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#!/usr/bin/python3
from datetime import datetime, timedelta
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from scipy.integrate import solve_ivp
from scipy.optimize import minimize
import argparse
import os
parser = argparse.ArgumentParser()
parser.add_argument('--mode', '-m', dest = 'mode', help = 'change the mode of the model (SIR, Linear, ESIR, SEIR); default: SIR', default = 'SIR', choices = ['SIR', 'Linear', 'ESIR', 'SEIR'])
parser.add_argument('--data', '-d', dest = 'include_data', help = 'change the type of data to present in the graph (Actual, S, I, R, E); default: Actual S I R', nargs = '*', default = ['Actual', 'S', 'I', 'R'], choices = ['Actual', 'S', 'I', 'R', 'E'])
parser.add_argument('--folder', '-f', dest = 'folder', default = 'data', help = 'the folder in which to find the data files; defaults to looking in the data folder')
parser.add_argument('--disease', '-D', dest = 'disease', default = 'COVID-19', help = 'the disease to model; defaults to COVID-19')
parser.add_argument('--out', '-o', dest = 'out', default = None, help = 'the name of the graph and csv files; defaults to the name of the disease')
parser.add_argument('--start', '-s', dest = 'start', default = '1/22/20', help = 'the date where the data starts (defaults to the start date of COVID-19 (1/22/20))')
parser.add_argument('--end', '-e', dest = 'end', default = None, help = 'the date where the data stops (defaults to whereever the input data ends)')
parser.add_argument('--incubation', '-i', dest = 'incubation_period', default = None, help = 'the incubation period of the disease (only applicable if using SEIR model; ignored otherwise); none by default')
parser.add_argument('--predict', '-p', dest = 'prediction_range', default = None, help = 'the number of days to predict the course of the disease (defaults to None, meaning the model will not predict beyond the given data)')
parser.add_argument('--country', '-c', dest = 'country', default = 'US', help = 'the country that is being modeled (defaults to US)')
parser.add_argument('--popcountry', '-pc', dest = 'popcountry', default = '3328200000', help = 'the population of the country (defaults to US population)')
parser.add_argument('--popmodel', '-pm', dest = 'popmodel', default = '10000', help = 'the population of the model (defaults to 10000)')
parser.add_argument('--initial', '-I', dest = 'initial', default = '1', help = 'initial infected people (defaults to 1)')
args = parser.parse_args()
# Running a model for a million population is quite hard, so here we've reduced the population and modified the actual stats to match
correction_factor = int(args.popmodel) / int(args.popcountry)
S_0 = (int(args.popcountry) - int(args.initial)) / int(args.popcountry)
I_0 = int(args.initial) / int(args.popcountry)
R_0 = 0
E_0 = 0
class Learner(object):
def __init__(self, country):
self.country = country
def load_confirmed(self, country):
"""
Load confirmed cases
"""
df = pd.read_csv(f'{args.folder}/{args.disease}-Confirmed.csv')
country_df = df[df['Country/Region'] == country]
if args.end != None:
confirmed_sums = np.sum([reg.loc[args.start:args.end].values for reg in country_df.iloc], axis = 0)
else:
confirmed_sums = np.sum([reg.loc[args.start:].values for reg in country_df.iloc], axis = 0)
if args.end != None:
new_data = pd.DataFrame(confirmed_sums, country_df.iloc[0].loc[args.start:args.end].index.tolist())
else:
new_data = pd.DataFrame(confirmed_sums, country_df.iloc[0].loc[args.start:].index.tolist())
return new_data
def load_recovered(self, country):
"""
Load recovered cases
"""
df = pd.read_csv(f'{args.folder}/{args.disease}-Recovered.csv')
country_df = df[df['Country/Region'] == country]
if args.end != None:
out = country_df.iloc[0].loc[args.start:args.end]
else:
out = country_df.iloc[0].loc[args.start:]
return out
def extend_index(self, index, new_size):
values = index.values
current = datetime.strptime(index[-1], '%m/%d/%y')
while len(values) < new_size:
current = current + timedelta(days=1)
values = np.append(values, datetime.strftime(current, '%m/%d/%y'))
return values
def predict(self, data, beta = None, gamma = None, mu = None, sigma = None):
"""
Predict how the number of people in each compartment can be changed through time toward the future.
The model is formulated with the given beta and gamma (or others).
Returns the "solved" system of initial value problems, to be "graded" by the loss function
"""
new_index = self.extend_index(data.index, args.prediction_range if args.prediction_range != None else len(data.index))
size = len(new_index)
def model(t, y):
S = y[0]
I = y[1]
R = y[2]
if args.mode == 'SEIR':
E = y[3]
if args.mode == 'Linear':
return [-beta * S, beta * S - gamma * I, gamma * I]
elif args.mode == 'SIR':
return [-beta * S * I, beta * S * I - gamma * I, gamma * I]
elif args.mode == 'ESIR':
if mu != None:
return [mu - beta * S * I - mu * S, beta * S * I - gamma * I - mu * I, gamma * I - mu * R]
else:
raise Exception('Expected mu for ESIR model')
elif args.mode == 'SEIR':
if mu != None and sigma != None:
return [mu - beta * S * I - mu * S, beta * S * I - sigma * E - mu * E, sigma * E - gamma * I - mu * I, gamma * I - mu * R]
elif mu == None:
raise Exception('Expected mu for SEIR model')
elif sigma == None:
raise Exception('Expected sigma for SEIR model')
extended_actual = np.concatenate((data.values.flatten(), [0] * (size - len(data.values))))
if args.mode == 'SEIR':
result = solve_ivp(model, [0, size], [S_0,I_0,R_0,E_0], t_eval=np.arange(0, size, 1), vectorized=True)
else:
result = solve_ivp(model, [0, size], [S_0,I_0,R_0], t_eval=np.arange(0, size, 1), vectorized=True)
return new_index, extended_actual, result
def train(self):
"""
Run the optimization to estimate the beta and gamma fitting the given confirmed cases.
"""
confirmed_data = self.load_confirmed(self.country)
recovered_data = self.load_recovered(self.country)
if not os.path.isdir('out'):
os.mkdir('out')
if args.mode == 'Linear':
optimal = minimize(
loss_linear,
[0.01, 0.01],
args=(confirmed_data, recovered_data),
method='L-BFGS-B',
bounds=[(0.001, 1.0), (0.001, 1.0)]
)
beta, gamma = optimal.x
print(f'Beta: {beta}, Gamma: {gamma}, R0: {beta/gamma}')
new_index, extended_actual, prediction = self.predict(confirmed_data, beta = beta, gamma = gamma)
print(f'Predicted I: {prediction.y[1][-1] * int(args.popmodel)}, Actual I: {extended_actual[-1] * correction_factor}')
df = compose_df(prediction, extended_actual, correction_factor, new_index)
with open(f'out/{args.disease}-{args.mode}-data.csv', 'w+') as file:
file.write(f'Beta: {beta}\nGamma: {gamma}\nR0: {beta/gamma}\n')
file.write(f'Predicted I: {prediction.y[1][-1] * int(args.popmodel)}\nActual I: {extended_actual[-1] * correction_factor}')
elif args.mode == 'SIR':
optimal = minimize(
loss_sir,
[0.01, 0.01],
args=(confirmed_data, recovered_data),
method='L-BFGS-B',
bounds=[(0.001, 1.0), (0.001, 1.0)]
)
beta, gamma = optimal.x
print(f'Beta: {beta}, Gamma: {gamma}, R0: {beta/gamma}')
new_index, extended_actual, prediction = self.predict(confirmed_data, beta = beta, gamma = gamma)
print(f'Predicted I: {prediction.y[1][-1] * int(args.popmodel)}, Actual I: {extended_actual[-1] * correction_factor}')
df = compose_df(prediction, extended_actual, correction_factor, new_index)
with open(f'out/{args.disease}-{args.mode}-data.csv', 'w+') as file:
file.write(f'Beta: {beta}\nGamma: {gamma}\nR0: {beta/gamma}\n')
file.write(f'Predicted I: {prediction.y[1][-1] * int(args.popmodel)}\nActual I: {extended_actual[-1] * correction_factor}')
elif args.mode == 'ESIR':
optimal = minimize(
loss_esir,
[0.01, 0.01, 0.01],
args=(confirmed_data, recovered_data),
method='L-BFGS-B',
bounds=[(0.001, 1.0), (0.001, 1.0), (0.001, 1.0)]
)
beta, gamma, mu = optimal.x
print(f'Beta: {beta}, Gamma: {gamma}, Mu: {mu} R0: {beta/(gamma + mu)}')
new_index, extended_actual, prediction = self.predict(confirmed_data, beta = beta, gamma = gamma, mu = mu)
print(f'Predicted I: {prediction.y[1][-1] * int(args.popmodel)}, Actual I: {extended_actual[-1] * correction_factor}')
df = compose_df(prediction, extended_actual, correction_factor, new_index)
with open(f'out/{args.disease}-{args.mode}-data.csv', 'w+') as file:
file.write(f'Beta: {beta}\nGamma: {gamma}\nMu: {mu}\nR0: {beta/(gamma + mu)}\n')
file.write(f'Predicted I: {prediction.y[1][-1] * int(args.popmodel)}\nActual I: {extended_actual[-1] * correction_factor}')
elif args.mode == 'SEIR':
# exposed_data = self.load_exposed(self.country)
optimal = minimize(
loss_seir,
[0.01, 0.01, 0.01, 0.01],
args=(confirmed_data, recovered_data),
method='L-BFGS-B',
bounds=[(0.001, 1.0), (0.001, 1.0), (0.001, 1.0), (0.001, 1.0)]
)
beta, gamma, mu, sigma = optimal.x
print(f'Beta: {beta}, Gamma: {gamma}, Mu: {mu}, Sigma: {sigma} R0: {(beta * sigma)/((mu + gamma) * (mu + sigma))}')
new_index, extended_actual, prediction = self.predict(confirmed_data, beta = beta, gamma = gamma, mu = mu, sigma = sigma)
print(f'Predicted I: {prediction.y[1][-1] * int(args.popmodel)}, Actual I: {extended_actual[-1] * correction_factor}')
df = compose_df(prediction, extended_actual, correction_factor, new_index)
with open(f'out/{args.disease}-{args.mode}-data.csv', 'w+') as file:
file.write(f'Beta: {beta}\nGamma: {gamma}\nMu: {mu}\nSigma: {sigma}\nR0: {(beta * sigma)/((mu + gamma) * (mu + sigma))}\n')
file.write(f'Predicted I: {prediction.y[1][-1] * int(args.popmodel)}\nActual I: {extended_actual[-1] * correction_factor}')
fig, ax = plt.subplots(figsize=(15, 10))
ax.set_title(f'{args.disease} cases over time ({args.mode} Model)')
df.plot(ax=ax)
fig.savefig(f"{args.out if args.out != None else args.disease}-{args.mode}.png")
df.to_csv(f'out/{args.disease}-{args.mode}-prediction.csv')
def filter_zeroes(arr):
out = np.array(arr)
for index in range(len(out)):
if out[index] == 0:
out[index] = None
return out
def compose_df(prediction, actual, correction_factor, index):
df_dict = {}
for data in args.include_data:
if data == 'Actual':
df_dict['Actual'] = filter_zeroes(actual * correction_factor)
elif data == 'S':
df_dict['S'] = prediction.y[0] * int(args.popmodel)
elif data == 'I':
df_dict['I'] = prediction.y[1] * int(args.popmodel)
elif data == 'R':
df_dict['R'] = prediction.y[2] * int(args.popmodel)
elif data == 'E':
df_dict['E'] = prediction.y[3] * int(args.popmodel)
return pd.DataFrame(df_dict, index=index)
# Loss Functions - used to "train" the model
def loss_linear(point, confirmed, recovered):
size = len(confirmed)
beta, gamma = point
def model(t, y):
S = y[0]
I = y[1]
R = y[2]
return [-beta * S, beta * S - gamma * I, gamma * I]
solution = solve_ivp(model, [0, size], [S_0,I_0,R_0], t_eval=np.arange(0, size, 1), vectorized=True)
sol_inf = np.sqrt(np.mean((solution.y[1] - (confirmed.values.flatten() * correction_factor/int(args.popmodel)))**2))
sol_rec = np.sqrt(np.mean((solution.y[2] - (recovered.values * correction_factor/int(args.popmodel)))**2))
return sol_inf * 0.5 + sol_rec * 0.5
def loss_sir(point, confirmed, recovered):
size = len(confirmed)
beta, gamma = point
def model(t, y):
S = y[0]
I = y[1]
R = y[2]
return [-beta * S * I, beta * S * I - gamma * I, gamma * I]
solution = solve_ivp(model, [0, size], [S_0,I_0,R_0], t_eval=np.arange(0, size, 1), vectorized=True)
sol_inf = np.sqrt(np.mean((solution.y[1] - (confirmed.values.flatten() * correction_factor/int(args.popmodel)))**2))
sol_rec = np.sqrt(np.mean((solution.y[2] - (recovered.values * correction_factor/int(args.popmodel)))**2))
return sol_inf * 0.5 + sol_rec * 0.5
def loss_esir(point, confirmed, recovered):
size = len(confirmed)
beta, gamma, mu = point
def model(t, y):
S = y[0]
I = y[1]
R = y[2]
return [mu - beta * S * I - mu * S, beta * S * I - gamma * I - mu * I, gamma * I - mu * R]
solution = solve_ivp(model, [0, size], [S_0,I_0,R_0], t_eval=np.arange(0, size, 1), vectorized=True)
sol_inf = np.sqrt(np.mean((solution.y[1] - (confirmed.values.flatten() * correction_factor/int(args.popmodel)))**2))
sol_rec = np.sqrt(np.mean((solution.y[2] - (recovered.values * correction_factor/int(args.popmodel)))**2))
return sol_inf * 0.5 + sol_rec * 0.5
def loss_seir(point, confirmed, recovered):
size = len(confirmed)
beta, gamma, mu, sigma = point
def model(t, y):
S = y[0]
I = y[1]
R = y[2]
E = y[3]
return [mu - beta * S * I - mu * S, beta * S * I - sigma * E - mu * E, sigma * E * I - gamma * I - mu * I, gamma * I - mu * R]
solution = solve_ivp(model, [0, size], [S_0,I_0,R_0,E_0], t_eval=np.arange(0, size, 1), vectorized=True)
sol_inf = np.sqrt(np.mean((solution.y[1] - (confirmed.values.flatten() * correction_factor/int(args.popmodel)))**2))
sol_rec = np.sqrt(np.mean((solution.y[2] - (recovered.values * correction_factor/int(args.popmodel)))**2))
# sol_exp = np.sqrt(np.mean((solution.y[3] - (exposed.values * correction_factor/int(args.popmodel)))**2))
return sol_inf * 0.5 + sol_rec * 0.5
my_learner = Learner(args.country)
my_learner.train()
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