3807.sagews

b = 1/11
a = 6.8*b
t = 4

S = []
I = []
R = []

S.append(10000)
I.append(1000)
R.append(19000)

n = S[0]+I[0]+R[0]
print n
for i in srange(1,t+1,1):
       #print i      
       S.append( S[i-1]-a*I[i-1]*S[i-1]/n)
       I.append( I[i-1]+a*I[i-1]*S[i-1]/n -b*I[i-1])
       R.append( R[i-1]+b*I[i-1] )
       #print 'S ='
       #print S[i]
       #print 'I ='
       #print I[i]
       #print 'R ='
       #print R[i]
       #print S[i]+I[i]+R[i]
       
       
print 'S ='
print S
print 'I ='
print I
print 'R ='
print R

30 S = [10, 28/3, 12404/1485, 2550374036/363862125, 10637206663037619196/1985934690142734375] I = [1, 52/33, 39416/16335, 1287090064/363862125, 9668788250584078304/1985934690142734375] R = [19, 210/11, 6982/363, 3495506/179685, 79149486214/4002483375]

b = 1/11
a = 6.8*b
t = 100

S = []
I = []
R = []

S.append(10000)
I.append(1000)
R.append(19000)

n = S[0]+I[0]+R[0]

for i in srange(1,t+1,1):    
       #print i 
       S.append( S[i-1]-a*I[i-1]*(S[i-1]/n))      
       I.append( I[i-1]+a*I[i-1]*S[i-1]/n -b*I[i-1])
       R.append( R[i-1]+b*I[i-1] )

       #print 'S ='
       #print S[i]
       #print 'I ='
       #print I[i]
       #print 'R ='
       #print R[i]
       #print S[i]+I[i]+R[i]


s = list_plot(S,rgbcolor=(1,0.75,0), plotjoined=True, legend_label='$S-Anfaellige$')
i = list_plot(I,rgbcolor=(1,0,0), plotjoined=True, legend_label='$I-Infizierte$')
r = list_plot(R,rgbcolor=(0,1,0), plotjoined=True, legend_label='$R-Genesene$')


p = s+i+r
p.set_legend_options(loc = 4, shadow=True)
p.axes_label_color((0,0,1))
p.axes_labels(['$Zeit in Tagen$','$Anzahl der Menschen$'])
p.axes_range(0,t,-n/3,n)
show(p)

6000/11