/
model_code.py
445 lines (354 loc) · 18.4 KB
/
model_code.py
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import numpy as np
from multiprocessing import Pool
from itertools import product
import os
try:
import plotly.graph_objs as go
from plotly.subplots import make_subplots
from plotly.offline import init_notebook_mode, iplot
except ImportError:
print("Installing plotly. This may take a while.")
from pip._internal import main as pipmain
pipmain(['install', 'plotly'])
import plotly.graph_objs as go
from plotly.subplots import make_subplots
from plotly.offline import init_notebook_mode, iplot
class corona_model(object):
def __init__(self, ξ_base, A_rel, d_vaccine, rel_ρ, δ_param, \
ωR_param, π_D, R_0, rel_λ,initial_infect):
self.pop = 67_000_000
self.T_years = 5
self.Δ_time = 14
self.T = self.T_years * 365 * self.Δ_time
self.λ = 1
self.γ = 0
self.ξ_base_high= .999
self.r_high = .999
self.r = .98
self.δ = 1/(self.Δ_time*δ_param)
self.ωR = 1/(self.Δ_time*ωR_param)
self.ωD = self.ωR*π_D/(1-π_D)
self.λQ = rel_λ*self.λ
self.ρS = R_0/((self.λ/self.δ)*(rel_ρ + self.δ/(self.ωR+self.ωD)))
self.ρA = rel_ρ*self.ρS
self.InitialInfect = initial_infect
self.d_vaccine = d_vaccine
self.A_rel = A_rel
self.ξ_base = ξ_base
self.baseline = {
'τA' : 0.,
'ξ_U' : 0.,
'ξ_P' : 0.,
'ξ_N' : 0.,
'ξ_R' : 0.,
'r_U' : self.r,
'r_P' : 0.,
'r_N' : self.r,
'r_R' : self.r_high,
'd_start_exp' : 0.,
'experiment' : "baseline_vaccine_tag"
}
τ_A_daily_target = 0
ξ_U_daily_target = ξ_base
ξ_P_daily_target = self.ξ_base_high
ξ_N_daily_target = ξ_base
ξ_R_daily_target = 0
r_U_daily_target = 0
r_N_daily_target = 0
r_P_daily_target = 0
r_R_daily_target = self.r_high
self.policy_offset = 14
self.common_quarantine = {
'τA' : (1+τ_A_daily_target)**(1./self.Δ_time)-1,
'ξ_U' : (1+ξ_U_daily_target)**(1./self.Δ_time)-1,
'ξ_P' : (1+ξ_P_daily_target)**(1./self.Δ_time)-1,
'ξ_N' : (1+ξ_N_daily_target)**(1./self.Δ_time)-1,
'ξ_R' : (1+ξ_R_daily_target)**(1./self.Δ_time)-1,
'r_U' : (1+r_U_daily_target)**(1./self.Δ_time)-1,
'r_P' : (1+r_P_daily_target)**(1./self.Δ_time)-1,
'r_N' : (1+r_N_daily_target)**(1./self.Δ_time)-1,
'r_R' : (1+r_R_daily_target)**(1./self.Δ_time)-1,
'experiment' : "baseline_vaccine_tag"
}
def solve_case(self, model):
M0_vec = np.zeros(13)
M0_vec[4] = self.InitialInfect / self.pop
M0_vec[8] = 1. / self.pop
M0_vec[0] = 1 - np.sum(M0_vec)
Q_inds = [1,3,5,7,9,11]
NQ_inds = [0,2,4,6,8,10]
IANQ_inds = [4,6]
IAQ_inds = [5,7]
ISNQ_inds = [8]
ISQ_inds = [9]
NANQ_inds = [0,2]
RANQ_inds = [10]
NAQ_inds = [1,3]
RAQ_inds = [11]
M_t = np.zeros((13, self.T))
M_t[:,0] = M0_vec
for t in range(1,self.T):
Mt = M_t[:,t-1]
Mt_Q = np.sum(Mt[Q_inds])
Mt_NQ = np.sum(Mt[NQ_inds])
Mt_IANQ = np.sum(Mt[IANQ_inds])
Mt_IAQ = np.sum(Mt[IAQ_inds])
Mt_ISNQ = np.sum(Mt[ISNQ_inds])
Mt_ISQ = np.sum(Mt[ISQ_inds])
Mt_NANQ = np.sum(Mt[NANQ_inds])
Mt_RANQ = np.sum(Mt[RANQ_inds])
Mt_NAQ = np.sum(Mt[NAQ_inds])
Mt_RAQ = np.sum(Mt[RAQ_inds])
Mt_Total = self.λ*Mt_NQ + self.λQ*Mt_Q
Mt_I = self.λ*(Mt_IANQ + Mt_ISNQ) + self.λQ*(Mt_IAQ + Mt_ISQ)
Mt_N = self.λ*(Mt_NANQ + Mt_RANQ) + self.λQ*(Mt_NAQ + Mt_RAQ)
pit_I = Mt_I/Mt_Total
pit_IA = (self.λ*Mt_IANQ + self.λQ*Mt_IAQ)/Mt_I
pit_IS = (self.λ*Mt_ISNQ + self.λQ*Mt_ISQ)/Mt_I
alphat = pit_I*(pit_IS*self.ρS + pit_IA*self.ρA)
# A_daily just selects every 14th entry starting at the 14th entry (end of day each day)
if t <= model['d_start_exp']:
ξ_U_t = 0
ξ_P_t = 0
ξ_N_t = 0
ξ_R_t = 0
r_U_t = 0
r_P_t = 0
r_N_t = 0
r_R_t = 0
tau_t = 0
elif t >= self.d_vaccine:
ξ_U_t = model['ξ_U']
ξ_P_t = model['ξ_P']
ξ_N_t = model['ξ_N']
ξ_R_t = 0.
r_U_t = model['r_U']
r_P_t = model['r_P']
r_N_t = model['r_N']
r_R_t = model['r_R']
else:
ξ_U_t = model['ξ_U']
ξ_P_t = model['ξ_P']
ξ_N_t = model['ξ_N']
ξ_R_t = model['ξ_R']
r_U_t = model['r_U']
r_P_t = model['r_P']
r_N_t = model['r_N']
r_R_t = model['r_R']
tau_t = model['τA']
transition_matrix_t = np.zeros((13,13))
transition_matrix_t[0,1] = ξ_U_t
transition_matrix_t[0,2] = tau_t
transition_matrix_t[0,4] = self.λ*alphat
transition_matrix_t[1,0] = r_U_t
transition_matrix_t[1,3] = tau_t
transition_matrix_t[1,5] = self.λQ*alphat
transition_matrix_t[2,3] = ξ_N_t
transition_matrix_t[2,6] = self.λ*alphat
transition_matrix_t[3,2] = r_N_t
transition_matrix_t[3,7] = self.λQ*alphat
transition_matrix_t[4,5] = ξ_U_t
transition_matrix_t[4,6] = tau_t
transition_matrix_t[4,8] = self.δ
transition_matrix_t[5,4] = r_U_t
transition_matrix_t[5,7] = tau_t
transition_matrix_t[5,9] = self.δ
transition_matrix_t[6,7] = ξ_P_t
transition_matrix_t[6,8] = self.δ
transition_matrix_t[7,6] = r_P_t
transition_matrix_t[7,9] = self.δ
transition_matrix_t[8,9] = ξ_P_t
transition_matrix_t[8,10] = self.ωR
transition_matrix_t[8,12] = self.ωD
transition_matrix_t[9,8] = r_P_t
transition_matrix_t[9,11] = self.ωR
transition_matrix_t[9,12] = self.ωD
transition_matrix_t[10,4] = self.γ * self.λ*alphat
transition_matrix_t[10,11] = ξ_R_t
transition_matrix_t[11,5] = self.γ * self.λ*alphat
transition_matrix_t[11,10] = r_R_t
if t >= self.d_vaccine:
transition_matrix_t[0,10] = .001
transition_matrix_t[1,10] = .001
transition_matrix_t[2,10] = .001
transition_matrix_t[3,10] = .001
transition_matrix_t += np.diag(1 - np.sum(transition_matrix_t, axis=1))
assert np.min(transition_matrix_t) >= 0
assert np.max(transition_matrix_t) <= 1
M_t[:,t] = transition_matrix_t.T @ Mt
Y_t = np.sum(M_t[[0,2,4,6,10]], axis=0) + \
self.A_rel * np.sum(M_t[[1,3,5,7,11]], axis=0)
Reported_T_start = self.pop * (tau_t + self.δ) * (M_t[4] + M_t[5])
Reported_T_start[0] = 0
Reported_T = np.cumsum(Reported_T_start)
Reported_D = Reported_T[13::14]
Notinfected_D = np.sum(M_t[[0,1,2,3]], axis=0)[13::14]
Unreported_D = np.sum(M_t[[4,5]], axis=0)[13::14]
Infected_D = np.sum(M_t[[8,9]], axis=0)[13::14]
Recovered_D = np.sum(M_t[[10,11]], axis=0)[13::14]
Dead_D = M_t[12][13::14]
Infected_T = np.sum(M_t[4:10], axis=0)
Y_D = Y_t[13::14]
return Reported_D, Notinfected_D, Unreported_D, Infected_D, \
Recovered_D, Dead_D, Infected_T, Y_D, M_t
def solve_model(self):
Reported_D_base, Notinfected_D_base, Unreported_D_base, Infected_D_base, \
Recovered_D_base, Dead_D_base, Infected_T_base, Y_D_base, M_t_base = \
self.solve_case(self.baseline)
Tstar = np.argwhere(Reported_D_base>100)[0][0]
YearsPlot = 3
Tplot = np.arange(Tstar, min(Tstar + YearsPlot * 365, self.T/self.Δ_time) + .5, 1)
Xplot = np.arange(0, len(Tplot))
self.Tstar = Tstar
self.common_quarantine['d_start_exp'] = (Tstar+1) * self.Δ_time + \
self.policy_offset * self.Δ_time
Reported_D_com, Notinfected_D_com, Unreported_D_com, Infected_D_com, \
Recovered_D_com, Dead_D_com, Infected_T_com, Y_D_com, M_t_com = \
self.solve_case(self.common_quarantine)
return Reported_D_com, Infected_D_com, Dead_D_com, Y_D_com
def run_experiment(self, τ, Δ):
τ_A_daily_target = τ
r_U_daily_target = 0
r_N_daily_target = 0
r_P_daily_target = 0
r_R_daily_target = self.r_high
ξ_U_daily_target = self.ξ_base
ξ_P_daily_target = self.ξ_base_high
ξ_N_daily_target = self.ξ_base*Δ
ξ_R_daily_target = 0
self.test_and_quarantine = {
'τA' : (1+τ_A_daily_target)**(1./self.Δ_time)-1,
'ξ_U' : (1+ξ_U_daily_target)**(1./self.Δ_time)-1,
'ξ_P' : (1+ξ_P_daily_target)**(1./self.Δ_time)-1,
'ξ_N' : (1+ξ_N_daily_target)**(1./self.Δ_time)-1,
'ξ_R' : (1+ξ_R_daily_target)**(1./self.Δ_time)-1,
'r_U' : (1+r_U_daily_target)**(1./self.Δ_time)-1,
'r_P' : (1+r_P_daily_target)**(1./self.Δ_time)-1,
'r_N' : (1+r_N_daily_target)**(1./self.Δ_time)-1,
'r_R' : (1+r_R_daily_target)**(1./self.Δ_time)-1,
'experiment' : "baseline_vaccine_tag"
}
self.test_and_quarantine['d_start_exp'] = (self.Tstar+1) * self.Δ_time + \
self.policy_offset * self.Δ_time
Reported_D_test, Notinfected_D_test, Unreported_D_test, Infected_D_test, \
Recovered_D_test, Dead_D_test, Infected_T_test, Y_D_test, M_t_test = \
self.solve_case(self.test_and_quarantine)
return Reported_D_test, Infected_D_test, Dead_D_test, Y_D_test
def generate_plots(Δ, τ, ξ_base, A_rel, d_vaccine, rel_ρ, δ_param, \
ωR_param, π_D, R_0, rel_λ, initial_infect, slide_var):
colors = ['orange', 'green']
styles = ['dot', 'dash']
rmin = 0
rmax = 0
imin = 0
imax = 0
dmin = 0
dmax = 0
ymin = .5
ymax = 0
fig = make_subplots(2, 2, print_grid = False, \
subplot_titles=("A. Reported cases", "B. Current symptomatic cases", "C. Deaths - Cumulative", "D. Current output"),
vertical_spacing = .2)
model = corona_model(ξ_base, A_rel, d_vaccine, rel_ρ, δ_param, \
ωR_param, π_D, R_0, rel_λ, initial_infect)
Reported_D_com, Infected_D_com, Dead_D_com, Y_D_com = model.solve_model()
rmin = min(rmin, np.min(Reported_D_com) * 1.2)
rmax = max(rmax, np.max(Reported_D_com) * 1.2)
imin = min(imin, np.min(Infected_D_com) * 1.2)
imax = max(imax, np.max(Infected_D_com) * 1.2)
dmin = min(dmin, np.min(Dead_D_com) * 1.2)
dmax = max(dmax, np.max(Dead_D_com) * 1.2)
ymin = min(ymin, np.min(Y_D_com) * 1.2)
ymax = max(ymax, np.max(Y_D_com) * 1.2)
fig.add_scatter(y = Reported_D_com, row = 1, col = 1, visible = True, showlegend = True,
name = 'Common Quarantine', line = dict(color = (colors[0]), width = 3, dash = styles[0]))
fig.add_scatter(y = Infected_D_com, row = 1, col = 2, visible = True, showlegend = False,
name = 'Common Quarantine', line = dict(color = (colors[0]), width = 3, dash = styles[0]))
fig.add_scatter(y = Dead_D_com, row = 2, col = 1, visible = True, showlegend = False,
name = 'Common Quarantine', line = dict(color = (colors[0]), width = 3, dash = styles[0]))
fig.add_scatter(y = Y_D_com, row = 2, col = 2, visible = True, showlegend = False,
name = 'Common Quarantine', line = dict(color = (colors[0]), width = 3, dash = styles[0]))
if slide_var == 1: #Slide over τ
prd = product(τ, [Δ])
slider_vars = τ
slider_varname = "τ"
if slide_var == 2: #Slide over Δ
prd = product([τ], Δ)
slider_vars = Δ
slider_varname = "Δ"
pool = Pool(os.cpu_count())
results = pool.starmap(model.run_experiment, prd)
for j in range(len(slider_vars)):
rmin = min(rmin, np.min(results[j][0]) * 1.2)
rmax = max(rmax, np.max(results[j][0]) * 1.2)
imin = min(imin, np.min(results[j][1]) * 1.2)
imax = max(imax, np.max(results[j][1]) * 1.2)
dmin = min(dmin, np.min(results[j][2]) * 1.2)
dmax = max(dmax, np.max(results[j][2]) * 1.2)
ymin = min(ymin, np.min(results[j][3]) * 1.2)
ymax = max(ymax, np.max(results[j][3]) * 1.2)
fig.add_scatter(y = results[j][0], row = 1, col = 1, visible = j == 0, showlegend = True,
name = 'Quarantine & Test', line = dict(color = (colors[1]), width = 3, dash = styles[1]))
fig.add_scatter(y = results[j][1], row = 1, col = 2, visible = j == 0, showlegend = False,
name = 'Quarantine & Test', line = dict(color = (colors[1]), width = 3, dash = styles[1]))
fig.add_scatter(y = results[j][2], row = 2, col = 1, visible = j == 0, showlegend = False,
name = 'Quarantine & Test', line = dict(color = (colors[1]), width = 3, dash = styles[1]))
fig.add_scatter(y = results[j][3], row = 2, col = 2, visible = j == 0, showlegend = False,
name = 'Quarantine & Test', line = dict(color = (colors[1]), width = 3, dash = styles[1]))
steps = []
for i in range(len(slider_vars)):
step = dict(
method = 'restyle',
args = [{'visible': ['legendonly'] * len(fig.data)},
{'showlegend': ['False'] * len(fig.data)}],
label = slider_varname + ' = \n'+'{}'.format(round(slider_vars[i], 3))
)
step['args'][1]['showlegend'][0] = True
step['args'][1]['showlegend'][4 + i * 4] = True
for j in range(4):
step['args'][0]['visible'][int(j)] = True
for j in range(4):
step['args'][0]['visible'][4 + j + i * 4] = True
steps.append(step)
sliders = [dict(
steps = steps
)]
fig.layout.sliders = sliders
for i in fig['layout']['annotations']:
i['font'] = dict(color='black', size = 16)
fig['layout'].update(height=800, width=1000, showlegend = False)
fig['layout']['xaxis1'].update(title = go.layout.xaxis.Title(
text='Days since 100th case (5/3/2020)', font=dict(color='black')), range = [0, 600], \
gridcolor = 'rgb(220,220,220)', showline=True, linewidth=1, linecolor='black', mirror=True)
fig['layout']['xaxis2'].update(title = go.layout.xaxis.Title(
text='Days since 100th case (5/3/2020)', font=dict(color='black')), range = [0, 600], \
gridcolor = 'rgb(220,220,220)', showline=True, linewidth=1, linecolor='black', mirror=True)
fig['layout']['xaxis3'].update(title = go.layout.xaxis.Title(
text='Days since 100th case (5/3/2020)', font=dict(color='black')), range = [0, 600], \
gridcolor = 'rgb(220,220,220)', showline=True, linewidth=1, linecolor='black', mirror=True)
fig['layout']['xaxis4'].update(title = go.layout.xaxis.Title(
text='Days since 100th case (5/3/2020)', font=dict(color='black')), range = [0, 600], \
gridcolor = 'rgb(220,220,220)', showline=True, linewidth=1, linecolor='black', mirror=True)
fig['layout']['yaxis1'].update(title=go.layout.yaxis.Title(
text='Logarithm - Base 10', font=dict(color='black')), type='log', range = [rmin, np.log10(10_000_000)], gridcolor = 'rgb(220,220,220)', \
showline=True, linewidth=1, linecolor='black', mirror=True)
fig['layout']['yaxis2'].update(title=go.layout.yaxis.Title(
text='Fraction of Initial Population', font=dict(color='black')), range=[imin, imax], gridcolor = 'rgb(220,220,220)', showline=True, linewidth=1, linecolor='black', mirror=True)
fig['layout']['yaxis3'].update(title=go.layout.yaxis.Title(
text='Fraction of Initial Population', font=dict(color='black')), range = [dmin, dmax], gridcolor = 'rgb(220,220,220)', showline=True, linewidth=1, linecolor='black', mirror=True)
fig['layout']['yaxis4'].update(title=go.layout.yaxis.Title(
text='Output', font=dict(color='black')), range = [ymin, 1.05], gridcolor = 'rgb(220,220,220)', showline=True, linewidth=1, linecolor='black', mirror=True)
# fig['layout']['margin'].update(l=70, r=70, t=20, b=70)
fig['layout']['plot_bgcolor'] = 'rgba(0,0,0,0)'
return fig
def generate_plots_2d(Δ, τ, ξ_base, A_rel, d_vaccine, rel_ρ, δ_param, \
ωR_param, π_D, R_0, rel_λ, initial_infect):
model = corona_model(ξ_base, A_rel, d_vaccine, rel_ρ, δ_param, \
ωR_param, π_D, R_0, rel_λ, initial_infect)
Reported_D, Infected_D, Dead_D, Y_D, Reported_D_com, Infected_D_com, \
Dead_D_com, Y_D_com = model.solve_model()
prd = product(τ, Δ)
pool = Pool(os.cpu_count())
results = pool.starmap(model.run_experiment, prd)
return Reported_D, Infected_D, Dead_D, Y_D, Reported_D_com, Infected_D_com, \
Dead_D_com, Y_D_com, results, prd