def sim_and_plot(G, tau, gamma, rho, tmax, tcount, ax):
t, S, I, R= EoN.fast_SIR(G, tau, gamma, rho = rho, tmax = tmax)
report_times = scipy.linspace(0, tmax, tcount)
I = EoN.subsample(report_times, t, I)
ax.plot(report_times, I/N, color='grey', linewidth=5, alpha=0.3)
t, S, I, R = EoN.SIR_heterogeneous_meanfield_from_graph(G, tau, gamma, rho=rho,
tmax=tmax, tcount=tcount)
ax.plot(t, I/N, '--')
t, S, I, R = EoN.SIR_compact_pairwise_from_graph(G, tau, gamma, rho=rho,
tmax=tmax, tcount=tcount)
ax.plot(t, I/N)
t, S, I, R = EoN.SIR_homogeneous_pairwise_from_graph(G, tau, gamma, rho=rho,
tmax=tmax, tcount=tcount)
ax.plot(t, I/N, '-.')
# In[7]:
#we expect a homogeneous model to perform poorly because the degree
#distribution is very heterogeneous
t, S, I, R = EoN.SIR_homogeneous_pairwise_from_graph(G,
tau,
gamma,
rho=rho,
tmax=tmax)
plt.plot(t, I, '-.', label='Homogeneous pairwise', linewidth=5)
#meanfield models will generally overestimate SIR growth because they
#treat partnerships as constantly changing.
t, S, I, R = EoN.SIR_heterogeneous_meanfield_from_graph(G,
tau,
gamma,
rho=rho,
tmax=tmax)
plt.plot(t, I, ':', label='Heterogeneous meanfield', linewidth=5)
#The EBCM model does not account for degree correlations or clustering
t, S, I, R = EoN.EBCM_from_graph(G, tau, gamma, rho=rho, tmax=tmax)
plt.plot(t, I, '--', label='EBCM approximation', linewidth=5)
#the preferential mixing model captures degree correlations.
t, S, I, R = EoN.EBCM_pref_mix_from_graph(G, tau, gamma, rho=rho, tmax=tmax)
plt.plot(t, I, label='Pref mix EBCM', linewidth=5, dashes=[4, 2, 1, 2, 1, 2])
plt.xlabel('$t$')
plt.ylabel('Number infected')
plt.legend()
# plt.savefig('SIR_BA_model_vs_sim.png')
# The preferential mixing version of the EBCM approach provides the best approximation to the (gray) simulated epidemics.
