Upgrading Epidemiological Models into War Models

Hello. This presentation is titled Upgrading Epidemiological Models into War Models. My name is Anton Antonov, I'm a long time Mathematica user and I'm a senior research scientist. This is the outline of the talk we're going to show basic analogy between epidemic and warm modeling. I'm going to very quickly model moving from Lanchester combat models to urban warfare modeling. And so there are a variety of additional elements to discuss and hopefully they'll make sense when I go through it. I have changed the presentation a little bit and from the proclaimed abstract because, well, yeah, there are decades in which nothing happens and there are weeks in which decades happen. And I think it's more interesting to discuss the material here. In this presentation. There are three panels I'm going to be using. So this left panel is going to have a mind map. This is the mind map, sorry, this is the panel, the middle one with the presentation and the third panel is the one with some additional materials. All right, so there are a variety of topics I would like to discuss, but I'm going to skip. For example, why were we using Manchester models? What are the alternatives of those? Why industrial warfare is considered, stuff like that. There's also certain type of modeling questions like can we actually model this? Why do. Do we simulate nuclear weapons? Or why we do not, how drones change the warfare and so forth. Right. You can probably select some questions from here and if we have time, I'm going to answer some of them. All right, so first, because the title of the presentation is Upgrading Epidemiological Models. Epidemiological models, of course are strict subset of war models because war modeling could include biological warfare. And so here, this is what you see. It's a diagram which explains how, say, summarizes how say some epidemic is being handled in Covid. We had severely infected population. We had also normally infected population. They moved to recovered to also have susceptible. And we have certain beds and of course, in order, hospital beds and of course we need materials and medical supplies in order just to. In order to help the people who have been infected, we need to have sufficient. Sufficient hospital beds, people who are not engaged in the economic activity. This means that we are losing money. Of course, also say the research, the medical supplies and so forth. Right. Also requires money. So it's an interesting question, how do we follow this? How do we follow the money expenditures? There's a direct analogy with wars. In some sense, you're fighting the virus and you're your kind of soldiers, the medical personnel and your hardware is the hospital Beds and so forth. Ammunition is the medical supplies. Now if we turn this into war modeling, right, the severely symptomatic population, this is the severely wounded population who most likely is going to die, they cannot fight anymore. The lightly wanted soldiers, they might go back to the battlefield instead of. So this recovery population is basically going to be the soldiers susceptible. This is the population you'd be using to have your soldiers. This is say males within certain age limits. But some societies have a different setup for that. All right, so there are a variety of modeling elements. I'm not sure how well this MINELAB is being shown here. I'm not going to go through all of this, but I have selected certain type of modeling. I'm mostly using system dynamics modeling and there's a certain granularity level to be selected. And so is it, for example, on a battle level, is it between two countries? Is it global, Is it between multiple countries? All right, so one of the important things which I want to mention here, what I'm not modeling here, I'm not discussing how I'm model. This is nuclear war exchange. And consider this, this problem. We have only one nuclear bomb. And you want to ask, you want to answer this question, you know, given that you have only one nuclear bomb in given, in a given geographical area, where should you, should you throw that bomb in order to maximize the damage on the floor and the fauna, say from nuclear fallout, etc. That can be solved with a variety of form, variety of methods. But for example, it can be solved with finite element methods. And you have some kind of, you might have certain calibration optimization process which uses this kind of finite element simulation which is for the actual fallout, how it spreads out and et cetera. We're not doing this here. So these are the generalized Lanchester combat equations. I'm going to explain in more detail what is happening, but I would like to point out what these terms here, they are very similar to the terms in infection, diseases. So it's pretty, pretty much the same. These terms here, they correspond to guerrilla war or they're also called the Lotka Volterra terms. So what is the probability you have say two types of the two warring parties, two special forces type of teams which are in a forest or in a city and that they're chasing each other. So this is more like a guerrilla warfare. This is the local terror terms Altern. If you have a front line, you'll be using this term. And just because you have an army that might, sorry, you'll be using this term, this is the front line. And just because you have an army, it might happen that you'll be losing soldiers right through the way your weaponry is operated and etc. For example, the American Abrams M1 tank, if you're not trained how to kind of interact with it, so to speak, you might injure yourself just trying to enter in it. All right, so we have the so called Lanchester proper model which is using this local Volterra terms and we have the Osipo model which is using the, the frontline terms. Osipov is a Russian general who discovered the equations, published them one year before Lanchester. Different people, I mean from different. Basically Russians say that Osipov discovered them first. First Anglo Saxonic authors, they say, well, these equations were in the air. Whatever the case is, Osipov very importantly, he calibrated those models, those equations to battles in the first World War and some very important conclusions came out from it. Another element to kind of consider him is that in certain situations, like say for example in the Vietnam War on urban warfare, for example, you might have one of the. One of the sites is fighting, is fighting a guerrilla war, but the other side is finding a frontline. They know the front line very well. Imagine people who know the terrain very well, okay, can hide within the population very well. Then basically they basically, yeah, they having typical aim kind of fire. Right now the army which is fighting them, they basically don't know. They basically don't know where to shoot, who to shoot and so forth. All right, so moving on, I'm going to show this launches the equations. This is basic, very basic, but you know, very needed to prepare the ground of the simulations. I'm going to show this models. I'm going to show an example over the battle of Iwo Jima. So this is the island of Iwo jima. It's approximately 8 square miles, maybe around 20 kilometers I think if you use the system now. So we had approximately 70,000 soldiers, American USA soldiers and approximately 21,000 Japanese soldiers. Japanese soldiers. All of them died. Actually not all of them. Some of them were taken as prisoners of war, but they were taken as prisoners of war because they were found unconscious. So the Japanese soldiers, they really wanted to fight to the last one. This is important because it has some consequences about the modeling. This is one of the most significant battles for the United States military. It's also very well documented. Quite a lot of people have been calibrating, discussing it in a certain simulational setup. And I'm going to. This is what I'm going to do next, I'm going to find that particular notebook here in which I have. I'm going to be discussing the Evo Jima model and so how it is, how I'm using packlet called Monadic system dynamics, which is, you can see it here in the, in the, in the setup. And so what exactly is happening here? Right, So I have looked into the articles which they have discussed what is happening with the Iwo Jima landing of the United States forces. These functions here, they show how the US Military forces were present, so to speak, to the island. And this orange line shows how the army of the Japanese declined and went to zero. Right. So the articles there, they have been written like say 60, 70 years ago and. They have been calibrating theoretically. So that's very interesting. But I actually here what you see for this simulation, I'm actually using efficiency rates of the armies which are from the calib. From these calibrations, from this theoretical calibrations. It's interesting. Can we actually do it automatically? Can I do it with this framework instead of doing it theoretically, can I do it computationally using ND solve and then minimize. And this is what is happening here. Basically. I'm finding that exactly. Very little difference with this calibration process. I'm finding very little difference with the theoretical results. So what is happening here? I have taken, I have taken certain time series. This time series, there's some misleading. I'm only calibrating for the starting points and the ending points. You can see it here in this, you can see it in the distance function which I'm using here. This Euclidean distance is taking the first point and the last point. Right. So. All right, so another thing to take into account and why I'm discussing this at all. Right. So this is actually. And because I said I'm going to be discussing urban warfare because of the, the way Japanese build fortress, fortified themselves this. And they had underground tunnels. They basically fought with much greater efficiency. So you can see it in this, in this, in these terms here. Right. Basically Japanese will like say five times, six times more efficient than the Americans. 60 of this, 70,000, 70,000American soldiers. 60,000 didn't see any Japanese soldier. So Japanese they have been hiding, you know, like in the. They reduce. And so they have been operating at night and so forth. So it is a little bit like guerrilla warfare. Not guerrilla warfare, but urban warfare. And another thing, the Japanese did actually lost the battle because they were not nine times efficient, more efficient. They're only five times more efficient in the Killing of the enemy soldiers. This is the so called quadratic law which is from the Lanchester equation. And basically this phase space diagram is showing that if I change some of the elements here, basically in order to win, you need to be above this red line. So this is important because actually launches the models, they have this property. But even if you change the actual functions of efficiency, if they're kind of time dependent or something else, you still have this construction. That's not the case with the local terra terms. And here I'm going to use the opportunity to link to discuss an article of. Let me see, I think you can look at this lot of Volterra models of the Wolfram language and for example the face space portrait, it's very different. All right, so I'm going to move on. I think I spent way too much time discussing this. One of the most important extensions for this type of modeling is how do you model will to fight? And this is one of the reasons for. It's one of the problem, five reasons or 20 to say. But this is an upgrade from epidemiological modeling. But viruses, they don't, they don't negotiate with them, they don't just decide to fight, right? But most armies, most militaries, the soldiers they give up fighting after certain, certain fraction of them have died. Usually it is Usipov, he was saying that it's really 20, 25% Russian. What matter Ukrainian soldiers, they can go up to 40%. But you can see here. But this is an important ability to have. Right? And Andy solve actually supports this very nicely with the when event. And so you can see here I have made some simulation. I have plugged in some kind of numbers for the will to fight of the, of the, of the, of the, of the one of the armies A and then you know, whatever happened afterwards. All right, so let me see, I think I had some other elements here. Well, this is also incorporated these elements, right? They have been incorporated into this system dynamics mode which I've been using to do the computations. So why Evo Jima is like urban warfare this here. I mean I have my own kind of point of view on this. This table here has been generated with using large language models ChatGPT so don't trust it that much. It's somewhat, it's somewhat correct about certain things. But there are quite a lot of sources which disagree with some of the statements here. Mostly the, you know, like say the efficiency, what happened, you know, other civilians concerned, so forth. Right, whatever. So here I'm comparing the second battle of Fallujah with. In Iraq, you know, 2012, I think with Iwo Juma. And so there are quite a lot of similarities. Like think of, I mean they're basically I guess several battles like that but say more recently the battle of Bakhmut in Ukraine which happened this year I think March, March, May. All right, so one of the ways to extend this type of simulations is to use. Is to, is to do multi, multilateral confrontation simulation. That's very interesting. This means that you actually have, you're not just having two, two enemies or two warring states. You might have say multiple and they interact with, with each other in variety of ways. So I've been following a certain article which is originally. Let me see. It's in Russian but it does have a, it does have a fairly, fairly, fairly well described abstract in English. And I also translated it with, with Google Translate. So what you see this table here, it's done with Google Translate. It. It's pretty good right, the translation here. So we have different types of interaction. For example, I mean I'm not going to go through all of the interactions but you can see two parties. They can be in direct conflict. They have a standard wall. Alternatively you can have one of the parties to conduct a guerrilla war against the other. Right. We can also have a party which is coercing certain party. Right. And so forth. If this is a little bit too abstract, say portion. I mean in many ways for example with like for example in NATO alliance quite a lot of the NATO states in European Union they're more or less. We can say they were forced to. To give their weapons and ammunition to the war in Ukraine or special military operation, whatever. So well but then what they're going to be doing right after they don't have weapons and ammunition they need to buy it from the American companies which represent the military industrial complex. So this here, right this, this terms here where this combination of positive and negative type of terms they actually reflect this type of. This type of interaction between the states. It's like you know, this parasitic relationship. There's a symbiotic relationship with the so called commensalism in which means that one of the sites benefits but the other side neither benefits. Noise Its resource is being diminished. Again this here, it's, it's. It shows how the whole model can be put into this system dynamics model income My modeling function System dynamics modeling packlet. I'm sorry Monot. And what exactly we get after we do the simulations you can see in this particular case. So this is the resource of the fifth, fifth party. Right. It starts out strong but then diminishes completely due to alliances and whatever the configuration of the interaction between the different, the different sides of this conflict landscape. All right, so just a one. All right, so comprehensive modeling. That's actually I was wondering how much I should discuss this. And these are a must in some sense. They are very important to some extent the battle in the Lanchester models, very important. But even with say with COVID it was very interesting. How do you combine, how do you combine the epidemiological simulations with the economic, economic data, economic performance and whatever economic goals we can have in those in different countries. And so one of the things which I was, I was working on and hopefully I have a very handy, very handy apologies here. So I participated in a hackathon called Ver vs Virus this in Germany. Right. And the idea here is to have. To simulate different, different type of economical activity in Germany. To have this geospatial component to simulate the travel and the interaction between the different geographical regions. And knowing that, to know how people are going to be affected. So you can see we basically have this type of three dimensional waves of infections we can investigate. So then that needs to be also tied up with the actual economy, with the actual economical data. So it is an interesting question, what is the economical model you might be using? And so the reason I'm mentioning Germany is what Germany maintains a very good record of how many beds they have, how many. What is the demographic of the different people which are involved into the different industries? Age, demographic and Covid disproportionately affected the old people than the young people. So if you know, for example, certain industry, imagine your country has 500 industries. So a unit of one of the industries you choose, say housing requires a variety of some sort of a recipe from other industries. This is the so called input output analysis, right, Input output matrix. So you knowing which industries are affected in what way, you can actually simulate how this. How presumably, right, you can simulate how the industries of your countries are going to be affected. Turns out that the input output model, although it's great, it was a very certain Russian naturalized American citizen, but he was Russian originally. Leontief. He got, he got a Nobel award for it. I think it was almost immediately enthusiastically embraced by the United States government. But it's only for steady state. It actually doesn't work with this kind of shock environments. Absolutely. Analogously we can do this with war modeling. It's just instead of epidemiological terms like the Lotka volterra type of terms with say susceptible, meeting, infected and so forth. We actually have the war models and of course we have two of this. Right. We have two of these pictures, so to speak, for the two warring states. All right, so I mentioned this, but this is very serious. But the equations are huge. Right. So I actually want to mention something else. I was very quickly changed my presentation here after listening to Steven Wolfram's keynote. Yeah, large language models, extremely important. But this can. We can use large language models to do system dynamics. I'm actually quite impressed how well, system dynamics can be done using large language models. One of the more important things is that we can translate verbal descriptions into vulnerable language. The other way around language into verbal descriptions into diagrams. From diagrams you can go to vram language and so forth. Right. So your mind, which might vary, but I would like to point out that most of the time equations are wrong. Most of the time, say like 60% sometimes, often enough they're also right. They give you a good start. So this here, it's a description of such a comprehensive model. Right. If I evaluate this, we should be getting. Something is going to be getting here. Well, is this working? I'm going to move to the next slide and I'm going to show you how this moral description which I was just showing, right. This here is. Is being used to generate, to generate, generate mathematical code. I'm using the prompt code writer and I'm saying Write Wolfram language code 4, blah. And then this is the model description and then we get some kind of code. Right. Similarly, I can use this to get certain Mermaid GS diagram generated. And you can see it here. You know, it's like this is the diagram very busy. Right. So at this point this probably has finished. Yeah, we can see. I mean, this is a little bit too. Let me see. I mean, it's still generating. I'm not going to, I'm not going to interrupt, just going to move on. All right. So really do not trust large language model hallucinations about wars or about anything else for that matter. It is very interesting to actually figure out what is your balance of scaffolding or massaging prompts and descriptions. And to a degree just sit down and just do the math, so to speak by yourself. This is such an example here. In this example you can see I have this flowchart which tells how we actually do different type of large language model pipelines. And so. And very interestingly, this can be simulated very well. I mean, I basically gave this JavaScript Mermaid JSS to diagram code to ChatGPT. And I got some Mathematica code. And this mathematical code basically immediately worked. So let me find it here. Right. Immediately gave some results. All right, so I'm going to probably skip, very importantly is do you do vertical or special moral extensions? Right. So we can see this analogy between rock paper, scissors and guerrilla fighters or reconnaissance fighters, Tanks and infantry. Infantry. Infantry is attacked by tanks. And so. But guerrilla fighters, they can hide, they can use say rpg, whatever, you know, they can destroy T tanks so they can defend against it. Now in order to defend against tanks, you need to have infantry which comes the fields and then yeah, basically, you know, cleans up the gorilla fighter. So in order the tanks to, to kind of operate. Right. And so it is a rock, paper, scissors. Interesting question. What is this rock, paper, scissors? Desserts pock think. Right. And Chuck Norris beats them all. Why I'm mentioning this. Drone warfare changed quite a lot. This was quite unexpected. And drones are not here, they're not represented in this diagram. But this diagram actually it's fairly faithful, corresponds to this one here. All right, I need to move on. We have only few minutes to kind of discuss this model. So the geospatial model, which is, I'm saying, saying is going to be applicable for urban warfare. This is what I'm going for the rest of this article. Imagine you have this country, this artificially country, these nodes here were cities, these cities where somebody infected got here. And everybody is basically trying to run away from this city and go here, right? So we're going up and to the left and so we can simulate this process. One way to simulate it, one of the things we might expect is to have certain wave which is being seen from bottom right to top left. So this is what you see here. So this is a visual confirmation, but this is a type of geospatial modeling of the infections. It's working. Now I was thinking that this can be applied in, in, in, in the situations with you know, like say what we do, you know, in say some big country, like say instead of Ukraine, you have like here is usa. But imagine this was Ukraine, right. Turns out that no, modern warfare doesn't work like that. Actually, if anything the, the density of the popula of the soldiers on the field rapidly decreased. So I probably, I, I had some visual aids for it. Let me actually see here. So let me see. This is, I mean I spent some time doing it. So let's see. So no, we don't have this, right? We don't have this. We have something like that very sparse type of military warfare. So similarly, this actually though can be used to simulate. To simulate. It's very similar to urban warfare. Right, so I'm going to make this analogy here. So I cannot do this type of continental. Continental type of advances into, for the, for certain laws. But I'm claiming that this is actually a good enough setup, good enough setup for, from the epidemiological models, they can be upgraded to do, to do. To do city fighting. And you can see this is for the pollution schematic. And so how we can separate it into certain squares and we basically can clear the squares with the base. A host army invades an invading army. All right, so what is the host army? The invading army, what exactly. I'm saying, so we can use variety of methods to do this simulation. But you can also see like say this random lines were basically tunnels underneath, like how it's in Iwo Jimmy, how it was in Fallujah, how it is in other cities. And the so called invading army, they're fighting on this regular grid. And there's an algorithm which we can discuss about this. Basically all of these nodes, they have certain permeability or difficulty. And so basically the invading army need to go through, they need some decision process. Do you stay, do you go back, do you advance? Do you have enough ammunition and people to advance and so forth. Right, so this is what has been spelled out and I'm out of time and I apologize. So I see some questions here. Somebody said that the Japanese soldiers built maze of caves. Yes, I mentioned that. Can, can I apply this? Well documented? Yes. Yeah, there are variety of discussions, variety of, I mean, Lanchester equations. They have been modeled by many people about or trying to be fit by many people into variety of scenarios from antiquity, from the Middle Ages, more like the world, Normandy and so forth. All right, thank you. Any other questions? I don't see any. All right, since I don't see any other questions, I'm going to close up the presentation. Thank you for your attention. Good luck.