You Can Run, You Can Hide: The Epidemiology and Statistical Mechanics of Zombies

This publication explores the mathematical modeling of a fictional zombie disease (SZR model) to teach epidemiological and statistical mechanics techniques. The authors progress from a simple deterministic differential equation model to a complex stochastic lattice simulation and finally to a full-scale geographic simulation across the United States. They demonstrate that the SZR model, unlike the classic SIR model, is density-dependent and can lead to runaway outbreaks depending on the virulence parameters. Key findings include the observation of a phase transition on two-dimensional lattices, which places the zombie model within the percolation universality class. The authors further enhance the realism of their models by incorporating census-based population grids, a latent 'exposed' state, and zombie mobility. Through 7,000 simulations, the authors identify geographical patterns of susceptibility. The analysis reveals that the greatest risk for rapid contagion often resides in regions between large metropolitan hubs, rather than in the cities themselves. The work provides a compelling, playful, yet scientifically rigorous framework for understanding disease transmission, percolation, and critical phenomena.

We use a popular fictional disease, zombies, in order to introduce techniques used in modern epidemiology modelling, and ideas and techniques used in the numerical study of critical phenomena. We consider variants of zombie models, from fully connected continuous time dynamics to a full scale exact stochastic dynamic simulation of a zombie outbreak on the continental United States. Along the way, we offer a closed form analytical expression for the fully connected differential equation, and demonstrate that the single person per site two dimensional square lattice version of zombies lies in the percolation universality class. We end with a quantitative study of the full scale US outbreak, including the average susceptibility of different geographical regions.

The discussion reflects on the SZR model's dynamics as a useful tool for epidemiology and social science. The authors highlight that the model effectively demonstrates the risks of disease in scenarios where the susceptible population is actively involved in removal, which can be likened to real-world outbreaks where healthcare infrastructure is compromised. Future research could explore more complex social dynamics, such as the spread of ideas or opinions, using the SZR framework.