from matplotlib.pylab import plot, ylim, show, xlabel, ylabel
from numpy import log
N=1000
ro = 300

for I_0 in range(10,900,50):
    S_0 = N - I_0
    S = range(1,S_0,1)
    
    I = N - ro*log(S_0) + ro*log(S) - S
    plot(S,I)
    ylim([0,N])
    xlabel('S')
    ylabel('I')
show()