ABSTRACT When zombies attack: Mathematical modelling of an outbreak of zombie infection

The purpose of this paper is to demonstrate that mathematical modelling is so flexible that it can even be applied to unrealistic scenarios like an outbreak of zombie infection. Therefore five different models of possible situations with zombies are being compared. The zombies used in the models are based on the prototype popular-culture zombies who are slowly moving, cannibalistic and undead. The timescale of the outbreak is considered to be short so that natural birth and death rates are being ignored. In the Basic Model a frame is provided for the further models. Three basic classes are being defined: the Susceptible (S) – human being who can become a zombie, the Zombie (Z) and the Removed (R) – individual who has died a natural death or who has been attacked by a zombie. The other four models are called: Model with Latent Infection, Model with Quarantine, Model with Treatment and Impulsive Eradication. The Euler’s method is used to calculate the results of each model because it is the easiest and least time-consuming way. The findings of the calculation of the various models indicate that in general the collapse of civilisation is seen as the outcome of a zombie attack. However, the time to eradication is slightly delayed with the second and the third model. Eradication is prevented through the production of a treatment in the fourth model but humans only exist in small numbers. In order to fully prevent the eradication of humans the sixth model is applied. In this model zombies are being strategically destroyed by attacking them several times. After ten days all zombies are being eliminated. Therefore, in order to prevent human eradication due to a zombie attack it is recommended to attack them aggressively.  Even though the scenario of a zombie attack is considered to be unrealistic, these various models can be related other models of infectious disease. The key difference between other models of infectious disease and these five models is that dead individuals can come back to life.

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