Cellular automata are the system used in Conway’s Game of Life. Based on simple rules, each cell’s value is a combination of those around it. Given an initial starting state, entire worlds can be generated using simple rules.
Combining the ideas of cellular automata to graph theory and network-based simulation methods, a more real-world based (although very computationally expensive) method. Similar to SIR and its variants, it operates on rules. However, it is able to accommodate more than 3 or 4 compartments but small communities across the world.
Say that community A represents Wuhan, the beginning of the outbreak, and the thickness or presence of a line indicates a connection between neighbors. Let us create a rule that how quickly a neighbor is infected depends on how long a connection is, and that how severe a neighbor’s infection is a function of how long the neighbor has been infected and how thick the connection is with an infected community.
Logically, community B, D, then E would be infected and have the worst cases. Also, throughout time, inevitably, all the communities will be affected. However, the reality is that community H, the only connection to the ‘mainland’ of community A, would have begun quarantining and/or shut down travel between itself and community F. This is a fact that many models fail to acknowledge — how communities react is continually changing. Manually-implemented ‘exposure’ can adjust the strength of a connection.
These simulations are akin to a rumor spreading through a social media network — they can effectively model how an epidemic spreads not through mathematical corollaries but with simulations of the real thing.
Graph theory simulations are necessarily a scaled-down and simplified version of a real-world simulation. They are the most real-world and context-based models, but with that advantage comes the burden of manually implementing the effects of legislation and quarantining into the simulation. Armed with a machine learning model that predicts legislation, a graph theory simulation may be the best model we have. However, due to its implementation and computational complexity, it takes a long time to make one. Lower-level implementations of this idea are being implemented.
In addition, the extra complexity may not be worth a small gain in accuracy that models like SIR or even sigmoid may be able to provide.
