# The ping pong vaccination programming challenge

Vaccination programmes work best when the majority of the population are vaccinated. One way scientists simulate the effects of disease and vaccination programmes is by using computer simulations. But what is a computer simulation?

You can visualise what a simulation is with ping pong balls bouncing around a crowd. Imagine having a large room full of people. A virus is represented by a ping pong ball, bouncing from person to person, infecting each person it touches. Each person who is hit by a ping pong ball and not already infected becomes infected. That means they toss that ping pong ball back into the crowd to infect more people, but they also toss an extra one too (and then they sit down: dead). Start with a few ping pong balls. Quickly the virus spreads everywhere and lots of people sit down (die). You have run a physical simulation of how a virus spreads!

Now start again but ‘vaccinate’ 80 per cent of the people first: give them a baseball cap to wear to show who is who. If those people get a ping pong ball, they just destroy it: they infect noone else. Start with the same number of ping pong balls. This time, the virus quickly dies out and only a few people sit down (die). Not only are the vaccinated people protected but they protect many of the un-protected people too who might have died.

Now (if you can program) you can write a program to do the same thing, and so simulate and explore the spread of infection, which is easier perhaps than getting a thousand people to chuck ping pong balls about. Create a grid (an array) of 1000 cells. Each represents a person. They can be infected or not. They can also be vaccinated or not. Start with five random cells (so people marked as infected). Run a series of rounds. After each round, a newly infected cell randomly chooses two others to infect. If not infected already and not vaccinated, then they become newly infected. If already infected or vaccinated, they do not pass the infection on.

You can run lots of different experiments with different conditions. For example, experiment with different proportions of people infected at the start or explore what percentage of people need to be vaccinated for the virus to quickly die out. Is 50 per cent enough? You could also change how many people one person infects, or for how long a person can infect others before dying. Perhaps they each keep causing new infections for three rounds before stopping instead of only one. In what situations does the virus infect lots of people and when does it die out quickly?

What you are doing here is computer modelling or simulating the effects of the virus in different scenarios, and that is essentially how computer scientists make the predictions that governments use to make decisions about lockdowns and mask wearing, if they are “following the science”. Of course, such models are only as good as the data that goes into them, such as how many other people does each person infect. In reality, this is data provided by surveys, experimental studies, and so on.

– Paul Curzon, Queen Mary University of London, Spring 2021