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

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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, 1125Colonel 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 aboutthrough 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, beforebecoming 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
Azombie 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


E-mail address: E-mail address: ‡ E-mail address: § E-mail address:


pmunz@connect.carleton.ca iahudea@connect.carleton.ca jimad050@uottawa.ca rsmith43@uottawa.ca. Corresponding author.

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Philip Munz, IoanHudea, Joe Imad et al.

voodoo). These stories described people as being controlled by a powerful sorcerer. The walking dead became popular in the modern horror fiction mainly because of the success of George A. Romero’s 1968 film, Night of the Living Dead [2]. There are several possible etymologies of the word zombie. One of the possible origins is jumbie, which comes from the Carribean term forghost. Another possible origin is the word nzambi which in Kongo means ‘spirit of a dead person’. According to the Merriam-Webster dictionary, the word zombie originates from the word zonbi, used in the Louisiana Creole or the Haitian Creole. According to the Creole culture, a zonbi represents a person who died and was then brought to life without speech or free will. The followers of Vodou believethat a dead person can be revived by a sorcerer [3]. After being revived, the zombies remain under the control of the sorcerer because they have no will of their own. Zombi is also another name for a Voodoo snake god. It is said that the sorcerer uses a ‘zombie powder’ for the zombification. This powder contains an extremely powerful neurotoxin that temporarily paralyzes the human nervous system andit creates a state of hibernation. The main organs, such as the heart and lungs, and all of the bodily functions, operate at minimal levels during this state of hibernation. What turns these human beings into zombies is the lack of oxygen to the brain. As a result of this, they suffer from brain damage. A popular belief in the Middle Ages was that the souls of the dead could return to earth oneday and haunt the living [4]. In France, during the Middle Ages, they believed that the dead would usually awaken to avenge some sort of crime committed against them during their life. These awakened dead took the form of an emaciated corpse and they wandered around graveyards at night. The idea of the zombie also appears in several other cultures, such as China, Japan, the Pacific, India, Persia,...
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