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callibration.py
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# -*- coding: utf-8 -*-
"""
Created on Tue Jan 11 17:45:56 2022
@author: ISA
"""
import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
from scipy.optimize import minimize
from scipy.optimize import minimize_scalar
import pandas as pd
from scipy.optimize import leastsq
###############################################################################
########## WITH WEEKLY DATA
###############################################################################
#t = np.arange(0,84,7)
t = np.linspace(0, 77, 77+1)
d = {'Week': [t[0],t[7],t[14],t[21],t[28],t[35],t[42],t[49],t[56],t[63],t[70],t[77]],
'incidence': [10,206.1705794,2813.420201,11827.9453,30497.58655,10757.66954,
7071.878779,3046.752723,1314.222882,765.9763902,201.3800578,109.8982006]}
df = pd.DataFrame(data=d)
#d = {'Week': t, 'incidence': [0,206.1705794,2813.420201,11827.9453,30497.58655,10757.66954,7071.878779,3046.752723,1314.222882,765.9763902,201.3800578,109.8982006]}
#df = pd.DataFrame(data=d)
def peak_infections(x, df):
# Weeks for which the ODE system will be solved
#weeks = df.Week.to_numpy()
# Total population, N.
N = 100000
# Initial number of infected and recovered individuals, I0 and R0.
#I0, R0 = 10, 0
# Everyone else, S0, is susceptible to infection initially.
R0 = 0
beta = x[0]
I0 = x[1]
gamma = x[2]
S0 = N - I0 - R0
J0 = I0
# Contact rate, beta, and mean recovery rate, gamma, (in 1/days).
#reproductive no. R zero is beta/gamma
#gamma = 1/6 #rate should be in weeks now
# A grid of time points
times = np.arange(0,84,7)
# The SIR model differential equations.
def deriv(y, times, N, beta, gamma):
S, I, R, J = y
dS = ((-beta * S * I) / N)
dI = ((beta * S * I) / N) - (gamma * I)
dR = (gamma * I)
dJ = ((beta * S * I) / N) #incidence
return dS, dI, dR, dJ
# Initial conditions are S0, I0, R0
# Integrate the SIR equations over the time grid, t.
solve = odeint(deriv, (S0, I0, R0, J0), times, args=(N, beta, gamma))
S, I, R, J = solve.T
return I/N
def residual(x, df):
# Total population, N.
StartingPop = 100000
incidence = df.incidence.to_numpy()/StartingPop
return np.sum((peak_infections(x,df) - incidence) ** 2)
x0 = [0.5, 10, 1/6] #beta, i0, gamma
res = minimize(residual, x0, args=(df), method="Nelder-Mead", options={'fatol':1e-04}).x
print(res)
initial_infecteds = np.arange(1,31,1)
initial_beta = np.arange(0,1,1/10)
#initial_gamma = np.arange(1/10,1/6,1/30)
def fit_infecteds(i):
guesses = [0.5, i, 1/6] #beta, i0, gamma
res = minimize(residual, guesses, args=(df), method="Nelder-Mead", options={'fatol':1e-04}).x
print(res, f'for a value of I0={i}')
for i in initial_infecteds:
fit_infecteds(i)
def fit_beta(j):
guesses = [j, 10, 1/6] #beta, i0, gamma
res = minimize(residual, guesses, args=(df), method="Nelder-Mead", options={'fatol':1e-04}).x
print(res, f'for a value of {j}')
for j in initial_beta:
fit_beta(j)
fig = plt.figure(facecolor='w')
ax = fig.add_subplot(111, facecolor='#dddddd', axisbelow=True)
#ax.plot(t, S, 'b', alpha=1, lw=2, label='Susceptible')
#ax.plot(t, I, 'r', alpha=1, lw=2, label='Infected')
#ax.plot(t, R, 'black', alpha=1, lw=2, label='Recovered')
#ax.plot(t, J, 'green', alpha=1, lw=2, label='Incidence')
#ax.plot(t, J, 'red', alpha=1, lw=2, label='Cumulative incidence')
ax.plot(d['Week'], df.incidence.to_numpy(), label="Real data")
ax.plot(d['Week'], peak_infections([0.66,1.41,0.21], df)*100000, label="Model with optimal values")
ax.set_xlabel('Time in days')
ax.set_ylabel('Number')
#ax.set_ylim(0,1.1)
#ax.yaxis.set_tick_params(length=0)
#ax.xaxis.set_tick_params(length=0)
ax.grid(b=True, which='major', c='w', lw=2, ls='-')
legend = ax.legend()
legend.get_frame().set_alpha(0.5)
#for spine in ('top', 'right', 'bottom', 'left'):
# ax.spines[spine].set_visible(False)
plt.show()
import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
from scipy.optimize import minimize
import pandas as pd
from scipy.optimize import leastsq
#t = np.arange(0,84,7)
t = np.linspace(0, 77, 77+1)
d = {'Week': [t[7],t[14],t[21],t[28],t[35],t[42],t[49],t[56],t[63],t[70],t[77]], 'incidence': [206.1705794,2813.420201,11827.9453,30497.58655,10757.66954,7071.878779,3046.752723,1314.222882,765.9763902,201.3800578,109.8982006]}
df = pd.DataFrame(data=d)
#d = {'Week': t, 'incidence': [0,206.1705794,2813.420201,11827.9453,30497.58655,10757.66954,7071.878779,3046.752723,1314.222882,765.9763902,201.3800578,109.8982006]}
#df = pd.DataFrame(data=d)
def peak_infections(beta, df):
# Weeks for which the ODE system will be solved
#weeks = df.Week.to_numpy()
# Total population, N.
N = 100000
# Initial number of infected and recovered individuals, I0 and R0.
I0, R0 = 1.41351201, 0
# Everyone else, S0, is susceptible to infection initially.
S0 = N - I0 - R0
J0 = I0
# Contact rate, beta, and mean recovery rate, gamma, (in 1/days).
#reproductive no. R zero is beta/gamma
gamma = 0.21620529 #rate should be in weeks now
# A grid of time points
t7 = np.arange(7,84,7)
# The SIR model differential equations.
def deriv(y, t7, N, beta, gamma):
S, I, R, J = y
dS = ((-beta * S * I) / N)
dI = ((beta * S * I) / N) - (gamma * I)
dR = (gamma * I)
dJ = ((beta * S * I) / N)
return dS, dI, dR, dJ
# Initial conditions are S0, I0, R0
# Integrate the SIR equations over the time grid, t.
solve = odeint(deriv, (S0, I0, R0, J0), t7, args=(N, beta, gamma))
S, I, R, J = solve.T
return np.max(I)/N
def residual(x, df):
# Total population, N.
N = 100000
incidence = df.incidence.to_numpy()/N
return np.sum((peak_infections(x, df) - incidence) ** 2)
x0 = 0.66411585
res = minimize(residual, x0, args=(df), method="Nelder-Mead").x
print(res)
fig = plt.figure(facecolor='w')
ax = fig.add_subplot(111, facecolor='#dddddd', axisbelow=True)
#ax.plot(t, S, 'b', alpha=1, lw=2, label='Susceptible')
#ax.plot(t, I, 'r', alpha=1, lw=2, label='Infected')
#ax.plot(t, R, 'black', alpha=1, lw=2, label='Recovered')
#ax.plot(t, J, 'green', alpha=1, lw=2, label='Incidence')
#ax.plot(t, J, 'red', alpha=1, lw=2, label='Cumulative incidence')
ax.plot(d['Week'], df.incidence.to_numpy()/100000, label="Real data")
ax.plot(d['Week'], peak_infections(0.53, df)*100000, label="Model with 0.66")
ax.set_xlabel('Time in days')
ax.set_ylabel('Number')
#ax.set_ylim(0,1.1)
#ax.yaxis.set_tick_params(length=0)
#ax.xaxis.set_tick_params(length=0)
ax.grid(b=True, which='major', c='w', lw=2, ls='-')
legend = ax.legend()
legend.get_frame().set_alpha(0.5)
#for spine in ('top', 'right', 'bottom', 'left'):
# ax.spines[spine].set_visible(False)
plt.show()
import matplotlib.pyplot as plt
plt.plot(d['Week'], df.incidence.to_numpy()/100000, label="Real data")
plt.plot(d['Week'], peak_infections(.72, df), label="Model with 0.72")
plt.plot(d['Week'], peak_infections(.42, df), label="Model with .42")
plt.legend()
# =============================================================================
# res2 = leastsq(residual, x0,args=(df))
# print(res2)
#
# results = minimize_scalar(residual,(0.4, 0.5),args=(df))
# print(results)
# results['fun']
#
# =============================================================================
###############################################################################
########## --------------------------
###############################################################################
def peak_infections_days(beta, days = 100):
# Total population, N.
N = 1000
# Initial number of infected and recovered individuals, I0 and R0.
I0, R0 = 10, 0
# Everyone else, S0, is susceptible to infection initially.
S0 = N - I0 - R0
J0 = I0
# Contact rate, beta, and mean recovery rate, gamma, (in 1/days).
#reproductive no. R zero is beta/gamma
gamma = 1/7
# A grid of time points (in days)
t = np.linspace(0, days, days + 1)
# The SIR model differential equations.
def deriv(y, t, N, beta, gamma):
S, I, R, J = y
dS = ((-beta * S * I) / N)
dI = ((beta * S * I) / N) - (gamma * I)
dR = (gamma * I)
dJ = ((beta * S * I) / N)
return dS, dI, dR, dJ
# Initial conditions are S0, I0, R0
# Integrate the SIR equations over the time grid, t.
solve = odeint(deriv, (S0, I0, R0, J0), t, args=(N, beta, gamma))
S, I, R, J = solve.T
return np.max(I)/N
#scipy.optimize
data = pd.read_csv('data.csv')
x = data['Week']
y = data['incidence']
plt.plot(x,y)
def residual(x):
return (peak_infections_days(x) - 0.1) ** 2
res = minimize(residual, 0.5, method="Nelder-Mead").x
print(res)
best = leastsq(residual, x0)
print(best)