def SIS_process(G, degree_prob, tmax, tau, gamma):
N = G.order()
plt.figure(5)
plt.clf()
plt.figure(6)
plt.clf()
for index, starting_node in enumerate([x * N / 10. for x in range(10)]):
plt.figure(5)
t, S, I = EoN.fast_SIS(G,
tau,
gamma,
initial_infecteds=[starting_node],
tmax=tmax)
#print(I[-1])
subt = scipy.linspace(0, tmax, 501)
subI = EoN.subsample(subt, t, I)
plt.plot(subt, subI)
if I[-1] > 100:
plt.figure(6)
shift = EoN.get_time_shift(t, I, 1000)
plt.plot(subt - shift, subI)
plt.figure(5)
plt.savefig('sw_SIS_epi_N{}_p{}_k{}_tau{}.pdf'.format(N, p, k, tau))
plt.figure(6)
plt.savefig('sw_SIS_epi_N{}_p{}_k{}_tau{}_shifted.pdf'.format(
N, p, k, tau))
def process_degree_distribution(N, Pk, color, Psi, DPsi, symbol, label, count):
report_times = scipy.linspace(0, 30, 3000)
sums = 0 * report_times
for cnt in range(count):
G = generate_network(Pk, N)
t, S, I, R = EoN.fast_SIR(G, tau, gamma, rho=rho)
plt.plot(t, I * 1. / N, '-', color=color, alpha=0.1, linewidth=1)
subsampled_I = EoN.subsample(report_times, t, I)
sums += subsampled_I * 1. / N
ave = sums / count
plt.plot(report_times, ave, color='k')
#Do EBCM
N = G.order(
) #N is arbitrary, but included because our implementation of EBCM assumes N is given.
t, S, I, R = EoN.EBCM_uniform_introduction(N,
Psi,
DPsi,
tau,
gamma,
rho,
tmin=0,
tmax=10,
tcount=41)
plt.plot(t, I / N, symbol, color=color, markeredgecolor='k', label=label)
for cnt in range(3): #do 3 highlighted simulations
G = generate_network(Pk, N)
t, S, I, R = EoN.fast_SIR(G, tau, gamma, rho=rho)
plt.plot(t, I * 1. / N, '-', color='k', linewidth=0.1)
def simulate_process(graph_function, iterations, tmax, tcount, rho, kave, tau,
gamma, symbol):
Isum = scipy.zeros(tcount)
report_times = scipy.linspace(0, tmax, tcount)
for counter in range(iterations):
G = graph_function()
t, S, I = EoN.fast_SIS(G, tau, gamma, rho=rho, tmax=tmax)
I = EoN.subsample(report_times, t, I)
Isum += I
plt.plot(report_times, Isum * 1. / (N * iterations), symbol)
def SIR_process(G, degree_prob, tau, gamma, tmax=10):
N = G.order()
plt.figure(2)
plt.clf()
plt.figure(3)
plt.clf()
plt.figure(5)
plt.clf()
for index, starting_node in enumerate([x * N / 100. for x in range(100)]):
plt.figure(2)
t, S, I, R = EoN.fast_SIR(G,
tau,
gamma,
initial_infecteds=[starting_node])
subt = scipy.linspace(0, t[-1], 101)
subI, subR = EoN.subsample(subt, t, I, R)
plt.plot(subt, subI)
if R[-1] > 500:
plt.figure(3)
shift = EoN.get_time_shift(t, R, threshold)
plt.plot(subt - shift, subI)
plt.figure(5)
plt.plot(subt - shift, subR)
#t, S, I, R = EoN.EBCM(degree_prob, tau, gamma, rho)
rho = 1. / N
def psi(x):
return sum(degree_prob[k] * x**k for k in degree_prob)
def psiPrime(x):
return sum(k * degree_prob[k] * x**(k - 1) for k in degree_prob)
t, S, I, R = EoN.EBCM_uniform_introduction(N,
psi,
psiPrime,
tau,
gamma,
rho,
tmax=tmax)
shift = EoN.get_time_shift(t, R, threshold)
plt.figure(2)
#plt.savefig('sw_SIR_epi_N{}_p{}_k{}_tau{}.pdf'.format(N,p,k,tau))
plt.figure(3)
plt.plot(t - shift, I, '--')
plt.xlabel('$t$', fontsize=18)
plt.ylabel('$I$', fontsize=18)
#plt.set_xtick_labels(fontsize = 15)
xmax = get_xmax(t - shift, I)
plt.axis(xmax=xmax)
plt.savefig('sw_SIR_epi_N{}_p{}_k{}_tau{}_shifted.pdf'.format(
N, p, k, tau))
plt.figure(5)
plt.plot(t - shift, R, '--')
def process_degree_distribution(Gbig, Gsmall, color, Psi, DPsi, symbol):
t, S, I, R = EoN.fast_SIR(Gsmall, tau, gamma, rho=rho)
plt.plot(t, I * 1. / Gsmall.order(), ':', color=color)
t, S, I, R = EoN.fast_SIR(Gbig, tau, gamma, rho=rho)
plt.plot(t, I * 1. / Gbig.order(), color=color)
N = Gbig.order(
) #N is arbitrary, but included because our implementation of EBCM assumes N is given.
t, S, I, R = EoN.EBCM(N, lambda x: (1 - rho) * Psi(x), lambda x:
(1 - rho) * DPsi(x), tau, gamma, 1 - rho)
I = EoN.subsample(report_times, t, I)
plt.plot(report_times, I / N, symbol, color=color, markeredgecolor='k')
def sim_and_plot(G, tau, gamma, rho, tmax, tcount, ax):
t, S, I = EoN.fast_SIS(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, = EoN.SIS_heterogeneous_meanfield_from_graph(G, tau, gamma, rho=rho,
tmax=tmax, tcount=tcount)
ax.plot(t, I/N, '--')
t, S, I = EoN.SIS_compact_pairwise_from_graph(G, tau, gamma, rho=rho,
tmax=tmax, tcount=tcount)
ax.plot(t, I/N)
t, S, I = EoN.SIS_homogeneous_pairwise_from_graph(G, tau, gamma, rho=rho,
tmax=tmax, tcount=tcount)
ax.plot(t, I/N, '-.')
report_times = scipy.linspace(tmin, tmax, 21) #for simulations
plt.figure(0)
tau = 0.005
G = nx.complete_graph(N)
t, S, I = complete_graph_lumped(N, tau, gamma, I0, tmin, tmax, tcount)
plt.plot(t, I/N, label = 'Prediction')
#now check with simulation
obs_I = 0*report_times
print("done with complete graph ODE. Now simulating")
for counter in range(iterations):
IC = random.sample(range(N),I0)
t, S, I = EoN.fast_SIS(G, tau, gamma, initial_infecteds = IC, tmax = tmax)
obs_I += EoN.subsample(report_times, t, I)
plt.plot(report_times, obs_I*1./(iterations*N), 'o', label='Simulation')
plt.axis(ymin=0, ymax=1)
plt.xlabel('$t$')
plt.ylabel('$[I]$')
plt.legend()
plt.savefig('fig2p11a.png')
print("done with complete graph. Now star --- warning, this may be slow")
iterations = 200
tmax = 40
tau_c = gamma/kave
rho = 0.05
tcount=1001
report_times = scipy.linspace(0,tmax,tcount)
for tau, label in zip([0.9*tau_c, tau_c, 1.1*tau_c, 1.5*tau_c],['a', 'b', 'c', 'd']):
plt.clf()
Isum = scipy.zeros(len(report_times))
for counter in range(iterations):
G = nx.configuration_model([kave]*N)
t, S, I = EoN.fast_SIS(G, tau, gamma, tmax=tmax, rho=rho)
I=I*1./N
I = EoN.subsample(report_times, t, I)
Isum += I
plt.plot(report_times, Isum/iterations, color = 'grey', linewidth = 5, alpha=0.3)
S0 = (1-rho)*N
I0 = rho*N
t, S, I = EoN.SIS_homogeneous_meanfield(S0, I0, kave, tau, gamma, tmin=0, tmax=tmax,
tcount=tcount)
plt.plot(t, I/N, '--')
S0 = (1-rho)*N
I0 = rho*N
SI0 = (1-rho)*N*kave*rho
SS0 = (1-rho)*N*kave*(1-rho)
t, S, I = EoN.SIS_homogeneous_pairwise(S0, I0, SI0, SS0, kave, tau, gamma, tmin = 0,
tau = 1.
gamma = 1.
colors = [
'#5AB3E6', '#FF2000', '#009A80', '#E69A00', '#CD9AB3', '#0073B3', '#F0E442'
]
kave = 5
G = nx.fast_gnp_random_graph(N, kave / (N - 1.))
initial_infecteds = random.sample(range(N), int(0.01 * N))
print('simulating')
t, S, I, R = EoN.fast_SIR(G, tau, gamma, initial_infecteds=initial_infecteds)
report_times = scipy.linspace(0, 10, 101)
S, I, R = EoN.subsample(report_times, t, S, I, R)
plt.plot(report_times, S, color=colors[1], label='simulation')
plt.plot(report_times, I, color=colors[1])
plt.plot(report_times, R, color=colors[1])
print('doing ODE models')
t, S, I, R = EoN.SIR_effective_degree_from_graph(
G, tau, gamma, initial_infecteds=initial_infecteds, tmax=10, tcount=51)
plt.plot(t, S, color=colors[2], dashes=[6, 6], label='effective degree')
plt.plot(t, I, color=colors[2], dashes=[6, 6])
plt.plot(t, R, color=colors[2], dashes=[6, 6])
t, S, I, R = EoN.SIR_heterogeneous_pairwise_from_graph(
G, tau, gamma, initial_infecteds=initial_infecteds, tmax=10, tcount=51)
plt.plot(t,
def rec_time_fxn(u, K, gamma):
duration = 0
for counter in range(K):
duration += random.expovariate(K * gamma)
return duration
def trans_time_fxn(u, v, tau):
return random.expovariate(tau)
display_ts = scipy.linspace(0, 50, 26)
for G, filename in ([regular, 'fig9p2a.png'], [ER, 'fig9p2b.png']):
plt.clf()
Isum = scipy.zeros(len(display_ts))
for K, symbol in ([1, 's'], [3, 'd']):
for counter in range(iterations):
t, S, I, R = EoN.fast_nonMarkov_SIR(G,
trans_time_fxn=trans_time_fxn,
trans_time_args=(tau, ),
rec_time_fxn=rec_time_fxn,
rec_time_args=(K, gamma),
rho=rho)
newI = EoN.subsample(display_ts, t, I)
Isum += newI
Isum /= iterations
plt.plot(display_ts, Isum, symbol)
plt.xlabel('$t$')
plt.ylabel('Prevalence')
plt.savefig(filename)
