When zombies attack!: mathematical modelling of an outbreak of zombie infection

In: Infectious Disease Modelling Research Progress ISBN 978-1-60741-347-9 c Editors: J.M. Tchuenche and C. Chiyaka, pp. 133-150 2009 Nova Science Publishers, Inc.

Chapter 4

W HEN Z OMBIES ATTACK !: M ATHEMATICAL M ODELLING OF AN O UTBREAK OF Z OMBIE I NFECTION
Philip Munz1∗ Ioan Hudea1† Joe Imad2‡ Robert J. Smith?3§ , , , 1 School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada 2 Department of Mathematics, The University of Ottawa, 585 King Edward Ave, Ottawa ON K1N 6N5, Canada 2 Department of Mathematics and Faculty of Medicine, The University of Ottawa, 585 King Edward Ave, Ottawa ON K1N 6N5, Canada

Abstract Zombies are a popular figure in pop culture/entertainment and they are usually portrayed as being brought about through an outbreak or epidemic. Consequently, we model a zombie attack, using biological assumptions based on popular zombie movies. We introduce a basic model for zombie infection, determine equilibria and their stability, and illustrate the outcome with numerical solutions. We then refine the model to introduce a latent period of zombification, whereby humans are infected, but not infectious, before becoming undead. We then modify the model to include the effects of possible quarantine or a cure. Finally, we examine the impact of regular, impulsive reductions in the number of zombies and derive conditions under which eradication can occur. We show that only quick, aggressive attacks can stave off the doomsday scenario: the collapse of society as zombies overtake us all.

1. Introduction
A zombie is a reanimated human corpse that feeds on living human flesh [1]. Stories about zombies originated in the Afro-Caribbean spiritual belief system of Vodou (anglicised
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E-mail address: E-mail address: ‡ E-mail address: § E-mail address:
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[e-mail] [e-mail] [e-mail] [e-mail]. Corresponding author.

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Philip Munz, Ioan