- Physical Review Journals
All JournalsPhysics Magazine

Physical Review E

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 3.0 License. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

You can run, you can hide: The epidemiology and statistical mechanics of zombies

Alexander A. Alemi1,*, Matthew Bierbaum1,†, Christopher R. Myers1,2,‡, and James P. Sethna1,§

  • 1Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
  • 2Institute of Biotechnology, Cornell University, Ithaca, New York 14853, USA

  • *aaa244@cornell.edu
  • †mkb72@cornell.edu
  • ‡c.myers@cornell.edu
  • §sethna@lassp.cornell.edu
PDF

Phys. Rev. E 92, 052801 – Published 2 November, 2015

DOI: https://doi.org/10.1103/PhysRevE.92.052801

Abstract

We use a popular fictional disease, zombies, in order to introduce techniques used in modern epidemiology modeling, 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.

View figure in article

Article Text

Supplemental Material

References (26)

  1. M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals (Princeton University Press, Princeton, NJ, 2008).
  2. P. Munz, I. Hudea, J. Imad, and R. J. Smith? When zombies attack!: Mathematical modeling of an outbreak of zombie infection, Infect. Dis. Model. Res. Prog. 4, 133 (2009).
  3. C. Witkowski and B. Blais, Bayesian analysis of epidemics-zombies, influenza, and other diseases, arXiv:1311.6376.
  4. F. Nunez, C. Ravello, H. Urbina, and T. Perez-Acle, A rule-based model of a hypothetical zombie outbreak: Insights on the role of emotional factors during behavioral adaptation of an artificial population, arXiv:1210.4469.
  5. R. Hochreiter and C. Waldhauser, Zombie politics: Evolutionary algorithms to counteract the spread of negative opinions, arXiv:1401.6420.
  6. E. Sander and C. M. Topaz, The zombie swarm: Epidemics in the presence of social attraction and repulsion, in Mathematical Modelling of Zombies, edited by R. Smith? (University of Ottawa Press, Ottawa, 2014).
  7. B. Mota, Optimum survival strategies against zombie infestations-a population dynamics approach, Bull. Am. Phys. Soc. 59, 1252P (2014).
  8. A. Cartmel et al., Mathematical Modelling of Zombies (University of Ottawa Press, Ottawa, 2014).
  9. R. Smith? Braaaiiinnnsss!: From Academics to Zombies (University of Ottawa Press, Ottawa, 2011).
  10. M. Brooks, The Zombie Survival Guide: Complete Protection from the Living Dead (Broadway books, New York, 2003).
  11. M. Brooks, World War Z: An Oral History of the Zombie War (Broadway Paperbacks, New York, 2013).
  12. U. S. Department of Health, Human Services Centers for Disease Control, and Prevention, Preparedness 101: Zombie pandemic, http://www.cdc.gov/phpr/zombies/.
  13. U. S. Department of Health, Human Services Centers for Disease Control, and Prevention, Preparedness 101: Zombie apocalypse, http://blogs.cdc.gov/publichealthmatters/2011/05/preparedness-101-zombie-apocalypse/.
  14. http://mattbierbaum.github.io/zombies-usa/.
  15. D. T. Gillespie, A. Hellander, and L. R. Petzold, Perspective: Stochastic algorithms for chemical kinetics, J. Chem. Phys. 138, 170901 (2013).
  16. Wikipedia, Branching process — wikipedia, the free encyclopedia, https://en.wikipedia.org/wiki/Branching_process [online; accessed 29-July-2015].
  17. M. E. J. Newman, I. Jensen, and R. M. Ziff, Percolation and epidemics in a two-dimensional small world, Phys. Rev. E 65, 021904 (2002).
  18. P. Grassberger, On the critical behavior of the general epidemic process and dynamical percolation, Math. Biosci. 63, 157 (1983).
  19. J. L. Cardy and P. Grassberger, Epidemic models and percolation, J. Phys. A: Math. Gen. 18, L267 (1985).
  20. T. Tomé and R. M. Ziff, Critical behavior of the susceptible-infected-recovered model on a square lattice, Phys. Rev. E 82, 051921 (2010).
  21. J. P. Sethna, K. A. Dahmen, and C. R. Myers, Crackling noise, Nature (London) 410, 242 (2001).
  22. N. Araújo, P. Grassberger, B. Kahng, K. J. Schrenk, and R. M. Ziff, Recent advances and open challenges in percolation, Eur. Phys. J. Spec. Top. 223, 2307 (2014).
  23. https://github.com/meetar/dotmap.
  24. M. A. Gibson and J. Bruck, Efficient exact stochastic simulation of chemical systems with many species and many channels, J. Phys. Chem. A 104, 1876 (2000).
  25. J. Fu, S. Wu, H. Li, and L. R. Petzold, The time dependent propensity function for acceleration of spatial stochastic simulation of reaction-diffusion systems, J. Comput. Phys. 274, 524 (2014).
  26. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevE.92.052801 for a movie rendition of the simulated zombie outbreak in Fig. 11.

Outline

Information

Phys. Rev. E 92, 052801– Published 2 November, 2015
  • Received 4 June 2015
Creative Commons Logo

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation