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Zombie pandemic simulation in France
Model of a Zombie outbreak in France, starting in Grenoble
This is a rewrite from this blog post by Max Berrgren:
with a different country, a slightly different model, and different
libraries. The map of population density is taken from Wikimedia Commons
I use a modified SIR model. "Modified" because I didn't fully understood
SIR when I wrote the code. The population is divided in 3 categories:
S = Sane people
I = People who have been beaten, they are Incubating, soon-to-be Zombies
R = Rampaging Zombies, who bite sane people.
The rules are as follows:
- Sane citizen don't move (the army forbids it) until they get biten
by a zombie
- Biten people move fast (they don't control themselves) and after
some time they are tranformed into zombies. As a consequence, some
cities like Paris will be contaminated by these people, ahead of the
main zombie wave.
- Zombies walk slowly and bite people.
All units are really much arbitrary and tuned to make a sexy animation.
See the resulting animation here:
Blue represents sane citizen, red zombies, and green/yellow infected
people. Looks like Maubeuge, in the north-east, will (finally) be the
place to go.
Numpy for numerical computations.
Scipy for the convolution that computes the dispersion
MoviePy for the animation (requires FFMPEG installed)
ImageMagick if you want to make a gif
Copyright Zulko 2014, Licence Public Domain (Creative Commons 0)
@NSA, @DGSE => This is just for science. No plans.
import urllib
import numpy as np
from scipy.ndimage.filters import convolve
import moviepy.editor as mpy
filename = (""
urllib.urlretrieve(filename, "france_density.png")
infection_rate = 0.3
incubation_rate = 0.1
dispersion_rates = [0, 0.07, 0.03] # for S, I, R
# This kernel models how the people/zombies at one position
# spread to the neighboring positions
dispersion_kernel = np.array([[0.5, 1 , 0.5],
[1 , -6, 1],
[0.5, 1, 0.5]])
france = mpy.ImageClip("france_density.png").resize(width=400)
SIR = np.zeros( (3,france.h, france.w), dtype=float)
SIR[0] = france.get_frame(0).mean(axis=2)/255
start = int(0.6*france.h), int(0.737*france.w)
SIR[1,start[0], start[1]] = 0.8 # infection in Grenoble at t=0
dt = 1.0 # one update = one hour of real time
hours_per_second= 7*24 # one second in the video = one week in the model
world = {'SIR':SIR, 't':0}
##### MODEL
def infection(SIR, infection_rate, incubation_rate):
""" Computes the evolution of #Sane, #Infected, #Rampaging"""
newly_infected = infection_rate*R*S
newly_rampaging = incubation_rate*I
dS = - newly_infected
dI = newly_infected - newly_rampaging
dR = newly_rampaging
return np.array([dS, dI, dR])
def dispersion(SIR, dispersion_kernel, dispersion_rates):
""" Computes the dispersion (spread) of people """
return np.array( [convolve(e, dispersion_kernel, cval=0)*r
for (e,r) in zip(SIR, dispersion_rates)])
def update(world):
""" spread the epidemic for one time step """
infect = infection(world['SIR'], infection_rate, incubation_rate)
disperse = dispersion(world['SIR'], dispersion_kernel, dispersion_rates)
world['SIR'] += dt*( infect + disperse)
world['t'] += dt
def world_to_npimage(world):
""" Converts the world's map into a RGB image for the final video."""
coefs = np.array([2,25,25]).reshape((3,1,1))
accentuated_world = 255*coefs*world['SIR']
image = accentuated_world[::-1].swapaxes(0,2).swapaxes(0,1)
return np.minimum(255, image)
def make_frame(t):
""" Return the frame for time t """
while world['t'] < hours_per_second*t:
return world_to_npimage(world)
animation = mpy.VideoClip(make_frame, duration=25)
# You can write the result as a gif (veeery slow) or a video:
#animation.write_gif(make_frame, fps=15)
animation.write_videofile('test.mp4', fps=20)
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Zulko commented Sep 29, 2016

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