The purpose of this paper is
to demonstrate the flexibility of mathematical modelling and to show how it can
respond to a wide variety of challenges, such as infectious diseases.
To do this, the scenario of a zombie outbreak infecting humans was
considered and the slow moving, cannibalistic and undead classical pop-culture
zombie chosen as model. Mathematical analyses of a zombie outbreak infection
were conducted and altogether four models presented. The first one, called the basic model, considers three basic
classes, the Susceptible (S), the Zombie (Z) and the Removed (R). It suggests
that an outbreak of zombies will lead to the collapse of civilisation and in a
short outbreak, everybody will be infected. The second one, referred to as the model with latent infection, indicates that susceptibles remain infected for some period of time before either
dying a natural death or becoming a zombie. In this case, the collapse of
civilisation still takes place but takes approximately twice as long. The third
model includes quarantine of the
infected but there is still no chance for them to escape. Even though the eradication
of humans is slightly delayed in this model, zombies are either completely
eradicated or they take over completely in the end. The final model, called the model with treatment, allows to
cure ‘zombie-ism’ and to return to human form again. Upon examination of these
facts, it becomes clear that the only, effective way to survive an outbreak of
zombies is to deal with it quickly and attack more than once.
In order to obtain all of those above-mentioned models, mathematical
analyses and Euler’s method were applied.
Results suggest that the only, significant difference between the models
concerning a non-realistic zombie outbreak and other models of real infectious
diseases is the fact that the dead can come back to live again. However, the
fact that mathematical modelling can even be applied to non-realistic
challenges proves beyond a doubt its flexibility.
[324 words]
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