Tuesday, October 31, 2017

Happy Halloween....

As today is Halloween, I thought I would write a brief post on zombies and how they can be used to demonstrate disease models (even the Centers for Disease Control and Prevention (CDC) has a post about Zombies preparedness). There are several good examples of using zombie outbreaks as demonstrations for the utility of modeling (or just showing how modeling concepts can be applied to the spread of zombies). 

These range from exploring  the spatial and temporal dynamics of a zombie epidemic (e.g. Sander and Topaz, 2014). To that of the work of Alemi et al. (2015), who produced a "danger map" of what would happen if the continental United States  was overrun with zombies (an interactive version is available here and shown below). In their paper, they demonstrate how epidemiological processes akin to a Susceptible-Infected-Recovered (SIR) model (which we have wrote about before) can be used to model the spread of zombies. As its a zombie model, the SIR changes to a SZR model (Munz et al., 2009), where:
 "S represents the susceptible population, the uninfected humans, Z represents the infected state, zombies, and R represents our removed state, in  this  case  zombies  that  have  been  terminated  by  humans (canonically  by  destroying  their  brain  so  as  to  render  them inoperable)." (Alemi et al., 2015)
Zombie Town USA

Below you can see an attempt of modeling a zombie outbreak (only the SI parts) in one of the buildings on the George Mason Fairfax campus utilizing NetLogo (you can download the model code from here).

More complex individual based models have also been created like the one shown below by Horio and Arrowsmith (2015) which was used to showcase how zombies can be used to describe complex adaptive systems and agent-based modeling.


If readers know of any over good Halloween (horror) like models, please let us know.

Alemi, A.A., Bierbaum, M., Myers, C.R. and Sethna, J.P. (2015), 'You Can Run, You Can Hide: The Epidemiology and Statistical Mechanics of Zombies', Physical Review E, 92(5): 052801.
Horio, B. and Arrowsmith, N. (2015), 'The Pedagogy of Zombies', OR/MS Today, 42(5).
Munz, P., Hudea, I., Imad, J. and Smith, R.J. (2009), 'When Zombies Attack!: Mathematical Modelling of an Outbreak of Zombie Infection', in Tchuenche, J.M. and Chiyaka, C. (eds.), Infectious Disease Modelling Research Progress, Nova Science Publishers, Hauppauge, NY, pp. 133-150.
Sander, E. and Topaz, C.M. (2014), 'The Zombie Swarm: Epidemics In The Presence of Social Attraction And Repulsion', in Smith, R. (ed.) Mathematical Modelling of Zombies, University of Ottawa Press, Ottawa, Canada, pp. 265-300.

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