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models.py
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models.py
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from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import networkx as networkx
import numpy as numpy
import scipy as scipy
import scipy.integrate
class SEIRSModel():
"""
A class to simulate the Deterministic SEIRS Model
===================================================
Params: beta Rate of transmission (exposure)
sigma Rate of infection (upon exposure)
gamma Rate of recovery (upon infection)
xi Rate of re-susceptibility (upon recovery)
mu_I Rate of infection-related death
mu_0 Rate of baseline death
nu Rate of baseline birth
beta_D Rate of transmission (exposure) for individuals with detected infections
sigma_D Rate of infection (upon exposure) for individuals with detected infections
gamma_D Rate of recovery (upon infection) for individuals with detected infections
mu_D Rate of infection-related death for individuals with detected infections
theta_E Rate of baseline testing for exposed individuals
theta_I Rate of baseline testing for infectious individuals
psi_E Probability of positive test results for exposed individuals
psi_I Probability of positive test results for exposed individuals
q Probability of quarantined individuals interacting with others
initE Init number of exposed individuals
initI Init number of infectious individuals
initD_E Init number of detected infectious individuals
initD_I Init number of detected infectious individuals
initR Init number of recovered individuals
initF Init number of infection-related fatalities
(all remaining nodes initialized susceptible)
"""
def __init__(self, initN, beta, sigma, gamma, xi=0, mu_I=0, mu_0=0, nu=0, p=0,
beta_D=None, sigma_D=None, gamma_D=None, mu_D=None,
theta_E=0, theta_I=0, psi_E=0, psi_I=0, q=0,
initE=0, initI=10, initD_E=0, initD_I=0, initR=0, initF=0):
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Model Parameters:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
self.beta = beta
self.sigma = sigma
self.gamma = gamma
self.xi = xi
self.mu_I = mu_I
self.mu_0 = mu_0
self.nu = nu
self.p = p
# Testing-related parameters:
self.beta_D = beta_D if beta_D is not None else self.beta
self.sigma_D = sigma_D if sigma_D is not None else self.sigma
self.gamma_D = gamma_D if gamma_D is not None else self.gamma
self.mu_D = mu_D if mu_D is not None else self.mu_I
self.theta_E = theta_E if theta_E is not None else self.theta_E
self.theta_I = theta_I if theta_I is not None else self.theta_I
self.psi_E = psi_E if psi_E is not None else self.psi_E
self.psi_I = psi_I if psi_I is not None else self.psi_I
self.q = q if q is not None else self.q
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Initialize Timekeeping:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
self.t = 0
self.tmax = 0 # will be set when run() is called
self.tseries = numpy.array([0])
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Initialize Counts of inidividuals with each state:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
self.N = numpy.array([int(initN)])
self.numE = numpy.array([int(initE)])
self.numI = numpy.array([int(initI)])
self.numD_E = numpy.array([int(initD_E)])
self.numD_I = numpy.array([int(initD_I)])
self.numR = numpy.array([int(initR)])
self.numF = numpy.array([int(initF)])
self.numS = numpy.array([self.N[-1] - self.numE[-1] - self.numI[-1] - self.numD_E[-1] - self.numD_I[-1] - self.numR[-1] - self.numF[-1]])
assert(self.numS[0] >= 0), "The specified initial population size N must be greater than or equal to the initial compartment counts."
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
@staticmethod
def system_dfes(t, variables, beta, sigma, gamma, xi, mu_I, mu_0, nu,
beta_D, sigma_D, gamma_D, mu_D, theta_E, theta_I, psi_E, psi_I, q):
S, E, I, D_E, D_I, R, F = variables # varibles is a list with compartment counts as elements
N = S + E + I + D_E + D_I + R
dS = - (beta*S*I)/N - q*(beta_D*S*D_I)/N + xi*R + nu*N - mu_0*S
dE = (beta*S*I)/N + q*(beta_D*S*D_I)/N - sigma*E - theta_E*psi_E*E - mu_0*E
dI = sigma*E - gamma*I - mu_I*I - theta_I*psi_I*I - mu_0*I
dDE = theta_E*psi_E*E - sigma_D*D_E - mu_0*D_E
dDI = theta_I*psi_I*I + sigma_D*D_E - gamma_D*D_I - mu_D*D_I - mu_0*D_I
dR = gamma*I + gamma_D*D_I - xi*R - mu_0*R
dF = mu_I*I + mu_D*D_I
return [dS, dE, dI, dDE, dDI, dR, dF]
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def run_epoch(self, runtime, dt=0.1):
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Create a list of times at which the ODE solver should output system values.
# Append this list of times as the model's timeseries
t_eval = numpy.arange(start=self.t, stop=self.t+runtime, step=dt)
# Define the range of time values for the integration:
t_span = (self.t, self.t+runtime)
# Define the initial conditions as the system's current state:
# (which will be the t=0 condition if this is the first run of this model,
# else where the last sim left off)
init_cond = [self.numS[-1], self.numE[-1], self.numI[-1], self.numD_E[-1], self.numD_I[-1], self.numR[-1], self.numF[-1]]
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Solve the system of differential eqns:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
solution = scipy.integrate.solve_ivp(lambda t, X: SEIRSModel.system_dfes(t, X, self.beta, self.sigma, self.gamma, self.xi, self.mu_I, self.mu_0, self.nu,
self.beta_D, self.sigma_D, self.gamma_D, self.mu_D, self.theta_E, self.theta_I, self.psi_E, self.psi_I, self.q
),
t_span=[self.t, self.tmax], y0=init_cond, t_eval=t_eval
)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Store the solution output as the model's time series and data series:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
self.tseries = numpy.append(self.tseries, solution['t'])
self.numS = numpy.append(self.numS, solution['y'][0])
self.numE = numpy.append(self.numE, solution['y'][1])
self.numI = numpy.append(self.numI, solution['y'][2])
self.numD_E = numpy.append(self.numD_E, solution['y'][3])
self.numD_I = numpy.append(self.numD_I, solution['y'][4])
self.numR = numpy.append(self.numR, solution['y'][5])
self.numF = numpy.append(self.numF, solution['y'][6])
self.t = self.tseries[-1]
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def run(self, T, dt=0.1, checkpoints=None, verbose=False):
if(T>0):
self.tmax += T
else:
return False
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Pre-process checkpoint values:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if(checkpoints):
numCheckpoints = len(checkpoints['t'])
paramNames = ['beta', 'sigma', 'gamma', 'xi', 'mu_I', 'mu_0', 'nu',
'beta_D', 'sigma_D', 'gamma_D', 'mu_D',
'theta_E', 'theta_I', 'psi_E', 'psi_I', 'q']
for param in paramNames:
# For params that don't have given checkpoint values (or bad value given),
# set their checkpoint values to the value they have now for all checkpoints.
if(param not in list(checkpoints.keys())
or not isinstance(checkpoints[param], (list, numpy.ndarray))
or len(checkpoints[param])!=numCheckpoints):
checkpoints[param] = [getattr(self, param)]*numCheckpoints
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Run the simulation loop:
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if(not checkpoints):
self.run_epoch(runtime=self.tmax, dt=dt)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
print("t = %.2f" % self.t)
if(verbose):
print("\t S = " + str(self.numS[-1]))
print("\t E = " + str(self.numE[-1]))
print("\t I = " + str(self.numI[-1]))
print("\t D_E = " + str(self.numD_E[-1]))
print("\t D_I = " + str(self.numD_I[-1]))
print("\t R = " + str(self.numR[-1]))
print("\t F = " + str(self.numF[-1]))
else: # checkpoints provided
for checkpointIdx, checkpointTime in enumerate(checkpoints['t']):
# Run the sim until the next checkpoint time:
self.run_epoch(runtime=checkpointTime-self.t, dt=dt)
# Having reached the checkpoint, update applicable parameters:
print("[Checkpoint: Updating parameters]")
for param in paramNames:
setattr(self, param, checkpoints[param][checkpointIdx])
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
print("t = %.2f" % self.t)
if(verbose):
print("\t S = " + str(self.numS[-1]))
print("\t E = " + str(self.numE[-1]))
print("\t I = " + str(self.numI[-1]))
print("\t D_E = " + str(self.numD_E[-1]))
print("\t D_I = " + str(self.numD_I[-1]))
print("\t R = " + str(self.numR[-1]))
print("\t F = " + str(self.numF[-1]))
if(self.t < self.tmax):
self.run_epoch(runtime=self.tmax-self.t, dt=dt)
return True
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def plot(self, ax=None, plot_S='line', plot_E='line', plot_I='line',plot_R='line', plot_F='line',
plot_D_E='line', plot_D_I='line', combine_D=True,
color_S='tab:green', color_E='orange', color_I='crimson', color_R='tab:blue', color_F='black',
color_D_E='mediumorchid', color_D_I='mediumorchid', color_reference='#E0E0E0',
dashed_reference_results=None, dashed_reference_label='reference',
shaded_reference_results=None, shaded_reference_label='reference',
vlines=[], vline_colors=[], vline_styles=[], vline_labels=[],
ylim=None, xlim=None, legend=True, title=None, side_title=None, plot_percentages=True):
import matplotlib.pyplot as pyplot
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Create an Axes object if None provided:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if(not ax):
fig, ax = pyplot.subplots()
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Prepare data series to be plotted:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Fseries = self.numF/self.N if plot_percentages else self.numF
Eseries = self.numE/self.N if plot_percentages else self.numE
Dseries = (self.numD_E+self.numD_I)/self.N if plot_percentages else (self.numD_E+self.numD_I)
D_Eseries = self.numD_E/self.N if plot_percentages else self.numD_E
D_Iseries = self.numD_I/self.N if plot_percentages else self.numD_I
Iseries = self.numI/self.N if plot_percentages else self.numI
Rseries = self.numR/self.N if plot_percentages else self.numR
Sseries = self.numS/self.N if plot_percentages else self.numS
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Draw the reference data:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if(dashed_reference_results):
dashedReference_tseries = dashed_reference_results.tseries[::int(self.N/100)]
dashedReference_IDEstack = (dashed_reference_results.numI + dashed_reference_results.numD_I + dashed_reference_results.numD_E + dashed_reference_results.numE)[::int(self.N/100)] / (self.N if plot_percentages else 1)
ax.plot(dashedReference_tseries, dashedReference_IDEstack, color='#E0E0E0', linestyle='--', label='$I+D+E$ ('+dashed_reference_label+')', zorder=0)
if(shaded_reference_results):
shadedReference_tseries = shaded_reference_results.tseries
shadedReference_IDEstack = (shaded_reference_results.numI + shaded_reference_results.numD_I + shaded_reference_results.numD_E + shaded_reference_results.numE) / (self.N if plot_percentages else 1)
ax.fill_between(shaded_reference_results.tseries, shadedReference_IDEstack, 0, color='#EFEFEF', label='$I+D+E$ ('+shaded_reference_label+')', zorder=0)
ax.plot(shaded_reference_results.tseries, shadedReference_IDEstack, color='#E0E0E0', zorder=1)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Draw the stacked variables:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
topstack = numpy.zeros_like(self.tseries)
if(any(Fseries) and plot_F=='stacked'):
ax.fill_between(numpy.ma.masked_where(Fseries<=0, self.tseries), numpy.ma.masked_where(Fseries<=0, topstack+Fseries), topstack, color=color_F, alpha=0.5, label='$F$', zorder=2)
ax.plot( numpy.ma.masked_where(Fseries<=0, self.tseries), numpy.ma.masked_where(Fseries<=0, topstack+Fseries), color=color_F, zorder=3)
topstack = topstack+Fseries
if(any(Eseries) and plot_E=='stacked'):
ax.fill_between(numpy.ma.masked_where(Eseries<=0, self.tseries), numpy.ma.masked_where(Eseries<=0, topstack+Eseries), topstack, color=color_E, alpha=0.5, label='$E$', zorder=2)
ax.plot( numpy.ma.masked_where(Eseries<=0, self.tseries), numpy.ma.masked_where(Eseries<=0, topstack+Eseries), color=color_E, zorder=3)
topstack = topstack+Eseries
if(combine_D and plot_D_E=='stacked' and plot_D_I=='stacked'):
ax.fill_between(numpy.ma.masked_where(Dseries<=0, self.tseries), numpy.ma.masked_where(Dseries<=0, topstack+Dseries), topstack, color=color_D_E, alpha=0.5, label='$D_{all}$', zorder=2)
ax.plot( numpy.ma.masked_where(Dseries<=0, self.tseries), numpy.ma.masked_where(Dseries<=0, topstack+Dseries), color=color_D_E, zorder=3)
topstack = topstack+Dseries
else:
if(any(D_Eseries) and plot_D_E=='stacked'):
ax.fill_between(numpy.ma.masked_where(D_Eseries<=0, self.tseries), numpy.ma.masked_where(D_Eseries<=0, topstack+D_Eseries), topstack, color=color_D_E, alpha=0.5, label='$D_E$', zorder=2)
ax.plot( numpy.ma.masked_where(D_Eseries<=0, self.tseries), numpy.ma.masked_where(D_Eseries<=0, topstack+D_Eseries), color=color_D_E, zorder=3)
topstack = topstack+D_Eseries
if(any(D_Iseries) and plot_D_I=='stacked'):
ax.fill_between(numpy.ma.masked_where(D_Iseries<=0, self.tseries), numpy.ma.masked_where(D_Iseries<=0, topstack+D_Iseries), topstack, color=color_D_I, alpha=0.5, label='$D_I$', zorder=2)
ax.plot( numpy.ma.masked_where(D_Iseries<=0, self.tseries), numpy.ma.masked_where(D_Iseries<=0, topstack+D_Iseries), color=color_D_I, zorder=3)
topstack = topstack+D_Iseries
if(any(Iseries) and plot_I=='stacked'):
ax.fill_between(numpy.ma.masked_where(Iseries<=0, self.tseries), numpy.ma.masked_where(Iseries<=0, topstack+Iseries), topstack, color=color_I, alpha=0.5, label='$I$', zorder=2)
ax.plot( numpy.ma.masked_where(Iseries<=0, self.tseries), numpy.ma.masked_where(Iseries<=0, topstack+Iseries), color=color_I, zorder=3)
topstack = topstack+Iseries
if(any(Rseries) and plot_R=='stacked'):
ax.fill_between(numpy.ma.masked_where(Rseries<=0, self.tseries), numpy.ma.masked_where(Rseries<=0, topstack+Rseries), topstack, color=color_R, alpha=0.5, label='$R$', zorder=2)
ax.plot( numpy.ma.masked_where(Rseries<=0, self.tseries), numpy.ma.masked_where(Rseries<=0, topstack+Rseries), color=color_R, zorder=3)
topstack = topstack+Rseries
if(any(Sseries) and plot_S=='stacked'):
ax.fill_between(numpy.ma.masked_where(Sseries<=0, self.tseries), numpy.ma.masked_where(Sseries<=0, topstack+Sseries), topstack, color=color_S, alpha=0.5, label='$S$', zorder=2)
ax.plot( numpy.ma.masked_where(Sseries<=0, self.tseries), numpy.ma.masked_where(Sseries<=0, topstack+Sseries), color=color_S, zorder=3)
topstack = topstack+Sseries
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Draw the shaded variables:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if(any(Fseries) and plot_F=='shaded'):
ax.fill_between(numpy.ma.masked_where(Fseries<=0, self.tseries), numpy.ma.masked_where(Fseries<=0, Fseries), 0, color=color_F, alpha=0.5, label='$F$', zorder=4)
ax.plot( numpy.ma.masked_where(Fseries<=0, self.tseries), numpy.ma.masked_where(Fseries<=0, Fseries), color=color_F, zorder=5)
if(any(Eseries) and plot_E=='shaded'):
ax.fill_between(numpy.ma.masked_where(Eseries<=0, self.tseries), numpy.ma.masked_where(Eseries<=0, Eseries), 0, color=color_E, alpha=0.5, label='$E$', zorder=4)
ax.plot( numpy.ma.masked_where(Eseries<=0, self.tseries), numpy.ma.masked_where(Eseries<=0, Eseries), color=color_E, zorder=5)
if(combine_D and (any(Dseries) and plot_D_E=='shaded' and plot_D_E=='shaded')):
ax.fill_between(numpy.ma.masked_where(Dseries<=0, self.tseries), numpy.ma.masked_where(Dseries<=0, Dseries), 0, color=color_D_E, alpha=0.5, label='$D_{all}$', zorder=4)
ax.plot( numpy.ma.masked_where(Dseries<=0, self.tseries), numpy.ma.masked_where(Dseries<=0, Dseries), color=color_D_E, zorder=5)
else:
if(any(D_Eseries) and plot_D_E=='shaded'):
ax.fill_between(numpy.ma.masked_where(D_Eseries<=0, self.tseries), numpy.ma.masked_where(D_Eseries<=0, D_Eseries), 0, color=color_D_E, alpha=0.5, label='$D_E$', zorder=4)
ax.plot( numpy.ma.masked_where(D_Eseries<=0, self.tseries), numpy.ma.masked_where(D_Eseries<=0, D_Eseries), color=color_D_E, zorder=5)
if(any(D_Iseries) and plot_D_I=='shaded'):
ax.fill_between(numpy.ma.masked_where(D_Iseries<=0, self.tseries), numpy.ma.masked_where(D_Iseries<=0, D_Iseries), 0, color=color_D_I, alpha=0.5, label='$D_I$', zorder=4)
ax.plot( numpy.ma.masked_where(D_Iseries<=0, self.tseries), numpy.ma.masked_where(D_Iseries<=0, D_Iseries), color=color_D_I, zorder=5)
if(any(Iseries) and plot_I=='shaded'):
ax.fill_between(numpy.ma.masked_where(Iseries<=0, self.tseries), numpy.ma.masked_where(Iseries<=0, Iseries), 0, color=color_I, alpha=0.5, label='$I$', zorder=4)
ax.plot( numpy.ma.masked_where(Iseries<=0, self.tseries), numpy.ma.masked_where(Iseries<=0, Iseries), color=color_I, zorder=5)
if(any(Sseries) and plot_S=='shaded'):
ax.fill_between(numpy.ma.masked_where(Sseries<=0, self.tseries), numpy.ma.masked_where(Sseries<=0, Sseries), 0, color=color_S, alpha=0.5, label='$S$', zorder=4)
ax.plot( numpy.ma.masked_where(Sseries<=0, self.tseries), numpy.ma.masked_where(Sseries<=0, Sseries), color=color_S, zorder=5)
if(any(Rseries) and plot_R=='shaded'):
ax.fill_between(numpy.ma.masked_where(Rseries<=0, self.tseries), numpy.ma.masked_where(Rseries<=0, Rseries), 0, color=color_R, alpha=0.5, label='$R$', zorder=4)
ax.plot( numpy.ma.masked_where(Rseries<=0, self.tseries), numpy.ma.masked_where(Rseries<=0, Rseries), color=color_R, zorder=5)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Draw the line variables:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if(any(Fseries) and plot_F=='line'):
ax.plot(numpy.ma.masked_where(Fseries<=0, self.tseries), numpy.ma.masked_where(Fseries<=0, Fseries), color=color_F, label='$F$', zorder=6)
if(any(Eseries) and plot_E=='line'):
ax.plot(numpy.ma.masked_where(Eseries<=0, self.tseries), numpy.ma.masked_where(Eseries<=0, Eseries), color=color_E, label='$E$', zorder=6)
if(combine_D and (any(Dseries) and plot_D_E=='line' and plot_D_E=='line')):
ax.plot(numpy.ma.masked_where(Dseries<=0, self.tseries), numpy.ma.masked_where(Dseries<=0, Dseries), color=color_D_E, label='$D_{all}$', zorder=6)
else:
if(any(D_Eseries) and plot_D_E=='line'):
ax.plot(numpy.ma.masked_where(D_Eseries<=0, self.tseries), numpy.ma.masked_where(D_Eseries<=0, D_Eseries), color=color_D_E, label='$D_E$', zorder=6)
if(any(D_Iseries) and plot_D_I=='line'):
ax.plot(numpy.ma.masked_where(D_Iseries<=0, self.tseries), numpy.ma.masked_where(D_Iseries<=0, D_Iseries), color=color_D_I, label='$D_I$', zorder=6)
if(any(Iseries) and plot_I=='line'):
ax.plot(numpy.ma.masked_where(Iseries<=0, self.tseries), numpy.ma.masked_where(Iseries<=0, Iseries), color=color_I, label='$I$', zorder=6)
if(any(Sseries) and plot_S=='line'):
ax.plot(numpy.ma.masked_where(Sseries<=0, self.tseries), numpy.ma.masked_where(Sseries<=0, Sseries), color=color_S, label='$S$', zorder=6)
if(any(Rseries) and plot_R=='line'):
ax.plot(numpy.ma.masked_where(Rseries<=0, self.tseries), numpy.ma.masked_where(Rseries<=0, Rseries), color=color_R, label='$R$', zorder=6)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Draw the vertical line annotations:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if(len(vlines)>0 and len(vline_colors)==0):
vline_colors = ['gray']*len(vlines)
if(len(vlines)>0 and len(vline_labels)==0):
vline_labels = [None]*len(vlines)
if(len(vlines)>0 and len(vline_styles)==0):
vline_styles = [':']*len(vlines)
for vline_x, vline_color, vline_style, vline_label in zip(vlines, vline_colors, vline_styles, vline_labels):
if(vline_x is not None):
ax.axvline(x=vline_x, color=vline_color, linestyle=vline_style, alpha=1, label=vline_label)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Draw the plot labels:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ax.set_xlabel('days')
ax.set_ylabel('percent of population' if plot_percentages else 'number of individuals')
ax.set_xlim(0, (max(self.tseries) if not xlim else xlim))
ax.set_ylim(0, ylim)
if(plot_percentages):
ax.set_yticklabels(['{:,.0%}'.format(y) for y in ax.get_yticks()])
if(legend):
legend_handles, legend_labels = ax.get_legend_handles_labels()
ax.legend(legend_handles[::-1], legend_labels[::-1], loc='upper right', facecolor='white', edgecolor='none', framealpha=0.9, prop={'size': 8})
if(title):
ax.set_title(title, size=12)
if(side_title):
ax.annotate(side_title, (0, 0.5), xytext=(-45, 0), ha='right', va='center',
size=12, rotation=90, xycoords='axes fraction', textcoords='offset points')
return ax
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def figure_basic(self, plot_S='line', plot_E='line', plot_I='line',plot_R='line', plot_F='line',
plot_D_E='line', plot_D_I='line', combine_D=True,
color_S='tab:green', color_E='orange', color_I='crimson', color_R='tab:blue', color_F='black',
color_D_E='mediumorchid', color_D_I='mediumorchid', color_reference='#E0E0E0',
dashed_reference_results=None, dashed_reference_label='reference',
shaded_reference_results=None, shaded_reference_label='reference',
vlines=[], vline_colors=[], vline_styles=[], vline_labels=[],
ylim=None, xlim=None, legend=True, title=None, side_title=None, plot_percentages=True,
figsize=(12,8), use_seaborn=True, show=True):
import matplotlib.pyplot as pyplot
fig, ax = pyplot.subplots(figsize=figsize)
if(use_seaborn):
import seaborn
seaborn.set_style('ticks')
seaborn.despine()
self.plot(ax=ax, plot_S=plot_S, plot_E=plot_E, plot_I=plot_I,plot_R=plot_R, plot_F=plot_F,
plot_D_E=plot_D_E, plot_D_I=plot_D_I, combine_D=combine_D,
color_S=color_S, color_E=color_E, color_I=color_I, color_R=color_R, color_F=color_F,
color_D_E=color_D_E, color_D_I=color_D_I, color_reference=color_reference,
dashed_reference_results=dashed_reference_results, dashed_reference_label=dashed_reference_label,
shaded_reference_results=shaded_reference_results, shaded_reference_label=shaded_reference_label,
vlines=vlines, vline_colors=vline_colors, vline_styles=vline_styles, vline_labels=vline_labels,
ylim=ylim, xlim=xlim, legend=legend, title=title, side_title=side_title, plot_percentages=plot_percentages)
if(show):
pyplot.show()
return fig, ax
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def figure_infections(self, plot_S=False, plot_E='stacked', plot_I='stacked',plot_R=False, plot_F=False,
plot_D_E='stacked', plot_D_I='stacked', combine_D=True,
color_S='tab:green', color_E='orange', color_I='crimson', color_R='tab:blue', color_F='black',
color_D_E='mediumorchid', color_D_I='mediumorchid', color_reference='#E0E0E0',
dashed_reference_results=None, dashed_reference_label='reference',
shaded_reference_results=None, shaded_reference_label='reference',
vlines=[], vline_colors=[], vline_styles=[], vline_labels=[],
ylim=None, xlim=None, legend=True, title=None, side_title=None, plot_percentages=True,
figsize=(12,8), use_seaborn=True, show=True):
import matplotlib.pyplot as pyplot
fig, ax = pyplot.subplots(figsize=figsize)
if(use_seaborn):
import seaborn
seaborn.set_style('ticks')
seaborn.despine()
self.plot(ax=ax, plot_S=plot_S, plot_E=plot_E, plot_I=plot_I,plot_R=plot_R, plot_F=plot_F,
plot_D_E=plot_D_E, plot_D_I=plot_D_I, combine_D=combine_D,
color_S=color_S, color_E=color_E, color_I=color_I, color_R=color_R, color_F=color_F,
color_D_E=color_D_E, color_D_I=color_D_I, color_reference=color_reference,
dashed_reference_results=dashed_reference_results, dashed_reference_label=dashed_reference_label,
shaded_reference_results=shaded_reference_results, shaded_reference_label=shaded_reference_label,
vlines=vlines, vline_colors=vline_colors, vline_styles=vline_styles, vline_labels=vline_labels,
ylim=ylim, xlim=xlim, legend=legend, title=title, side_title=side_title, plot_percentages=plot_percentages)
if(show):
pyplot.show()
return fig, ax
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
class SEIRSNetworkModel():
"""
A class to simulate the SEIRS Stochastic Network Model
===================================================
Params: G Network adjacency matrix (numpy array) or Networkx graph object.
beta Rate of transmission (exposure) (global)
beta_local Rate(s) of transmission (exposure) for adjacent individuals (optional)
sigma Rate of infection (upon exposure)
gamma Rate of recovery (upon infection)
xi Rate of re-susceptibility (upon recovery)
mu_I Rate of infection-related death
mu_0 Rate of baseline death
nu Rate of baseline birth
p Probability of interaction outside adjacent nodes
Q Quarantine adjacency matrix (numpy array) or Networkx graph object.
beta_D Rate of transmission (exposure) for individuals with detected infections (global)
beta_local Rate(s) of transmission (exposure) for adjacent individuals with detected infections (optional)
sigma_D Rate of infection (upon exposure) for individuals with detected infections
gamma_D Rate of recovery (upon infection) for individuals with detected infections
mu_D Rate of infection-related death for individuals with detected infections
theta_E Rate of baseline testing for exposed individuals
theta_I Rate of baseline testing for infectious individuals
phi_E Rate of contact tracing testing for exposed individuals
phi_I Rate of contact tracing testing for infectious individuals
psi_E Probability of positive test results for exposed individuals
psi_I Probability of positive test results for exposed individuals
q Probability of quarantined individuals interaction outside adjacent nodes
initE Init number of exposed individuals
initI Init number of infectious individuals
initD_E Init number of detected infectious individuals
initD_I Init number of detected infectious individuals
initR Init number of recovered individuals
initF Init number of infection-related fatalities
(all remaining nodes initialized susceptible)
"""
def __init__(self, G, beta, sigma, gamma, xi=0, mu_I=0, mu_0=0, nu=0, beta_local=None, p=0,
Q=None, beta_D=None, sigma_D=None, gamma_D=None, mu_D=None, beta_D_local=None,
theta_E=0, theta_I=0, phi_E=0, phi_I=0, psi_E=0, psi_I=0, q=0,
initE=0, initI=10, initD_E=0, initD_I=0, initR=0, initF=0,
node_groups=None, store_Xseries=False):
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Setup Adjacency matrix:
self.update_G(G)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Setup Quarantine Adjacency matrix:
if(Q is None):
Q = G # If no Q graph is provided, use G in its place
self.update_Q(Q)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Model Parameters:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
self.parameters = { 'beta':beta, 'sigma':sigma, 'gamma':gamma, 'xi':xi, 'mu_I':mu_I, 'mu_0':mu_0, 'nu':nu,
'beta_D':beta_D, 'sigma_D':sigma_D, 'gamma_D':gamma_D, 'mu_D':mu_D,
'beta_local':beta_local, 'beta_D_local':beta_D_local, 'p':p,'q':q,
'theta_E':theta_E, 'theta_I':theta_I, 'phi_E':phi_E, 'phi_I':phi_I, 'psi_E':phi_E, 'psi_I':psi_I }
self.update_parameters()
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Each node can undergo up to 4 transitions (sans vitality/re-susceptibility returns to S state),
# so there are ~numNodes*4 events/timesteps expected; initialize numNodes*5 timestep slots to start
# (will be expanded during run if needed)
self.tseries = numpy.zeros(5*self.numNodes)
self.numE = numpy.zeros(5*self.numNodes)
self.numI = numpy.zeros(5*self.numNodes)
self.numD_E = numpy.zeros(5*self.numNodes)
self.numD_I = numpy.zeros(5*self.numNodes)
self.numR = numpy.zeros(5*self.numNodes)
self.numF = numpy.zeros(5*self.numNodes)
self.numS = numpy.zeros(5*self.numNodes)
self.N = numpy.zeros(5*self.numNodes)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Initialize Timekeeping:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
self.t = 0
self.tmax = 0 # will be set when run() is called
self.tidx = 0
self.tseries[0] = 0
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Initialize Counts of inidividuals with each state:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
self.numE[0] = int(initE)
self.numI[0] = int(initI)
self.numD_E[0] = int(initD_E)
self.numD_I[0] = int(initD_I)
self.numR[0] = int(initR)
self.numF[0] = int(initF)
self.numS[0] = self.numNodes - self.numE[0] - self.numI[0] - self.numD_E[0] - self.numD_I[0] - self.numR[0] - self.numF[0]
self.N[0] = self.numS[0] + self.numE[0] + self.numI[0] + self.numD_E[0] + self.numD_I[0] + self.numR[0]
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Node states:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
self.S = 1
self.E = 2
self.I = 3
self.D_E = 4
self.D_I = 5
self.R = 6
self.F = 7
self.X = numpy.array([self.S]*int(self.numS[0]) + [self.E]*int(self.numE[0]) + [self.I]*int(self.numI[0]) + [self.D_E]*int(self.numD_E[0]) + [self.D_I]*int(self.numD_I[0]) + [self.R]*int(self.numR[0]) + [self.F]*int(self.numF[0])).reshape((self.numNodes,1))
numpy.random.shuffle(self.X)
self.store_Xseries = store_Xseries
if(store_Xseries):
self.Xseries = numpy.zeros(shape=(5*self.numNodes, self.numNodes), dtype='uint8')
self.Xseries[0,:] = self.X.T
self.transitions = {
'StoE': {'currentState':self.S, 'newState':self.E},
'EtoI': {'currentState':self.E, 'newState':self.I},
'ItoR': {'currentState':self.I, 'newState':self.R},
'ItoF': {'currentState':self.I, 'newState':self.F},
'RtoS': {'currentState':self.R, 'newState':self.S},
'EtoDE': {'currentState':self.E, 'newState':self.D_E},
'ItoDI': {'currentState':self.I, 'newState':self.D_I},
'DEtoDI': {'currentState':self.D_E, 'newState':self.D_I},
'DItoR': {'currentState':self.D_I, 'newState':self.R},
'DItoF': {'currentState':self.D_I, 'newState':self.F},
'_toS': {'currentState':True, 'newState':self.S},
}
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Initialize node subgroup data series:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
self.nodeGroupData = None
if(node_groups):
self.nodeGroupData = {}
for groupName, nodeList in node_groups.items():
self.nodeGroupData[groupName] = {'nodes': numpy.array(nodeList),
'mask': numpy.isin(range(self.numNodes), nodeList).reshape((self.numNodes,1))}
self.nodeGroupData[groupName]['numS'] = numpy.zeros(5*self.numNodes)
self.nodeGroupData[groupName]['numE'] = numpy.zeros(5*self.numNodes)
self.nodeGroupData[groupName]['numI'] = numpy.zeros(5*self.numNodes)
self.nodeGroupData[groupName]['numD_E'] = numpy.zeros(5*self.numNodes)
self.nodeGroupData[groupName]['numD_I'] = numpy.zeros(5*self.numNodes)
self.nodeGroupData[groupName]['numR'] = numpy.zeros(5*self.numNodes)
self.nodeGroupData[groupName]['numF'] = numpy.zeros(5*self.numNodes)
self.nodeGroupData[groupName]['N'] = numpy.zeros(5*self.numNodes)
self.nodeGroupData[groupName]['numS'][0] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.S)
self.nodeGroupData[groupName]['numE'][0] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.E)
self.nodeGroupData[groupName]['numI'][0] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.I)
self.nodeGroupData[groupName]['numD_E'][0] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.D_E)
self.nodeGroupData[groupName]['numD_I'][0] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.D_I)
self.nodeGroupData[groupName]['numR'][0] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.R)
self.nodeGroupData[groupName]['numF'][0] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.F)
self.nodeGroupData[groupName]['N'][0] = self.nodeGroupData[groupName]['numS'][0] + self.nodeGroupData[groupName]['numE'][0] + self.nodeGroupData[groupName]['numI'][0] + self.nodeGroupData[groupName]['numD_E'][0] + self.nodeGroupData[groupName]['numD_I'][0] + self.nodeGroupData[groupName]['numR'][0]
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def update_parameters(self):
import time
updatestart = time.time()
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Model parameters:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
self.beta = numpy.array(self.parameters['beta']).reshape((self.numNodes, 1)) if isinstance(self.parameters['beta'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['beta'], shape=(self.numNodes,1))
self.sigma = numpy.array(self.parameters['sigma']).reshape((self.numNodes, 1)) if isinstance(self.parameters['sigma'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['sigma'], shape=(self.numNodes,1))
self.gamma = numpy.array(self.parameters['gamma']).reshape((self.numNodes, 1)) if isinstance(self.parameters['gamma'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['gamma'], shape=(self.numNodes,1))
self.xi = numpy.array(self.parameters['xi']).reshape((self.numNodes, 1)) if isinstance(self.parameters['xi'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['xi'], shape=(self.numNodes,1))
self.mu_I = numpy.array(self.parameters['mu_I']).reshape((self.numNodes, 1)) if isinstance(self.parameters['mu_I'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['mu_I'], shape=(self.numNodes,1))
self.mu_0 = numpy.array(self.parameters['mu_0']).reshape((self.numNodes, 1)) if isinstance(self.parameters['mu_0'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['mu_0'], shape=(self.numNodes,1))
self.nu = numpy.array(self.parameters['nu']).reshape((self.numNodes, 1)) if isinstance(self.parameters['nu'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['nu'], shape=(self.numNodes,1))
self.p = numpy.array(self.parameters['p']).reshape((self.numNodes, 1)) if isinstance(self.parameters['p'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['p'], shape=(self.numNodes,1))
# Testing-related parameters:
self.beta_D = (numpy.array(self.parameters['beta_D']).reshape((self.numNodes, 1)) if isinstance(self.parameters['beta_D'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['beta_D'], shape=(self.numNodes,1))) if self.parameters['beta_D'] is not None else self.beta
self.sigma_D = (numpy.array(self.parameters['sigma_D']).reshape((self.numNodes, 1)) if isinstance(self.parameters['sigma_D'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['sigma_D'], shape=(self.numNodes,1))) if self.parameters['sigma_D'] is not None else self.sigma
self.gamma_D = (numpy.array(self.parameters['gamma_D']).reshape((self.numNodes, 1)) if isinstance(self.parameters['gamma_D'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['gamma_D'], shape=(self.numNodes,1))) if self.parameters['gamma_D'] is not None else self.gamma
self.mu_D = (numpy.array(self.parameters['mu_D']).reshape((self.numNodes, 1)) if isinstance(self.parameters['mu_D'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['mu_D'], shape=(self.numNodes,1))) if self.parameters['mu_D'] is not None else self.mu_I
self.theta_E = numpy.array(self.parameters['theta_E']).reshape((self.numNodes, 1)) if isinstance(self.parameters['theta_E'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['theta_E'], shape=(self.numNodes,1))
self.theta_I = numpy.array(self.parameters['theta_I']).reshape((self.numNodes, 1)) if isinstance(self.parameters['theta_I'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['theta_I'], shape=(self.numNodes,1))
self.phi_E = numpy.array(self.parameters['phi_E']).reshape((self.numNodes, 1)) if isinstance(self.parameters['phi_E'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['phi_E'], shape=(self.numNodes,1))
self.phi_I = numpy.array(self.parameters['phi_I']).reshape((self.numNodes, 1)) if isinstance(self.parameters['phi_I'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['phi_I'], shape=(self.numNodes,1))
self.psi_E = numpy.array(self.parameters['psi_E']).reshape((self.numNodes, 1)) if isinstance(self.parameters['psi_E'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['psi_E'], shape=(self.numNodes,1))
self.psi_I = numpy.array(self.parameters['psi_I']).reshape((self.numNodes, 1)) if isinstance(self.parameters['psi_I'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['psi_I'], shape=(self.numNodes,1))
self.q = numpy.array(self.parameters['q']).reshape((self.numNodes, 1)) if isinstance(self.parameters['q'], (list, numpy.ndarray)) else numpy.full(fill_value=self.parameters['q'], shape=(self.numNodes,1))
#Local transmission parameters:
if(self.parameters['beta_local'] is not None):
if(isinstance(self.parameters['beta_local'], (list, numpy.ndarray))):
if(isinstance(self.parameters['beta_local'], list)):
self.beta_local = numpy.array(self.parameters['beta_local'])
else: # is numpy.ndarray
self.beta_local = self.parameters['beta_local']
if(self.beta_local.ndim == 1):
self.beta_local.reshape((self.numNodes, 1))
elif(self.beta_local.ndim == 2):
self.beta_local.reshape((self.numNodes, self.numNodes))
else:
self.beta_local = numpy.full_like(self.beta, fill_value=self.parameters['beta_local'])
else:
self.beta_local = self.beta
#----------------------------------------
if(self.parameters['beta_D_local'] is not None):
if(isinstance(self.parameters['beta_D_local'], (list, numpy.ndarray))):
if(isinstance(self.parameters['beta_D_local'], list)):
self.beta_D_local = numpy.array(self.parameters['beta_D_local'])
else: # is numpy.ndarray
self.beta_D_local = self.parameters['beta_D_local']
if(self.beta_D_local.ndim == 1):
self.beta_D_local.reshape((self.numNodes, 1))
elif(self.beta_D_local.ndim == 2):
self.beta_D_local.reshape((self.numNodes, self.numNodes))
else:
self.beta_D_local = numpy.full_like(self.beta_D, fill_value=self.parameters['beta_D_local'])
else:
self.beta_D_local = self.beta_D
# Pre-multiply beta values by the adjacency matrix ("transmission weight connections")
if(self.beta_local.ndim == 1):
self.A_beta = scipy.sparse.csr_matrix.multiply(self.A, numpy.tile(self.beta_local, (1,self.numNodes))).tocsr()
elif(self.beta_local.ndim == 2):
self.A_beta = scipy.sparse.csr_matrix.multiply(self.A, self.beta_local).tocsr()
# Pre-multiply beta_D values by the quarantine adjacency matrix ("transmission weight connections")
if(self.beta_D_local.ndim == 1):
self.A_Q_beta_D = scipy.sparse.csr_matrix.multiply(self.A_Q, numpy.tile(self.beta_D_local, (1,self.numNodes))).tocsr()
elif(self.beta_D_local.ndim == 2):
self.A_Q_beta_D = scipy.sparse.csr_matrix.multiply(self.A_Q, self.beta_D_local).tocsr()
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Update scenario flags:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
self.update_scenario_flags()
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def node_degrees(self, Amat):
return Amat.sum(axis=0).reshape(self.numNodes,1) # sums of adj matrix cols
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def update_G(self, new_G):
self.G = new_G
# Adjacency matrix:
if type(new_G)==numpy.ndarray:
self.A = scipy.sparse.csr_matrix(new_G)
elif type(new_G)==networkx.classes.graph.Graph:
self.A = networkx.adj_matrix(new_G) # adj_matrix gives scipy.sparse csr_matrix
else:
raise BaseException("Input an adjacency matrix or networkx object only.")
self.numNodes = int(self.A.shape[1])
self.degree = numpy.asarray(self.node_degrees(self.A)).astype(float)
return
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def update_Q(self, new_Q):
self.Q = new_Q
# Quarantine Adjacency matrix:
if type(new_Q)==numpy.ndarray:
self.A_Q = scipy.sparse.csr_matrix(new_Q)
elif type(new_Q)==networkx.classes.graph.Graph:
self.A_Q = networkx.adj_matrix(new_Q) # adj_matrix gives scipy.sparse csr_matrix
else:
raise BaseException("Input an adjacency matrix or networkx object only.")
self.numNodes_Q = int(self.A_Q.shape[1])
self.degree_Q = numpy.asarray(self.node_degrees(self.A_Q)).astype(float)
assert(self.numNodes == self.numNodes_Q), "The normal and quarantine adjacency graphs must be of the same size."
return
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def update_scenario_flags(self):
self.testing_scenario = ( (numpy.any(self.psi_I) and (numpy.any(self.theta_I) or numpy.any(self.phi_I)))
or (numpy.any(self.psi_E) and (numpy.any(self.theta_E) or numpy.any(self.phi_E))) )
self.tracing_scenario = ( (numpy.any(self.psi_E) and numpy.any(self.phi_E))
or (numpy.any(self.psi_I) and numpy.any(self.phi_I)) )
self.vitality_scenario = (numpy.any(self.mu_0) and numpy.any(self.nu))
self.resusceptibility_scenario = (numpy.any(self.xi))
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def calc_propensities(self):
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Pre-calculate matrix multiplication terms that may be used in multiple propensity calculations,
# and check to see if their computation is necessary before doing the multiplication
numContacts_I = numpy.zeros(shape=(self.numNodes,1))
transmissionTerms_I = numpy.zeros(shape=(self.numNodes,1))
if(numpy.any(self.numI[self.tidx])
and numpy.any(self.beta!=0)):
transmissionTerms_I = numpy.asarray( scipy.sparse.csr_matrix.dot(self.A_beta, self.X==self.I) )
numQuarantineContacts_DI = numpy.zeros(shape=(self.numNodes,1))
transmissionTerms_DI = numpy.zeros(shape=(self.numNodes,1))
if(self.testing_scenario
and numpy.any(self.numD_I[self.tidx])
and numpy.any(self.beta_D)):
transmissionTerms_DI = numpy.asarray( scipy.sparse.csr_matrix.dot(self.A_Q_beta_D, self.X==self.D_I) )
numContacts_D = numpy.zeros(shape=(self.numNodes,1))
if(self.tracing_scenario
and (numpy.any(self.numD_E[self.tidx]) or numpy.any(self.numD_I[self.tidx]))):
numContacts_D = numpy.asarray( scipy.sparse.csr_matrix.dot(self.A, self.X==self.D_E)
+ scipy.sparse.csr_matrix.dot(self.A, self.X==self.D_I) )
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
propensities_StoE = ( self.p*((self.beta*self.numI[self.tidx] + self.q*self.beta_D*self.numD_I[self.tidx])/self.N[self.tidx])
+ (1-self.p)*numpy.divide((transmissionTerms_I + transmissionTerms_DI), self.degree, out=numpy.zeros_like(self.degree), where=self.degree!=0)
)*(self.X==self.S)
propensities_EtoI = self.sigma*(self.X==self.E)
propensities_ItoR = self.gamma*(self.X==self.I)
propensities_ItoF = self.mu_I*(self.X==self.I)
# propensities_EtoDE = ( self.theta_E + numpy.divide((self.phi_E*numContacts_D), self.degree, out=numpy.zeros_like(self.degree), where=self.degree!=0) )*self.psi_E*(self.X==self.E)
propensities_EtoDE = (self.theta_E + self.phi_E*numContacts_D)*self.psi_E*(self.X==self.E)
# propensities_ItoDI = ( self.theta_I + numpy.divide((self.phi_I*numContacts_D), self.degree, out=numpy.zeros_like(self.degree), where=self.degree!=0) )*self.psi_I*(self.X==self.I)
propensities_ItoDI = (self.theta_I + self.phi_I*numContacts_D)*self.psi_I*(self.X==self.I)
propensities_DEtoDI = self.sigma_D*(self.X==self.D_E)
propensities_DItoR = self.gamma_D*(self.X==self.D_I)
propensities_DItoF = self.mu_D*(self.X==self.D_I)
propensities_RtoS = self.xi*(self.X==self.R)
propensities__toS = self.nu*(self.X!=self.F)
propensities = numpy.hstack([propensities_StoE, propensities_EtoI,
propensities_ItoR, propensities_ItoF,
propensities_EtoDE, propensities_ItoDI, propensities_DEtoDI,
propensities_DItoR, propensities_DItoF,
propensities_RtoS, propensities__toS])
columns = ['StoE', 'EtoI', 'ItoR', 'ItoF', 'EtoDE', 'ItoDI', 'DEtoDI', 'DItoR', 'DItoF', 'RtoS', '_toS']
return propensities, columns
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def increase_data_series_length(self):
self.tseries= numpy.pad(self.tseries, [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.numS = numpy.pad(self.numS, [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.numE = numpy.pad(self.numE, [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.numI = numpy.pad(self.numI, [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.numD_E = numpy.pad(self.numD_E, [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.numD_I = numpy.pad(self.numD_I, [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.numR = numpy.pad(self.numR, [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.numF = numpy.pad(self.numF, [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.N = numpy.pad(self.N, [(0, 5*self.numNodes)], mode='constant', constant_values=0)
if(self.store_Xseries):
self.Xseries = numpy.pad(self.Xseries, [(0, 5*self.numNodes), (0,0)], mode=constant, constant_values=0)
if(self.nodeGroupData):
for groupName in self.nodeGroupData:
self.nodeGroupData[groupName]['numS'] = numpy.pad(self.nodeGroupData[groupName]['numS'], [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.nodeGroupData[groupName]['numE'] = numpy.pad(self.nodeGroupData[groupName]['numE'], [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.nodeGroupData[groupName]['numI'] = numpy.pad(self.nodeGroupData[groupName]['numI'], [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.nodeGroupData[groupName]['numD_E'] = numpy.pad(self.nodeGroupData[groupName]['numD_E'], [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.nodeGroupData[groupName]['numD_I'] = numpy.pad(self.nodeGroupData[groupName]['numD_I'], [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.nodeGroupData[groupName]['numR'] = numpy.pad(self.nodeGroupData[groupName]['numR'], [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.nodeGroupData[groupName]['numF'] = numpy.pad(self.nodeGroupData[groupName]['numF'], [(0, 5*self.numNodes)], mode='constant', constant_values=0)
self.nodeGroupData[groupName]['N'] = numpy.pad(self.nodeGroupData[groupName]['N'], [(0, 5*self.numNodes)], mode='constant', constant_values=0)
return None
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def finalize_data_series(self):
self.tseries= numpy.array(self.tseries, dtype=float)[:self.tidx+1]
self.numS = numpy.array(self.numS, dtype=float)[:self.tidx+1]
self.numE = numpy.array(self.numE, dtype=float)[:self.tidx+1]
self.numI = numpy.array(self.numI, dtype=float)[:self.tidx+1]
self.numD_E = numpy.array(self.numD_E, dtype=float)[:self.tidx+1]
self.numD_I = numpy.array(self.numD_I, dtype=float)[:self.tidx+1]
self.numR = numpy.array(self.numR, dtype=float)[:self.tidx+1]
self.numF = numpy.array(self.numF, dtype=float)[:self.tidx+1]
self.N = numpy.array(self.N, dtype=float)[:self.tidx+1]
if(self.store_Xseries):
self.Xseries = self.Xseries[:self.tidx+1, :]
if(self.nodeGroupData):
for groupName in self.nodeGroupData:
self.nodeGroupData[groupName]['numS'] = numpy.array(self.nodeGroupData[groupName]['numS'], dtype=float)[:self.tidx+1]
self.nodeGroupData[groupName]['numE'] = numpy.array(self.nodeGroupData[groupName]['numE'], dtype=float)[:self.tidx+1]
self.nodeGroupData[groupName]['numI'] = numpy.array(self.nodeGroupData[groupName]['numI'], dtype=float)[:self.tidx+1]
self.nodeGroupData[groupName]['numD_E'] = numpy.array(self.nodeGroupData[groupName]['numD_E'], dtype=float)[:self.tidx+1]
self.nodeGroupData[groupName]['numD_I'] = numpy.array(self.nodeGroupData[groupName]['numD_I'], dtype=float)[:self.tidx+1]
self.nodeGroupData[groupName]['numR'] = numpy.array(self.nodeGroupData[groupName]['numR'], dtype=float)[:self.tidx+1]
self.nodeGroupData[groupName]['numF'] = numpy.array(self.nodeGroupData[groupName]['numF'], dtype=float)[:self.tidx+1]
self.nodeGroupData[groupName]['N'] = numpy.array(self.nodeGroupData[groupName]['N'], dtype=float)[:self.tidx+1]
return None
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def run_iteration(self):
if(self.tidx >= len(self.tseries)-1):
# Room has run out in the timeseries storage arrays; double the size of these arrays:
self.increase_data_series_length()
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# 1. Generate 2 random numbers uniformly distributed in (0,1)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
r1 = numpy.random.rand()
r2 = numpy.random.rand()
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# 2. Calculate propensities
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
propensities, transitionTypes = self.calc_propensities()
# Terminate when probability of all events is 0:
if(propensities.sum() <= 0.0):
self.finalize_data_series()
return False
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# 3. Calculate alpha
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
propensities_flat = propensities.ravel(order='F')
cumsum = propensities_flat.cumsum()
alpha = propensities_flat.sum()
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# 4. Compute the time until the next event takes place
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
tau = (1/alpha)*numpy.log(float(1/r1))
self.t += tau
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# 5. Compute which event takes place
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
transitionIdx = numpy.searchsorted(cumsum,r2*alpha)
transitionNode = transitionIdx % self.numNodes
transitionType = transitionTypes[ int(transitionIdx/self.numNodes) ]
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# 6. Update node states and data series
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
assert(self.X[transitionNode] == self.transitions[transitionType]['currentState'] and self.X[transitionNode]!=self.F), "Assertion error: Node "+str(transitionNode)+" has unexpected current state "+str(self.X[transitionNode])+" given the intended transition of "+str(transitionType)+"."
self.X[transitionNode] = self.transitions[transitionType]['newState']
self.tidx += 1
self.tseries[self.tidx] = self.t
self.numS[self.tidx] = numpy.clip(numpy.count_nonzero(self.X==self.S), a_min=0, a_max=self.numNodes)
self.numE[self.tidx] = numpy.clip(numpy.count_nonzero(self.X==self.E), a_min=0, a_max=self.numNodes)
self.numI[self.tidx] = numpy.clip(numpy.count_nonzero(self.X==self.I), a_min=0, a_max=self.numNodes)
self.numD_E[self.tidx] = numpy.clip(numpy.count_nonzero(self.X==self.D_E), a_min=0, a_max=self.numNodes)
self.numD_I[self.tidx] = numpy.clip(numpy.count_nonzero(self.X==self.D_I), a_min=0, a_max=self.numNodes)
self.numR[self.tidx] = numpy.clip(numpy.count_nonzero(self.X==self.R), a_min=0, a_max=self.numNodes)
self.numF[self.tidx] = numpy.clip(numpy.count_nonzero(self.X==self.F), a_min=0, a_max=self.numNodes)
self.N[self.tidx] = numpy.clip((self.numS[self.tidx] + self.numE[self.tidx] + self.numI[self.tidx] + self.numD_E[self.tidx] + self.numD_I[self.tidx] + self.numR[self.tidx]), a_min=0, a_max=self.numNodes)
if(self.store_Xseries):
self.Xseries[self.tidx,:] = self.X.T
if(self.nodeGroupData):
for groupName in self.nodeGroupData:
self.nodeGroupData[groupName]['numS'][self.tidx] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.S)
self.nodeGroupData[groupName]['numE'][self.tidx] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.E)
self.nodeGroupData[groupName]['numI'][self.tidx] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.I)
self.nodeGroupData[groupName]['numD_E'][self.tidx] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.D_E)
self.nodeGroupData[groupName]['numD_I'][self.tidx] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.D_I)
self.nodeGroupData[groupName]['numR'][self.tidx] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.R)
self.nodeGroupData[groupName]['numF'][self.tidx] = numpy.count_nonzero(self.nodeGroupData[groupName]['mask']*self.X==self.F)
self.nodeGroupData[groupName]['N'][self.tidx] = numpy.clip((self.nodeGroupData[groupName]['numS'][0] + self.nodeGroupData[groupName]['numE'][0] + self.nodeGroupData[groupName]['numI'][0] + self.nodeGroupData[groupName]['numD_E'][0] + self.nodeGroupData[groupName]['numD_I'][0] + self.nodeGroupData[groupName]['numR'][0]), a_min=0, a_max=self.numNodes)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Terminate if tmax reached or num infectious and num exposed is 0:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if(self.t >= self.tmax or (self.numI[self.tidx]<1 and self.numE[self.tidx]<1 and self.numD_E[self.tidx]<1 and self.numD_I[self.tidx]<1)):
self.finalize_data_series()
return False
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
return True
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
def run(self, T, checkpoints=None, print_interval=10, verbose='t'):
if(T>0):
self.tmax += T
else:
return False
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Pre-process checkpoint values:
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if(checkpoints):
numCheckpoints = len(checkpoints['t'])
for chkpt_param, chkpt_values in checkpoints.items():
assert(isinstance(chkpt_values, (list, numpy.ndarray)) and len(chkpt_values)==numCheckpoints), "Expecting a list of values with length equal to number of checkpoint times ("+str(numCheckpoints)+") for each checkpoint parameter."
checkpointIdx = numpy.searchsorted(checkpoints['t'], self.t) # Finds 1st index in list greater than given val