Simulation

Epidemic

Introduction

This is a very brief post, with a simulation written in javascript. It’s a very simple model of how a dissease can spread into a population. You may get the code, adjust the parameters and watch different outcomes.
The idea of this project came from this: Why outbreaks like coronavirus spread exponentially, and how to ‘flatten the curve’. I highly recommend reading it.

Theory

I recommend watching this video, for some theory:

It’s a good start, there is a lot more information about this on the internet, so I won’t bother with formulae here.

Simulation

The model resembles a lot the one from the link pointed above, with an addition: this model also simulates death, not all ‘people’ recover.

Briefly, it’s just molecular dynamics in 2D, in a ‘box’, with elastic collisions. All ‘particles’ have the same mass and they can be either not infected, infected, cured and dead. The dead ones disappear from the simulation.
Once an infected ‘particle’ hits one that wasn’t infected yet, it will infect it. A ‘particle’ once having the illness, has a chance of dying (but only in the last two thirds of the infected period of time). After being sick for a while, if it doesn’t die in the meantime, it will recover and have immunity, so it cannot be infected again.

There is also a chart showing the number of infections over time. You’ll notice that it will level out under 100%, the difference being the ones that did not get an infection, being lucky, and the dead ones.

The code has a feature that it’s usually a bug: because of the too big time step, some ‘particles’ can stick together. Basically when the collide they overlap a little (more, if the time step is big) and if the cannot go apart in one time step, remaining overlapped, they will be considered as colliding again and so on. There are various ways of solving this but for this model I consider it a feature: people sometimes do something analogous.

The blue ‘particles’ are not infected, the red ones are infected and the green ones are cured. The ones that die disappear from the canvas.

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Canvas is not supported by your browser!

The computation will be a little slow on a phone, for this you should better use a desktop.

Related to this, for a better implementation on such molecular dynamics where there is short range interaction only, visit Event Driven Molecular Dynamics. It’s also 3D and with nicer graphics, using OpenGL.

The code

There are some comments in the code, hopefully it’s clear enough. I wrote it very fast, so it’s far from perfect but it seems to work as intended.

Conclusion

As usual, if you find mistakes or have suggestions, please point them out.

I’ll end up with a quote from Will the pandemic kill you? by Nobel Laureate Peter Doherty:

“What influenza also tells us is that, while viruses that spread via the respiratory route are the most likely cause of some future pandemic, only the most draconian and immediate restrictions on human travel are likely to limit the spread of infection, and then only briefly.”
“Such limitations are likely to be applied quickly if we are faced with a situation in which, for example, more than 30% of those affected develop severe or even fatal consequences. The more dangerous situation may be when mortality rates are in the 1-3% range, causing (ultimately) 70 million to 210 million deaths globally. Such an infection could “get away” before we realised what was happening.”

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