<gh_stars>1-10
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from scipy.integrate import odeint
import time as pctime


#  load data

print('Loading data')

data = pd.read_csv('https://github.com/pcm-dpc/COVID-19/raw/master/dati-andamento-nazionale/dpc-covid19-ita-andamento-nazionale.csv')
xdata=pd.to_numeric(range(data.shape[0]))
ydata=data['totale_casi']
ydata_death=data['deceduti']
ydata_rec=data['dimessi_guariti']

ydata_inf=ydata-ydata_rec-ydata_death

### definition of SIR 1.0

print('Initialization of SIR models')

# The SIR model differential equations.
def deriv_SIR(y, t, N, beta,gamma):
    S,I,R = y

    dSdt = -(beta*I/N)*S 
    dIdt = (beta*S/N)*I - gamma*I 
    dRdt = gamma*I 
    
    return dSdt, dIdt, dRdt

def SIR(N,beta,gamma,I0=1,R0=0,t=np.arange(0,365)):
    # Definition of the initial conditions
    # I0 and R0 denotes the number of initial infected people (I0) 
    # and the number of people that recovered and are immunized (R0)
    
    # t ise the timegrid
    
    S0=N-I0-R0  # number of people that can still contract the virus
    
    # Initial conditions vector
    y0 = S0, I0, R0

    # Integrate the SIR equations over the time grid, t.
    ret = odeint(deriv_SIR, y0, t, args=(N,beta,gamma))
    S, I, R = np.transpose(ret)
    
    return (t,S,I,R)


# ### definition of SIR 2.0 


# The SIR model differential equations.
def deriv_SIR_2(y, t, N, beta1,gamma,tau=10**6,t_thresh=14):
    S,I,R = y
    
    if t<=t_thresh:      # il lockdown nazionale inizia al 14° giorno 
        B=beta1
    else: 
        B=beta1*np.exp(-(t-t_thresh)/tau)

    dSdt = -(B*I/N)*S 
    dIdt = (B*S/N)*I - gamma*I 
    dRdt = gamma*I 
    
    return dSdt, dIdt, dRdt


def SIR_2(N,beta1,gamma,tau=10**6,t_thresh=14,I0=1,R0=0,t=np.arange(0,365)):
    # Definition of the initial conditions
    # I0 and R0 denotes the number of initial infected people (I0) 
    # and the number of people that recovered and are immunized (R0)
    
    # t ise the timegrid
    
    S0=N-I0-R0  # number of people that can still contract the virus
    
    # Initial conditions vector
    y0 = S0, I0, R0

    # Integrate the SIR equations over the time grid, t.
    ret = odeint(deriv_SIR_2, y0, t, args=(N,beta1,gamma,tau,t_thresh))
    S, I, R = np.transpose(ret)
    
    return (t,S,I,R)


# # fitting the active infected

print('Fitting the model')

# 3 parameter fit for the active infected

def optimizer_adv(R0,tau,t_thresh):
    
    asympt=3
    
    fin_result_updated=SIR_2(6*10**7,R0*1/21,1/21,tau,t_thresh,I0=asympt*ydata_inf[0])
    i_vec=fin_result_updated[2]/asympt
    
    pesi=np.exp(-np.arange(len(ydata_inf))/7)    # 
    pesi=pesi[::-1]
    
    accuracy=np.sum((ydata_inf-i_vec[0:len(ydata_inf)])**2)   #mean squared error. This is used for the optimization
    
    errperc=np.mean(np.abs((ydata_inf-i_vec[0:len(ydata_inf)])/ydata_inf))*100
    stdperc=np.std(np.abs((ydata_inf-i_vec[0:len(ydata_inf)])/ydata_inf))*100
    
    return accuracy,errperc,stdperc



# grid on 3 parameters
R0grid=np.linspace(7.5,8.5,50)
taugrid=np.linspace(25,27,200)
#ttreshgrid=np.linspace(0,10,15)

res_scan=[]
counter=0
counter2=0
cycle_tot=len(R0grid)*len(taugrid) #*len(ttreshgrid)

time1=pctime.time()

# minimization

for r in R0grid:
    for tau in taugrid:
        opt_res=optimizer_adv(r,tau,0)
        res_scan.append([r,tau,0,opt_res[0],opt_res[1],opt_res[2]])
        counter=counter+1
        counter2=counter2+1
        if counter2==cycle_tot/10:
            time2=pctime.time()
            remtime=round((time2-time1)/counter*(cycle_tot-counter),1)
            print('completed ',round(counter/cycle_tot*100,1),'%. Remaining time ',remtime,'sec')
            counter2=0
        
res_scan=np.array(res_scan)


df_res_scan=pd.DataFrame(res_scan)
df_res_scan.columns=['R0','tau','t_thresh','MSE','mean err%','std err%']

print(df_res_scan.sort_values(by='MSE').head())

par_ideal=np.array(df_res_scan.sort_values(by='MSE').iloc[0,0:])


fin_result_updated=SIR_2(6*10**7,par_ideal[0]*1/21,1/21,par_ideal[1],t_thresh=par_ideal[2],I0=3*ydata_inf[0])

t=fin_result_updated[0]
s_vec=fin_result_updated[1]
i_vec=fin_result_updated[2]
r_vec=fin_result_updated[3]


plt.figure(figsize=(7,5))
plt.plot(np.arange(len(ydata_inf)),ydata_inf,color='red',label='Active infected (data)')
plt.plot(t, i_vec/3, label='Active infected (model, best-fit)',color='blue',linestyle='--')
#plt.fill_between(t, i_vec*(1+par_ideal[5]/100*2.65)/3,i_vec*(1-par_ideal[5]/100*2.65)/3, label='Active infected (model, 99% of data)',color='blue',alpha=.2)
plt.plot(np.zeros(2)+70,[-1000,250000],color='purple')
plt.xticks(np.arange(0,100,7),['24 Feb','2 Mar','9 Mar','16 Mar','23 Mar','30 Mar','6 Apr','13 Apr','20 Apr','27 Apr','4 Mag','11 Mag','18 Mag','25 Mag','1 Giu'],rotation=30)
plt.xlim(0,100)
plt.ylim(100,2*10**5)
#plt.yscale('log')
plt.annotate("Lockdown", xy=(14,10000), xytext=(3,40000), arrowprops=dict(arrowstyle="->"),fontsize=13)
plt.xlabel('Data')
plt.ylabel('Counter')
plt.yscale('log')
plt.legend()
plt.grid(color='gray', linestyle='--', linewidth=0.5)
plt.tight_layout()
plt.savefig('output/fit_con_incertezza.png',dpi=300)
#plt.show()

print('Figure model-data saved')

#export

t_date=pd.to_datetime(t,unit='D',origin=pd.Timestamp('2020-02-24'))

export_v2 = pd.DataFrame({'date':t_date,'t':t,'s':s_vec,'i':i_vec,'r':r_vec})
export_v2.to_csv('output/nazionale.csv',index=False)


# # computation of national R0

# ### using data of last 5 days


today=len(xdata)

print('Computing R0 as function of time')

def minimizer(R0,t1=today-5,t2=today):
    
    #true data
    ydata_inf_2=np.array(ydata_inf[t1:t2])
    xdata_2=np.arange(0,len(ydata_inf_2))
    
    #print(ydata_inf_2)
    
    #model
    fin_result=SIR(60*10**6,1/14*R0,1/14,I0=ydata_inf_2[0])
    i_vec=fin_result[2]
    i_vec_2=i_vec[0:len(xdata_2)]
    
    #average error
    error=np.sum(np.abs(ydata_inf_2-i_vec_2)/ydata_inf_2)*100
    
    return error

minimizer_vec=np.vectorize(minimizer)


# ### scan of R0 over time


time_window=5

def minimizer_gen(t1,t2,xgrid=np.arange(0.1,5,0.01)):

    ygrid=minimizer_vec(xgrid,t1=t1,t2=t2)
    r0_ideal=round(xgrid[np.argmin(ygrid)],2)

    return r0_ideal

r0_time=[]
scangrid=np.linspace(0,5,100)

for i in range(0,today-(time_window-1)):
    min_val=minimizer_gen(i,i+time_window,xgrid=scangrid)
    r0_time.append(min_val)
    scangrid=np.linspace(0,min_val*2,100)  #the grid change over the time (this speed up the process)
    print('Day n',i,' R0=',min_val)
    print(i,i+time_window,len(ydata_inf))
    
r0_time=np.array(r0_time)


plt.figure(figsize=(5,5))
plt.plot(r0_time)
plt.xticks(np.arange(0-(time_window-5),80,7),['28 Feb','6 Mar','13 Mar','20 Mar','27 Mar','3 Apr','10 Apr','17 Apr','24 Apr','1 Mag','8 Mag','15 Mag'],rotation=20)
plt.xlim(0,today-4)
#plt.xlim(19,today-9)
plt.ylabel('$R_0$')
plt.ylim(0,5)
plt.grid()
plt.title('Evolution of $R_0$')
plt.savefig('output/r0-evo.png',dpi=300)
#plt.show()

print('Figure R0 saved')

# export R0 over time

df_r0=pd.DataFrame(pd.to_datetime(np.arange(len(r0_time)),unit='D',origin='2020-02-28'))
df_r0['R0']=r0_time
df_r0.columns=['Data','R0']

df_r0.to_csv('output/r0.csv',index=False)


# # Future forecasting

print('Future predictions as function of R0')

# The SIR model differential equations.
def deriv_SIR_2_future(y, t, N, beta1,gamma,newR0,tau=10**6,t_thresh=14):
    S,I,R = y
    
    if t<=t_thresh:      # il lockdown nazionale inizia al 14° giorno 
        B=beta1
    elif t>t_thresh and t<=70:
        B=beta1*np.exp(-(t-t_thresh)/tau)
    elif t>70:
        B=newR0*gamma
        #B=beta1*np.exp(-(70-t_thresh)/tau)+0.05*gamma*(t-70)
        #print(B,t)

    dSdt = -(B*I/N)*S 
    dIdt = (B*S/N)*I - gamma*I 
    dRdt = gamma*I 
    
    return dSdt, dIdt, dRdt


def SIR_2_future(N,beta1,gamma,newR0,tau=10**6,t_thresh=14,I0=1,R0=0,t=np.arange(0,365)):
    # Definition of the initial conditions
    # I0 and R0 denotes the number of initial infected people (I0) 
    # and the number of people that recovered and are immunized (R0)
    
    # t ise the timegrid
    
    S0=N-I0-R0  # number of people that can still contract the virus
    
    # Initial conditions vector
    y0 = S0, I0, R0

    # Integrate the SIR equations over the time grid, t.
    ret = odeint(deriv_SIR_2_future, y0, t, args=(N,beta1,gamma,newR0,tau,t_thresh))
    S, I, R = np.transpose(ret)
    
    return (t,S,I,R)



asympt=3

i_vec_future050=SIR_2_future(6*10**7,par_ideal[0]*1/21,1/21,0.5,par_ideal[1],t_thresh=par_ideal[2],I0=asympt*ydata_inf[0])[2]
i_vec_future100=SIR_2_future(6*10**7,par_ideal[0]*1/21,1/21,1.0,par_ideal[1],t_thresh=par_ideal[2],I0=asympt*ydata_inf[0])[2]
i_vec_future110=SIR_2_future(6*10**7,par_ideal[0]*1/21,1/21,1.1,par_ideal[1],t_thresh=par_ideal[2],I0=asympt*ydata_inf[0])[2]
i_vec_future120=SIR_2_future(6*10**7,par_ideal[0]*1/21,1/21,1.20,par_ideal[1],t_thresh=par_ideal[2],I0=asympt*ydata_inf[0])[2]


plt.figure(figsize=(7,5))
plt.plot(np.arange(len(ydata_inf)),ydata_inf,color='red',linestyle='None',marker='.',label='Infetti sintomatici attivi (dati)')
plt.fill_between(t, i_vec_future100/asympt,i_vec_future050/asympt,color='green',label='Modello, $R_0$ fra 0.5 e 1',alpha=0.5)
plt.fill_between(t, i_vec_future110/asympt,i_vec_future100/asympt,color='orange',label='Modello, $R_0$ fra 1 e 1.1',alpha=0.5)
plt.fill_between(t, i_vec_future120/asympt,i_vec_future110/asympt,color='red',label='Modello, $R_0$ fra 1.1 e 1.2',alpha=0.5)
#plt.plot(t, i_vec_future05/asympt, label='Modello, R$_0^{riapertura}$=0.5')
#plt.plot(t, i_vec_future10/asympt, label='Modello, R$_0^{riapertura}$=1')
#plt.plot(t, i_vec_future15/asympt, label='Modello, R$_0^{riapertura}$=1.1')
#plt.plot(t, i_vec_future20/asympt, label='Modello, R$_0^{riapertura}$=1.2')
#plt.fill_between(t, i_vec_future*(1+par_ideal[4]/100*2)/asympt,i_vec_future*(1-par_ideal[4]/100*2)/asympt, label='Infetti attivi (modello, 95% C.L.)',color='red',alpha=.2)
plt.plot(np.zeros(2)+70,[-1000,10**7],color='purple')
plt.xticks(np.arange(6,360,30),['1 Mar','1 Apr','1 Mag','1 Giu','1 Lug','1 Ago','1 Set','1 Ott','1 Nov','1 Dic','1 Gen','1 Feb'],rotation=30)
plt.xlim(0,360)
plt.ylim(100,ydata_inf.max()*4.3)
#plt.ylim(100,10**7)
#plt.yscale('log')
plt.annotate("Lockdown", xy=(14,ydata_inf.max()*0.1), xytext=(3,ydata_inf.max()*2), arrowprops=dict(arrowstyle="->"),fontsize=13)
plt.annotate("Riapertura", xy=(70,ydata_inf.max()), xytext=(80,ydata_inf.max()*2), arrowprops=dict(arrowstyle="->"),fontsize=13)
plt.xlabel('Data')
plt.ylabel('Counter')
plt.legend()
plt.grid(color='gray', linestyle='--', linewidth=0.5)
plt.title('2 asintomatici per ogni sintomatico')
plt.tight_layout()
plt.savefig('output/predizioni_future.png',dpi=300)
#plt.show()

print('Figure prediction saved')

#export

ydata_inf_toexport=np.empty(len(i_vec))
ydata_inf_toexport[0:len(ydata_inf)]=ydata_inf
ydata_inf_toexport[len(ydata_inf):]=np.nan

t_date=pd.to_datetime(t,unit='D',origin=pd.Timestamp('2020-02-24'))

export_forecast = pd.DataFrame({'date':t_date,'t':t,'R0=0.5':i_vec_future050/asympt,'R0=1':i_vec_future100/asympt,'R0=1.1':i_vec_future110/asympt,'R0=1.2':i_vec_future120/asympt,'infetti_reali':ydata_inf_toexport})
export_forecast.to_csv('output/predizioni_future_export.csv',index=False)

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from scipy.integrate import odeint
import time as pctime


#  load data

print('Loading data')

data = pd.read_csv('https://github.com/pcm-dpc/COVID-19/raw/master/dati-andamento-nazionale/dpc-covid19-ita-andamento-nazionale.csv')
xdata=pd.to_numeric(range(data.shape[0]))
ydata=data['totale_casi']
ydata_death=data['deceduti']
ydata_rec=data['dimessi_guariti']

ydata_inf=ydata-ydata_rec-ydata_death

### definition of SIR 1.0

print('Initialization of SIR models')

# The SIR model differential equations.
def deriv_SIR(y, t, N, beta,gamma):
    S,I,R = y

    dSdt = -(beta*I/N)*S 
    dIdt = (beta*S/N)*I - gamma*I 
    dRdt = gamma*I 
    
    return dSdt, dIdt, dRdt

def SIR(N,beta,gamma,I0=1,R0=0,t=np.arange(0,365)):
    # Definition of the initial conditions
    # I0 and R0 denotes the number of initial infected people (I0) 
    # and the number of people that recovered and are immunized (R0)
    
    # t ise the timegrid
    
    S0=N-I0-R0  # number of people that can still contract the virus
    
    # Initial conditions vector
    y0 = S0, I0, R0

    # Integrate the SIR equations over the time grid, t.
    ret = odeint(deriv_SIR, y0, t, args=(N,beta,gamma))
    S, I, R = np.transpose(ret)
    
    return (t,S,I,R)


# ### definition of SIR 2.0 


# The SIR model differential equations.
def deriv_SIR_2(y, t, N, beta1,gamma,tau=10**6,t_thresh=14):
    S,I,R = y
    
    if t<=t_thresh:      # il lockdown nazionale inizia al 14° giorno 
        B=beta1
    else: 
        B=beta1*np.exp(-(t-t_thresh)/tau)

    dSdt = -(B*I/N)*S 
    dIdt = (B*S/N)*I - gamma*I 
    dRdt = gamma*I 
    
    return dSdt, dIdt, dRdt


def SIR_2(N,beta1,gamma,tau=10**6,t_thresh=14,I0=1,R0=0,t=np.arange(0,365)):
    # Definition of the initial conditions
    # I0 and R0 denotes the number of initial infected people (I0) 
    # and the number of people that recovered and are immunized (R0)
    
    # t ise the timegrid
    
    S0=N-I0-R0  # number of people that can still contract the virus
    
    # Initial conditions vector
    y0 = S0, I0, R0

    # Integrate the SIR equations over the time grid, t.
    ret = odeint(deriv_SIR_2, y0, t, args=(N,beta1,gamma,tau,t_thresh))
    S, I, R = np.transpose(ret)
    
    return (t,S,I,R)


# # fitting the active infected

print('Fitting the model')

# 3 parameter fit for the active infected

def optimizer_adv(R0,tau,t_thresh):
    
    asympt=3
    
    fin_result_updated=SIR_2(6*10**7,R0*1/21,1/21,tau,t_thresh,I0=asympt*ydata_inf[0])
    i_vec=fin_result_updated[2]/asympt
    
    pesi=np.exp(-np.arange(len(ydata_inf))/7)    # 
    pesi=pesi[::-1]
    
    accuracy=np.sum((ydata_inf-i_vec[0:len(ydata_inf)])**2)   #mean squared error. This is used for the optimization
    
    errperc=np.mean(np.abs((ydata_inf-i_vec[0:len(ydata_inf)])/ydata_inf))*100
    stdperc=np.std(np.abs((ydata_inf-i_vec[0:len(ydata_inf)])/ydata_inf))*100
    
    return accuracy,errperc,stdperc



# grid on 3 parameters
R0grid=np.linspace(7.5,8.5,50)
taugrid=np.linspace(25,27,200)
#ttreshgrid=np.linspace(0,10,15)

res_scan=[]
counter=0
counter2=0
cycle_tot=len(R0grid)*len(taugrid) #*len(ttreshgrid)

time1=pctime.time()

# minimization

for r in R0grid:
    for tau in taugrid:
        opt_res=optimizer_adv(r,tau,0)
        res_scan.append([r,tau,0,opt_res[0],opt_res[1],opt_res[2]])
        counter=counter+1
        counter2=counter2+1
        if counter2==cycle_tot/10:
            time2=pctime.time()
            remtime=round((time2-time1)/counter*(cycle_tot-counter),1)
            print('completed ',round(counter/cycle_tot*100,1),'%. Remaining time ',remtime,'sec')
            counter2=0
        
res_scan=np.array(res_scan)


df_res_scan=pd.DataFrame(res_scan)
df_res_scan.columns=['R0','tau','t_thresh','MSE','mean err%','std err%']

print(df_res_scan.sort_values(by='MSE').head())

par_ideal=np.array(df_res_scan.sort_values(by='MSE').iloc[0,0:])


fin_result_updated=SIR_2(6*10**7,par_ideal[0]*1/21,1/21,par_ideal[1],t_thresh=par_ideal[2],I0=3*ydata_inf[0])

t=fin_result_updated[0]
s_vec=fin_result_updated[1]
i_vec=fin_result_updated[2]
r_vec=fin_result_updated[3]


plt.figure(figsize=(7,5))
plt.plot(np.arange(len(ydata_inf)),ydata_inf,color='red',label='Active infected (data)')
plt.plot(t, i_vec/3, label='Active infected (model, best-fit)',color='blue',linestyle='--')
#plt.fill_between(t, i_vec*(1+par_ideal[5]/100*2.65)/3,i_vec*(1-par_ideal[5]/100*2.65)/3, label='Active infected (model, 99% of data)',color='blue',alpha=.2)
plt.plot(np.zeros(2)+70,[-1000,250000],color='purple')
plt.xticks(np.arange(0,100,7),['24 Feb','2 Mar','9 Mar','16 Mar','23 Mar','30 Mar','6 Apr','13 Apr','20 Apr','27 Apr','4 Mag','11 Mag','18 Mag','25 Mag','1 Giu'],rotation=30)
plt.xlim(0,100)
plt.ylim(100,2*10**5)
#plt.yscale('log')
plt.annotate("Lockdown", xy=(14,10000), xytext=(3,40000), arrowprops=dict(arrowstyle="->"),fontsize=13)
plt.xlabel('Data')
plt.ylabel('Counter')
plt.yscale('log')
plt.legend()
plt.grid(color='gray', linestyle='--', linewidth=0.5)
plt.tight_layout()
plt.savefig('output/fit_con_incertezza.png',dpi=300)
#plt.show()

print('Figure model-data saved')

#export

t_date=pd.to_datetime(t,unit='D',origin=pd.Timestamp('2020-02-24'))

export_v2 = pd.DataFrame({'date':t_date,'t':t,'s':s_vec,'i':i_vec,'r':r_vec})
export_v2.to_csv('output/nazionale.csv',index=False)


# # computation of national R0

# ### using data of last 5 days


today=len(xdata)

print('Computing R0 as function of time')

def minimizer(R0,t1=today-5,t2=today):
    
    #true data
    ydata_inf_2=np.array(ydata_inf[t1:t2])
    xdata_2=np.arange(0,len(ydata_inf_2))
    
    #print(ydata_inf_2)
    
    #model
    fin_result=SIR(60*10**6,1/14*R0,1/14,I0=ydata_inf_2[0])
    i_vec=fin_result[2]
    i_vec_2=i_vec[0:len(xdata_2)]
    
    #average error
    error=np.sum(np.abs(ydata_inf_2-i_vec_2)/ydata_inf_2)*100
    
    return error

minimizer_vec=np.vectorize(minimizer)


# ### scan of R0 over time


time_window=5

def minimizer_gen(t1,t2,xgrid=np.arange(0.1,5,0.01)):

    ygrid=minimizer_vec(xgrid,t1=t1,t2=t2)
    r0_ideal=round(xgrid[np.argmin(ygrid)],2)

    return r0_ideal

r0_time=[]
scangrid=np.linspace(0,5,100)

for i in range(0,today-(time_window-1)):
    min_val=minimizer_gen(i,i+time_window,xgrid=scangrid)
    r0_time.append(min_val)
    scangrid=np.linspace(0,min_val*2,100)  #the grid change over the time (this speed up the process)
    print('Day n',i,' R0=',min_val)
    print(i,i+time_window,len(ydata_inf))
    
r0_time=np.array(r0_time)


plt.figure(figsize=(5,5))
plt.plot(r0_time)
plt.xticks(np.arange(0-(time_window-5),80,7),['28 Feb','6 Mar','13 Mar','20 Mar','27 Mar','3 Apr','10 Apr','17 Apr','24 Apr','1 Mag','8 Mag','15 Mag'],rotation=20)
plt.xlim(0,today-4)
#plt.xlim(19,today-9)
plt.ylabel('$R_0$')
plt.ylim(0,5)
plt.grid()
plt.title('Evolution of $R_0$')
plt.savefig('output/r0-evo.png',dpi=300)
#plt.show()

print('Figure R0 saved')

# export R0 over time

df_r0=pd.DataFrame(pd.to_datetime(np.arange(len(r0_time)),unit='D',origin='2020-02-28'))
df_r0['R0']=r0_time
df_r0.columns=['Data','R0']

df_r0.to_csv('output/r0.csv',index=False)


# # Future forecasting

print('Future predictions as function of R0')

# The SIR model differential equations.
def deriv_SIR_2_future(y, t, N, beta1,gamma,newR0,tau=10**6,t_thresh=14):
    S,I,R = y
    
    if t<=t_thresh:      # il lockdown nazionale inizia al 14° giorno 
        B=beta1
    elif t>t_thresh and t<=70:
        B=beta1*np.exp(-(t-t_thresh)/tau)
    elif t>70:
        B=newR0*gamma
        #B=beta1*np.exp(-(70-t_thresh)/tau)+0.05*gamma*(t-70)
        #print(B,t)

    dSdt = -(B*I/N)*S 
    dIdt = (B*S/N)*I - gamma*I 
    dRdt = gamma*I 
    
    return dSdt, dIdt, dRdt


def SIR_2_future(N,beta1,gamma,newR0,tau=10**6,t_thresh=14,I0=1,R0=0,t=np.arange(0,365)):
    # Definition of the initial conditions
    # I0 and R0 denotes the number of initial infected people (I0) 
    # and the number of people that recovered and are immunized (R0)
    
    # t ise the timegrid
    
    S0=N-I0-R0  # number of people that can still contract the virus
    
    # Initial conditions vector
    y0 = S0, I0, R0

    # Integrate the SIR equations over the time grid, t.
    ret = odeint(deriv_SIR_2_future, y0, t, args=(N,beta1,gamma,newR0,tau,t_thresh))
    S, I, R = np.transpose(ret)
    
    return (t,S,I,R)



asympt=3

i_vec_future050=SIR_2_future(6*10**7,par_ideal[0]*1/21,1/21,0.5,par_ideal[1],t_thresh=par_ideal[2],I0=asympt*ydata_inf[0])[2]
i_vec_future100=SIR_2_future(6*10**7,par_ideal[0]*1/21,1/21,1.0,par_ideal[1],t_thresh=par_ideal[2],I0=asympt*ydata_inf[0])[2]
i_vec_future110=SIR_2_future(6*10**7,par_ideal[0]*1/21,1/21,1.1,par_ideal[1],t_thresh=par_ideal[2],I0=asympt*ydata_inf[0])[2]
i_vec_future120=SIR_2_future(6*10**7,par_ideal[0]*1/21,1/21,1.20,par_ideal[1],t_thresh=par_ideal[2],I0=asympt*ydata_inf[0])[2]


plt.figure(figsize=(7,5))
plt.plot(np.arange(len(ydata_inf)),ydata_inf,color='red',linestyle='None',marker='.',label='Infetti sintomatici attivi (dati)')
plt.fill_between(t, i_vec_future100/asympt,i_vec_future050/asympt,color='green',label='Modello, $R_0$ fra 0.5 e 1',alpha=0.5)
plt.fill_between(t, i_vec_future110/asympt,i_vec_future100/asympt,color='orange',label='Modello, $R_0$ fra 1 e 1.1',alpha=0.5)
plt.fill_between(t, i_vec_future120/asympt,i_vec_future110/asympt,color='red',label='Modello, $R_0$ fra 1.1 e 1.2',alpha=0.5)
#plt.plot(t, i_vec_future05/asympt, label='Modello, R$_0^{riapertura}$=0.5')
#plt.plot(t, i_vec_future10/asympt, label='Modello, R$_0^{riapertura}$=1')
#plt.plot(t, i_vec_future15/asympt, label='Modello, R$_0^{riapertura}$=1.1')
#plt.plot(t, i_vec_future20/asympt, label='Modello, R$_0^{riapertura}$=1.2')
#plt.fill_between(t, i_vec_future*(1+par_ideal[4]/100*2)/asympt,i_vec_future*(1-par_ideal[4]/100*2)/asympt, label='Infetti attivi (modello, 95% C.L.)',color='red',alpha=.2)
plt.plot(np.zeros(2)+70,[-1000,10**7],color='purple')
plt.xticks(np.arange(6,360,30),['1 Mar','1 Apr','1 Mag','1 Giu','1 Lug','1 Ago','1 Set','1 Ott','1 Nov','1 Dic','1 Gen','1 Feb'],rotation=30)
plt.xlim(0,360)
plt.ylim(100,ydata_inf.max()*4.3)
#plt.ylim(100,10**7)
#plt.yscale('log')
plt.annotate("Lockdown", xy=(14,ydata_inf.max()*0.1), xytext=(3,ydata_inf.max()*2), arrowprops=dict(arrowstyle="->"),fontsize=13)
plt.annotate("Riapertura", xy=(70,ydata_inf.max()), xytext=(80,ydata_inf.max()*2), arrowprops=dict(arrowstyle="->"),fontsize=13)
plt.xlabel('Data')
plt.ylabel('Counter')
plt.legend()
plt.grid(color='gray', linestyle='--', linewidth=0.5)
plt.title('2 asintomatici per ogni sintomatico')
plt.tight_layout()
plt.savefig('output/predizioni_future.png',dpi=300)
#plt.show()

print('Figure prediction saved')

#export

ydata_inf_toexport=np.empty(len(i_vec))
ydata_inf_toexport[0:len(ydata_inf)]=ydata_inf
ydata_inf_toexport[len(ydata_inf):]=np.nan

t_date=pd.to_datetime(t,unit='D',origin=pd.Timestamp('2020-02-24'))

export_forecast = pd.DataFrame({'date':t_date,'t':t,'R0=0.5':i_vec_future050/asympt,'R0=1':i_vec_future100/asympt,'R0=1.1':i_vec_future110/asympt,'R0=1.2':i_vec_future120/asympt,'infetti_reali':ydata_inf_toexport})
export_forecast.to_csv('output/predizioni_future_export.csv',index=False)
#  load data ### definition of SIR 1.0 # The SIR model differential equations. # Definition of the initial conditions # I0 and R0 denotes the number of initial infected people (I0) # and the number of people that recovered and are immunized (R0) # t ise the timegrid # number of people that can still contract the virus # Initial conditions vector # Integrate the SIR equations over the time grid, t. # ### definition of SIR 2.0 # The SIR model differential equations. # il lockdown nazionale inizia al 14° giorno # Definition of the initial conditions # I0 and R0 denotes the number of initial infected people (I0) # and the number of people that recovered and are immunized (R0) # t ise the timegrid # number of people that can still contract the virus # Initial conditions vector # Integrate the SIR equations over the time grid, t. # # fitting the active infected # 3 parameter fit for the active infected # #mean squared error. This is used for the optimization # grid on 3 parameters #ttreshgrid=np.linspace(0,10,15) #*len(ttreshgrid) # minimization #plt.fill_between(t, i_vec*(1+par_ideal[5]/100*2.65)/3,i_vec*(1-par_ideal[5]/100*2.65)/3, label='Active infected (model, 99% of data)',color='blue',alpha=.2) #plt.yscale('log') #plt.show() #export # # computation of national R0 # ### using data of last 5 days #true data #print(ydata_inf_2) #model #average error # ### scan of R0 over time #the grid change over the time (this speed up the process) #plt.xlim(19,today-9) #plt.show() # export R0 over time # # Future forecasting # The SIR model differential equations. # il lockdown nazionale inizia al 14° giorno #B=beta1*np.exp(-(70-t_thresh)/tau)+0.05*gamma*(t-70) #print(B,t) # Definition of the initial conditions # I0 and R0 denotes the number of initial infected people (I0) # and the number of people that recovered and are immunized (R0) # t ise the timegrid # number of people that can still contract the virus # Initial conditions vector # Integrate the SIR equations over the time grid, t. #plt.plot(t, i_vec_future05/asympt, label='Modello, R$_0^{riapertura}$=0.5') #plt.plot(t, i_vec_future10/asympt, label='Modello, R$_0^{riapertura}$=1') #plt.plot(t, i_vec_future15/asympt, label='Modello, R$_0^{riapertura}$=1.1') #plt.plot(t, i_vec_future20/asympt, label='Modello, R$_0^{riapertura}$=1.2') #plt.fill_between(t, i_vec_future*(1+par_ideal[4]/100*2)/asympt,i_vec_future*(1-par_ideal[4]/100*2)/asympt, label='Infetti attivi (modello, 95% C.L.)',color='red',alpha=.2) #plt.ylim(100,10**7) #plt.yscale('log') #plt.show() #export