A Simulated Dance of Social Distancing
By now, you’ve probably seen a model or simulation of the benefits of social distancing in preventing the spread of COVID-19. One of the most popular of these animations depicts healthy people as dots of one color remaining stationary, while dots of another color represent infected persons dancing about the simulation infecting others. Some of these simulations have parameters that can be altered by users to approximate the effects of different government and healthcare policies or biological properties of the virus itself. These simulations follow the aphorism captured by statistician George Box in the quote “essentially, all models are wrong, but some models are useful.” They omit details and aggregate multiple real-world actions into abstract mathematical parameters; however, they importantly demonstrate that the spread of the infection is not entirely out of control. The myriad of moving dots also have the intuitive visual appeal as representing the actions taken by an individual, rather than presenting the aggregate seen in plots of exponential curves representing the number of infections, deaths or medical capacity at different times in the spread of the disease.
Cellular Automata: From Games to Physics Simulations
There are many ways to develop algorithms to simulate the spread of an infectious disease. Cellular automata are a large class of discrete (having a finite number of values/categories rather than being continuous values) models that could be used for such a simulation. Cellular automata consist of many neighboring cells, like the component squares on a sheet of graph paper, where each cell can exist in a pre-defined number of states, like “on” or “off”. The configuration of these cells has an initial state at generation/time=0 and then the simulation progresses through time by the application of rules that update the state of each cell subject to the previous generation’s configuration. It may sound complicated, but you might already have hands-on experience with cellular automata if you have played a game called “Lights Out” which challenges its players to turn off all of the lights on a game board using the singular move of toggling a light switch at a coordinate–the complicating factor being that this action also toggles the status of all adjacent lights. This flexible class of models was initially discovered in the 1940s at Los Alamos National Laboratory, but one of their most popular uses is in John Horton Conway’s Game of Life where the status of adjacent cells determines whether a cell of interest continues its “living” status (remains “on”), “dies” (it switches “off”), or the cell switches “on” as if by reproduction. The results of different initial configurations or tweaks to the game’s rules can be both surprising and mesmerizing. Cellular automata can even be used to simulate the behavior of physical systems, like fluid dynamics. In fact, under some restrictions, cellular automata can be seen to be equivalent to one of the oldest models in a branch of physics called statistical mechanics to demonstrate a phase transition (a change between states of matter): the Ising model of the alignment of magnetic north and south poles in ferromagnetism. So, somewhat surprisingly, we see that there is a connection between the processes underlying magnetism and the spread of infectious disease through the cellular automata model!
Peer edited by Kasey Skinner