WHEN ZOMBIES ATTACK! - MATHEMATICAL MODELLING OF AN OUTBREAK OF ZOMBIE INFECTION == Philip Munz1, Ioan Hudea1 ,, Joe Imad2, Robert J.pdf

WHEN ZOMBIES ATTACK! - MATHEMATICAL MODELLING OF AN OUTBREAK OF ZOMBIE INFECTION
Philip Munz1, Ioan Hudea1, Joe Imad2, Robert J


A zombie is a reanimated human corpse that feeds on living human flesh. Stories about zombies originated in the Afro-Caribbean spiritual belief system of Vodou (anglicised voodoo). These stories described people as being controlled by a powerful sorcerer.

2. The Basic Model
For the basic model, we consider three basic classes:
• Susceptible (S).
• Zombie (Z).
• Removed (R).
Susceptibles can become deceased through ‘natural’ causes, i.e., non-zombie-related death (parameter δ). The removed class consists of individuals who have died, either through attack or natural causes. Humans in the removed class can resurrect and become a zombie (parameter ζ). Susceptibles can become zombies through transmission via an encounter with a zombie (transmission parameter β). Only humans can become infected
through contact with zombies, and zombies only have a craving for human flesh so we do not consider any other life forms in the model. New zombies can only come from two sources:

In addition, we assume the birth rate is a constant, Π. Zombies move to the removed class upon being ‘defeated’. This can be done by removing the head or destroying the brain of the zombie (parameter α). We also assume that zombies do not attack/defeat other zombies.
Thus, the basic model is given by

S` = Π − βSZ − δS

Z` = βSZ + ζR − αSZ

R` = δS + αSZ − ζR ..................