Instead of digging into algorithms and data structures, today, you'll learn about epidemic modeling. In 9 minutes in this episode, you'll get a mathematical intuition on the spread of COVID-19 and the essential variables we can control, which can help us fight the virus.
Transcript
Episode 12 - COVID-19. Epidemic modeling with SIR.
00:00:02 - 00:05:03
welcome to the programming podcast. Here you can learn about computers in the brief and accessible way. I'm your host mean could get Laura and does it. Sort of the programming podcast. We are going to discuss slightly different topic instead of focusing on a purely software engineering or computer science concept that we can directly apply practice. We're going to discuss slightly more. Think we're going to talk about modal link of real world events with mathematical functions. In general the main purpose of these episodes is to show you how can model the currently happening go with nineteen pandemics and make predictions about it. Of course obviously our mold always going to be the most accurate one so not recommend you to use it in order to make assumptions. It's better to always follow the official information coming from the World Health Aussie Association but in the episode. I hope to give you a good idea of how the math that we're using his school. In particular derivatives functions and different equations could be used in practice in order to achieve something meaningful to make predictions which are very important for our lice. I'm also hoping to give you an intuition mathematical intuition or how the things that are happening around us can be impacted to a huge extent just by making a very tiny change in one of the formulas that we're going to discuss and this tiny change can be completely directed by a very small change in our own behavior as humans. So let's get started first. How can we do a real world event by using mathematical functions? Well this is a topic that we have been discussing. I guess since primary school resemble we can measure the velocity of an object over a certain period of time by taking the distance traveled and dividing it by the time passed right and this is a really accurate way to measure the average speed of an object. But imagine that we're dropping eyeglass from certain distance. We might be interested in calculating what is going to be diversity of glass when it hits the floor so we want to know. The instantaneous velocity of our class at a particular point in time. In order to do that we can take other equation which determines the motion of our objects and we can just find its derivative and substitute the time with a particular time but we are interested in. That's pretty much all of it. Of course if you have on this far too many times despite this abstract that's why I have applied on excellent reserves from the MIT. Which can explain you how this works in even more details but the good news is that we are not going to. Girotti too much today. We're just using them as an annotation for d formulas that through two together so I promise at the beginning that we are going to mold the real world epidemic or you want Bandera happening right now. One of the most popular APIARY MC models. All the AIR IS COOLED S. I R it comes from susceptible. Us infected and recovered so it measures. How does the racial susceptible 's infected entry covered? People during an epidemic varies over time in fact the World Health Organization they were using similar to predict what is going to be the impact and the spread of the nineteen hundred S. They're using a slightly more complicated model. Compared to what I'm going to show you today but knowing what we're going to talk about today you will be able to understand as their model yourself now first. Let's start by modeling recovery rate. So we're interested in how many people are going to get recovered at certain points in time. Let's see that we're interested at how many people are going to get recovered tomorrow for the purpose. We're going to take a look at. How many infected people? We have right now which we can measure with the function. I of T. Let's say of time and we can multiply this by apar- meter called a recovery rate since we're measuring. How many people were going to get recovered every day? We can calculate this recovery rates by taking the probability for a certain person to get today which we can estimate by taking the duration for which the illness continues which were Cogan. Nineteen is about two weeks so the property for a person run. The person from the infected wants to get recovered. Today is around one fourteenth right so we can measure the number of infected.
00:05:03 - 00:09:33
People are going to catch recovered today by multiplying the number of infected people today by one fourth. That's IT and since we're going to measure the rate of change of this function we can call it the drill tiff of the recovery function. How are going to measure the number of infected people today? Well it has something to do with. The number of people who get recovered just felt right so probably we need to find how many people are going to get infected and from this subtract the number of people going to get recovered and how many people are going to get infected. We'll this depends on the number of infected people today. The number of susceptible 's number of people who can get infected and enjoyable there's variable is called the transmission rate. It is pretty much determined by how many people give an infected person can interact with. And what is the pro ability for dispersal to infect of these people with whom they have interacted with so this means that we can model the number of infected people by taking This transmission rates multiplying kids by the number of infected people and the number of susceptible 's and also we need to subtract the number of recovered people which is gamma multiplied by the number of infected people. And that's pretty much everything now as you can see from here. We have a very interesting cost on this constant the transmission rates which determines how many people are going to get infected every day. I already told you that it depends on how many people the infect is already people interact with everyday so a tiny change in this era meter can lead to a significant change of the results and other interesting observation is that the number of infected people today depends to a huge extent by the number of infected people. Yesterday you ignore for a second that the number of infected people today depends also from the number EF recover people will make very simple mathematical model game for example era. Suppose that on average one person can infect to other people. This means that I we have one person right. After the next day we have to after it the next day these people infect to other people and so on and so forth. Eventually we're going to get really growing exponential function. We're going to get a function where we are multiplying. The number of people infected a certain point by to constantly and This is pretty terrible. If we let this function grow a lot for fifteen days we're going to get about thirty two thousand infected people. This is two on the power. Fifteen but on the other sites of the dynamics of infection for nineteen is a little bit. I so covet. Nineteen growth which two point six people according to who so every infected person can potentially transmitted disease to two to three other people. If you let disinfection grow for the same period fifteen days we're going to reach one point. Six million infected people see how this tiny change from two to two point. Six increased the number of infected people in orders of magnitude from thirty two thousand one point six media. Now you can see that this socialization. It's totally make sense. We are reducing the number of people that were interacting with but at the same time. We're reducing the risk for transmitting diseases. I hope this episode gave you a good intuition on what relatives are and how we can use them in tomato real world events. I also hope that you've got a very high level idea. How SL OUR MOTHER WORKS? And also by changing a tiny parameter with a tiny bit in this exponential function can lead to significantly different results. I shared a lot of different resources in the page associated with episodes. Thank you very much listening. Learn about the episode's he can pull them through their at 'em get you. The list of services and recordings is available at podcast dot M. dot com. Thanks for listening.