the rain precipitation and so on. So for instance, they use the polygon method or something like that. OK, first problem. Then you can attribute home to the place, or say the antenna and then the village, where you connect most frequently in the evening. Get that the assumption. OK. And then of course, you can reconstruct. For a certain user, you can extract the different antennas through which the user is going at different times. OK. So home and then these guys stay usually here. And then, well, I will see that in correspondence with the grandma gal, the tuba, he's there. OK, because using the phone and that that phone is not connected to the home antenna, but it is connected to the antenna closed to the grandma gal, the tuba. OK. And then here, she will come back home. OK. And therefore, this is the way that you can reconstruct this or this. And then of course, we because and then took the averages to describe the yearly mobility in a way. But you can do more than that. You might round the model, not on a yearly basis, but also model on a daily basis. I don't know if it would make sense, because it would be too huge. And the epidemiological data are not so detailed. OK. Hope I am sorry. I think it's time for the next speaker problem. Yes, I think we are perfect in time. So thanks again to Marino Gatto for giving this fantastic lecture. So next lecture is going to be about, again, models in disease ecology, but applied to COVID-19. So it will be on Wednesday. That's right, yeah. Yes, let me check on. Yes, it will be on Wednesday to 30 Italian time. So thanks again, Marino, and what we're going to do is to take.