import numpy as np
import math
import matplotlib.pyplot as plt  
%matplotlib inline
from matplotlib import rcParams
import matplotlib.image as mpimg
rcParams['font.family'] = 'serif'
rcParams['font.size'] = 16
rcParams['figure.figsize'] = 12, 8
from PIL import Image

beta = 0.010
gamma = 1

import numpy as np
import math
import matplotlib.pyplot as plt  
%matplotlib inline
from matplotlib import rcParams
import matplotlib.image as mpimg
rcParams['font.family'] = 'serif'
rcParams['font.size'] = 16
rcParams['figure.figsize'] = 12, 8
from PIL import Image

beta = 0.010
gamma = 1

def euler_step(u, f, dt):
  return u + dt * f(u)

 
def f(u):
  S = u[0]
  I = u[1]
  R = u[2]
 
  new = np.array([-beta*(S[1:-1, 1:-1]*I[1:-1, 1:-1] +
              S[0:-2, 1:-1]*I[0:-2, 1:-1] +
              S[2:, 1:-1]*I[2:, 1:-1] +
              S[1:-1, 0:-2]*I[1:-1, 0:-2] +
              S[1:-1, 2:]*I[1:-1, 2:]),
           beta*(S[1:-1, 1:-1]*I[1:-1, 1:-1] +
              S[0:-2, 1:-1]*I[0:-2, 1:-1] +
              S[2:, 1:-1]*I[2:, 1:-1] +
              S[1:-1, 0:-2]*I[1:-1, 0:-2] +
              S[1:-1, 2:]*I[1:-1, 2:]) - gamma*I[1:-1, 1:-1],
           gamma*I[1:-1, 1:-1]
          ])
 
  padding = np.zeros_like(u)
  padding[:,1:-1,1:-1] = new
  padding[0][padding[0] < 0] = 0
  padding[0][padding[0] > 255] = 255
  padding[1][padding[1] < 0] = 0
  padding[1][padding[1] > 255] = 255
  padding[2][padding[2] < 0] = 0
  padding[2][padding[2] > 255] = 255
 
  return padding

from PIL import Image
img = Image.open('popdens2.png')
img = img.resize((img.size[0]/2,img.size[1]/2))
img = 255 - np.asarray(img)
imgplot = plt.imshow(img)
imgplot.set_interpolation('nearest')

S_0 = img[:,:,1]
I_0 = np.zeros_like(S_0)
I_0[309,170] = 1 # patient zero

R_0 = np.zeros_like(S_0)

T = 900             # final time
dt = 1             # time increment
N = int(T/dt) + 1        # number of time-steps
t = np.linspace(0.0, T, N)   # time discretization
 
# initialize the array containing the solution for each time-step
u = np.empty((N, 3, S_0.shape[0], S_0.shape[1]))
u[0][0] = S_0
u[0][1] = I_0
u[0][2] = R_0

import matplotlib.cm as cm
theCM = cm.get_cmap("Reds")
theCM._init()
alphas = np.abs(np.linspace(0, 1, theCM.N))
theCM._lut[:-3,-1] = alphas

 
for n in range(N-1):
  u[n+1] = euler_step(u[n], f, dt)

from images2gif import writeGif
 
keyFrames = []
frames = 60.0
 
for i in range(0, N-1, int(N/frames)):
  imgplot = plt.imshow(img, vmin=0, vmax=255)
  imgplot.set_interpolation("nearest")
  imgplot = plt.imshow(u[i][1], vmin=0, cmap=theCM)
  imgplot.set_interpolation("nearest")
  filename = "outbreak" + str(i) + ".png"
  plt.savefig(filename)
  keyFrames.append(filename)
 
images = [Image.open(fn) for fn in keyFrames]
gifFilename = "outbreak.gif"
writeGif(gifFilename, images, duration=0.3)
plt.clf()