Simulating an epidemic

communities already have the disease spread. The additional lesson from this is that when we do these simulations for larger cities, the effect turns out to be that an infection that occurs in an urban center infects everyone in the center very quickly and spreads slowly to the outskirts. Let us now see how we can quantify the extent of this spread. Consider a person with a disease and count how many other people they can infect while they are sick. We will call the average of this number, including all those who were sick, the effective reproductive number, or R.

A more frequently used number is R_0, and this represents the value of R in a completely unprotected population, such as at the beginning of diffusion. This is called the "basic" reproductive number. You may have noticed that I show this number on the simulation screens and the way it is calculated is to look at each infected individual, count how many have been infected so far, predict how many people they will infect in total, based on the duration of the disease, and then find your average. For example, in our baseline simulation, R is about 2.2 in the peak growth phase, before the decline begins, when this population number reaches saturation.

On the other hand, when we double the infection radius, R reaches almost 8! This factor has a significant effect on the growth rate, causing explosive spread. This makes some sense; when you double the radius, there will be about 4 times as many infected people within it. When we reduced the infection rate by half, it varied between values ​​of 1.3 - 1.7. As long as R is greater than 1, the infection grows exponentially and this is considered "

epidemic

" growth. If R remains around the value 1, we are facing "endemic" growth. While when it is less than 1, we have a decrease. In comparison, the R0 for COVID-19 is estimated to be a little more than 2, which is about the expected average R0 value during the 1918 Spanish flu pandemic.

In comparison, seasonal flu has a much higher low value , about 1.3. In our travel

epidemic

game, when we enable the distance parameter and disable the travel parameter, R quickly drops below 2. As I said at the beginning, one of the things I was very curious to discover was the effect of controlling the trips to a place. common location, such as a shopping center or school. When I allowed our little dots to travel to these destinations, the R value jumped to 5.8! This may be a bit unfair, as we consider this form of infection to be the same as if it were caused by physical proximity such as a handshake or kiss.

We must accept that people who go to a school or a store do not have the capacity to spread infections, like, for example, people who live in the same house. To take this into account, let's cut the chances of infection in one day in half. This actually halves the maximum R value, but the effect of going back and forth in a market is still dramatic. Now let's try the case where, after reaching a threshold of infections, we apply social distancing, but people still visit a central location. You may have noticed that some of the points have escaped from their little cage... which shouldn't happen, but I'll knowingly leave this mistake unfixed.

It's up to everyone, seeing the chaos that's happening, to decide, "No, I ran away! I don't want to be a part of this!" This is how several people will react when they receive. a strict order of permanence Let's forget about these points and look at the graphs of two cases: 1. when no measurement is taken and 2. when along with the distance measurement, all points also stop coming and going in a central location. "Control" case (without any measures), the curve of the case when there is distancing but visits to a place almost completely eliminate the positive effect that social distancing has.

Now, what do you think will be more effective, distancing? Is this measure applied and do we also reduce comings and goings by a factor of 5 (5 times less)? The points on the left radically change your daily routines, while those on the right increase hygiene care. These two curves are almost identical, which surprised me, given that the scale factors are 5 times and 2 times, respectively. As I understand it, it turns out that maintaining strict hygiene, which is easier said than done, turns out to be a very successful measure! Of course, this may not be the case; Our goal with these experiments is to observe the effects of changes caused by changing just one parameter.

If you're curious, this is what it looks like when we enforce social distancing, limit the travel rate to a central point, and also slow the infection rate all at the same time. The combination of all these measures simultaneously is, indeed, very effective. But I want to emphasize again that the most desirable case is when the infected are consistently identified and isolated. Even in this simulation of the central market, when there are no control measures, a large outbreak is caused. If the comings and goings were effectively stopped, the epidemic would still be stopped. And our little points would not have to be rejected by each other or stop coming and going in the market.

In real epidemiology things are more sophisticated than this. With tactics such as “contact tracing” where not only known cases are identified and isolated, but also all people who have been in contact with those cases. Given the timing of this posting, I imagine one might expect it to be a PSA (Probabilistic Safety Analysis) on social distancing. But to be honest, this is not my main lesson. To be clear, when necessary, as it is now, social distancing absolutely saves lives, and as we've seen before, when people cheat or continue to gather regularly in a central location, it has disproportionately negative effects in the long run.

Term plan for the number of cases. The unpleasant truth, however, is that as long as the disease continues to exist, as soon as people begin to return to their normal lives and if some preventive measures are not taken, the second wave of infections will immediately begin. After doing all this, the deepest and most significant truth for me was that for the proper control of the disease, early comprehensive testing and the ability to isolate cases are of incomparable paramount importance; therapies that allow the treatment of cases and most important of all, how easy it is to underestimate all these facts when we live in good times.

I'm writing this during the pandemic, when some viewers can relate to the creepy dots on the edges of their boxes. But in the near future, many people will see it as a pandemic that does not happen at all, when a new pathogen that, instead of spreading in leaps and bounds, is found immediately and dominates. These pandemics will never end up in the history books because we may not appreciate the heroes behind them as much as they deserve. Living in a world of widespread travel and bustling urban centers makes fighting the spread of disease an uphill battle, that's for sure.

But this high level of interconnectedness also means the rapid diffusion, like never before, of ideas that can lead to systems and technologies that burst like tender tree buds in spring. It won't happen on its own, and obviously we make mistakes sometimes, but I'm fundamentally optimistic about our ability to learn from those mistakes. As you can imagine, these types of videos require many hours of work and effort. I don't add ads at the end and the current pandemic content on YouTube seems to be systematically demonetized, so I just wanted to take this opportunity to express a particularly warm thank you to everyone who supports these authors directly on Patreon.

These falsehoods made the difference.