Mathematical model for zombie-human population behaviour.

As a result of extreme boredom,I made the following analysis in Matlab:

"Nicholson-Bailey model for studying zombie-human population interaction"

As expected,Zombies were the parasitoids and humans were the hosts.This is the excrept of the m-file:

%Made by Srikumar Krishnamoorthy,TTU

%This model is directly based on the Nicholson Bailey Parasitoid model and

%the assumptions that are made are : 1.A Zombified Human cannot be

%zombified again. 2.A Zombie needs a human's 'life force to 'survive'(or

%whatever it is that zombies do) 3.There are equal number of Male and

%female humans at all times and they all are monogamously 'coupled' 4.No

%weapons can hurt a zombie.

r=1%r=No of offspring by a human that survive till adulthood(I assumed 2 children per couple or 1 chld per human

c=1%c=Searching efficincy or the probability that a zombie will encounter a human in his lifetime(Okay,'undeadtime' :P)

e=1%e=No of infections that a zombie makes on a human that result in the complete zombification of the human

H0=input('input initial population N0 of Humans: ')

Z0=input('input initial population P0 of Zombies: ')

n=input('input time period of run: ')

H=zeros(n+1,1);

A=zeros(n+1,1);

t=zeros(n+1,1);

H(1)=H0;

Z(1)=Z0;

for i=1:n

t(i)=i-1;

H(i+1)=r*H(i)*exp(-c*Z(i));

Z(i+1)=e*H(i)*(1-exp(-c*Z(i)));

end

t(n+1)=n;

plot(t,H,t,H,'o')

title('No of Humans'),pause

plot(t,Z,t,Z,'o')

title('No of Zombies'),pause

These are graphs of a few sample runs:

Conclusion :

Whatever the initial populations of the humans and the zombies may be,humans are doomed.

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