Modeling is one way for understanding analytic models. Python supplies many tools to do that.

First, the python script for SIR

# -*- coding: utf-8 -*- ################################### ### Written by Ilias Soumpasis # ### ilias.soumpasis@ucd.ie (work) # ### ilias.soumpasis@gmail.com # ################################### import scipy.integrate as spi import numpy as np import pylab as pl beta=1.4247 gamma=0.14286 TS=1.0 ND=70.0 S0=1-1e-6 I0=1e-6 INPUT = (S0, I0, 0.0) def diff_eqs(INP,t): '''The main set of equations''' Y=np.zeros((3)) V = INP Y[0] = - beta * V[0] * V[1] Y[1] = beta * V[0] * V[1] - gamma * V[1] Y[2] = gamma * V[1] return Y # For odeint t_start = 0.0; t_end = ND; t_inc = TS t_range = np.arange(t_start, t_end+t_inc, t_inc) RES = spi.odeint(diff_eqs,INPUT,t_range) print RES #Ploting pl.plot(RES[:,0], '-bs', label='Susceptibles') # I change -g to g-- # RES[:,0], '-g', pl.plot(RES[:,2], '-g^', label='Recovereds') # RES[:,2], '-k', pl.plot(RES[:,1], '-ro', label='Infectious') pl.legend(loc=0) pl.title('SIR epidemic without births or deaths') pl.xlabel('Time') pl.ylabel('Susceptibles, Recovereds, and Infectious') pl.savefig('2.1-SIR-high.png', dpi=900) # This does, too pl.show()

Second, the python script for SIS

# -*- coding: utf-8 -*- import scipy.integrate as spi import numpy as np import pylab as pl beta=1.4247 gamma=0.14286 I0=1e-6 ND=70 TS=1.0 INPUT = (1.0-I0, I0) def diff_eqs(INP,t): '''The main set of equations''' Y=np.zeros((2)) V = INP Y[0] = - beta * V[0] * V[1] + gamma * V[1] Y[1] = beta * V[0] * V[1] - gamma * V[1] return Y # For odeint t_start = 0.0; t_end = ND; t_inc = TS t_range = np.arange(t_start, t_end+t_inc, t_inc) RES = spi.odeint(diff_eqs,INPUT,t_range) print RES #Ploting pl.plot(RES[:,0], '-bs', label='Susceptibles') pl.plot(RES[:,1], '-ro', label='Infectious') pl.legend(loc=0) pl.title('SIS epidemic without births or deaths') pl.xlabel('Time') pl.ylabel('Susceptibles and Infectious') pl.savefig('2.5-SIS-high.png', dpi=900) # This does increase the resolution. pl.show()