Visualizes the data on an national level and models the deaths and infections of the next days using an exponential and a logistic model.
Disclaimer: Experts estimate that many of the infections remain unreported, and therefore the collected data does not necessarily give the full picture of the situation.
Covid-19 Outbreak Analysis Italy
import pandas as pd
from pandas.plotting import register_matplotlib_converters
import seaborn as sns
sns.set(style="whitegrid")
import matplotlib.pyplot as plt
import os
import matplotlib.dates as mdates
import numpy as np
from datetime import datetime
%matplotlib inline
register_matplotlib_converters()
now = datetime.now()
print("Updated at (UTC TIME):", now)
Updated at (UTC TIME): 2020-03-30 18:33:17.646055
National Data
Data of italian provinces
The data is fetched from the repository of the italian government, which is updated daily. First parse the date column:
url = 'https://raw.githubusercontent.com/pcm-dpc/COVID-19/master/dati-andamento-nazionale/dpc-covid19-ita-andamento-nazionale.csv'
df = pd.read_csv(url, error_bad_lines=False)
df['date'] = pd.to_datetime(df['data'])
Plot Trendlines using National Data
To get an overview of how the epidemic is evolving we can plot the trendlines of the different datapoints.
fig, ax = plt.subplots(figsize=(10,6))
sns.lineplot(x='date',y='totale_casi', data=df, label='Total cases', ax=ax, lw=2)
sns.lineplot(x='date',y='totale_attualmente_positivi', data=df, label='Total act. positives', ax=ax, lw=2)
sns.lineplot(x='date',y='totale_ospedalizzati', data=df, label='Total Hospitalized', ax=ax, lw=2)
sns.lineplot(x='date',y='terapia_intensiva', data=df, label='Intensive Care', ax=ax, lw=2)
plt.ylabel('Units', fontsize=14)
plt.xlabel('Date', fontsize=14)
plt.xticks(rotation=70)
ax.xaxis.set_major_locator(mdates.AutoDateLocator())
ax.xaxis.set_major_formatter(mdates.DateFormatter('%m.%d'))
plt.xticks(fontsize=12)
plt.yticks(fontsize=12)
plt.legend(fontsize=12)
plt.title('Covid-19 trendlines in Italy', fontsize=16)
Text(0.5, 1.0, 'Covid-19 trendlines in Italy')
fig, ax = plt.subplots(figsize=(10,6))
sns.lineplot(x='date',y='deceduti', data=df, label='Dead', ax=ax, lw=2)
sns.lineplot(x='date',y='dimessi_guariti', data=df, label='Recovered', ax=ax, lw=2)
plt.ylabel('Units', fontsize=14)
plt.xlabel('Date', fontsize=14)
plt.xticks(rotation=70)
ax.xaxis.set_major_locator(mdates.AutoDateLocator())
ax.xaxis.set_major_formatter(mdates.DateFormatter('%m.%d'))
plt.xticks(fontsize=12)
plt.yticks(fontsize=12)
plt.legend(fontsize=12)
plt.title('Covid-19 trendlines in Italy', fontsize=16)
Text(0.5, 1.0, 'Covid-19 trendlines in Italy')
Predicting Number of Deaths in Italy
We fit a linear regression model on the log of the death count
import statsmodels.api as sm
df_dead = pd.DataFrame()
days = [i for i in range(df.shape[0])]
df_dead['date'] = df['date']
df_dead['days'] = days
df_dead['deaths'] = df['deceduti']
df_dead['log_deaths'] = np.log(df_dead['deaths'])
df_dead.head()
| date | days | deaths | log_deaths | |
|---|---|---|---|---|
| 0 | 2020-02-24 18:00:00 | 0 | 7 | 1.945910 |
| 1 | 2020-02-25 18:00:00 | 1 | 10 | 2.302585 |
| 2 | 2020-02-26 18:00:00 | 2 | 12 | 2.484907 |
| 3 | 2020-02-27 18:00:00 | 3 | 17 | 2.833213 |
| 4 | 2020-02-28 18:00:00 | 4 | 21 | 3.044522 |
We will predict 2 days into the future
day_range = range(1, df.shape[0] + 2)
Fit the regression model and predict
X = df_dead.days
X = sm.add_constant(X)
y = df_dead.log_deaths
model = sm.OLS(y,X)
res = model.fit()
a = res.params.const
b = res.params.days
x_pred = [np.exp(a+b*x) for x in day_range]
Here we will do the same thing, but instead of fitting the model on the whole data, we will just use the past 4 days to get a recent trend of how the death count is evolving
df_dead2 = df_dead[df_dead.days > df.shape[0] -5]
X = df_dead2.days
X = sm.add_constant(X)
y = df_dead2.log_deaths
model = sm.OLS(y,X)
res = model.fit()
a = res.params.const
b = res.params.days
x_pred_2 = [np.exp(a+b*x) for x in day_range]
fig, ax = plt.subplots(figsize=(10,6))
plot = sns.lineplot(day_range, x_pred, label="Sim. Deaths")
plot = sns.lineplot(day_range, x_pred_2, label="Sim. Deaths (Based on last 4 days)")
plot = sns.lineplot(days, df_dead['deaths'], label="Real Deaths")
plt.ylabel('Deaths', fontsize=14)
plt.xlabel('Days since first case', fontsize=14)
plot.set_title("Cumulative Deaths in Italy")
Text(0.5, 1.0, 'Cumulative Deaths in Italy')
Predicting Number of Cases in Italy
Again we fit a linear regression model on the log of the infected count
import statsmodels.api as sm
df_inf = pd.DataFrame()
days = [i for i in range(df.shape[0])]
df_inf['date'] = df['date']
df_inf['days'] = days
df_inf['infected'] = df['totale_casi']
df_inf['log_infected'] = np.log(df_inf['infected'])
df_inf.head()
| date | days | infected | log_infected | |
|---|---|---|---|---|
| 0 | 2020-02-24 18:00:00 | 0 | 229 | 5.433722 |
| 1 | 2020-02-25 18:00:00 | 1 | 322 | 5.774552 |
| 2 | 2020-02-26 18:00:00 | 2 | 400 | 5.991465 |
| 3 | 2020-02-27 18:00:00 | 3 | 650 | 6.476972 |
| 4 | 2020-02-28 18:00:00 | 4 | 888 | 6.788972 |
Fit the model to the data
X = df_inf.days
X = sm.add_constant(X)
y = df_inf.log_infected
model = sm.OLS(y,X)
res = model.fit()
a_exp = res.params.const
b_exp = res.params.days
x_pred_infections = [np.exp(a_exp+ b_exp * x) for x in day_range]
Same thing, but just for the last 4 days to get current trend
df_inf_4days = df_inf[df_inf.days > df.shape[0] - 5]
X = df_inf_4days.days
X = sm.add_constant(X)
y = df_inf_4days.log_infected
model = sm.OLS(y,X)
res = model.fit()
a = res.params.const
b = res.params.days
x_pred_infections_4days = [np.exp(a+b*x) for x in day_range]
fig, ax = plt.subplots(figsize=(10,6))
plot = sns.lineplot(day_range, x_pred_infections, label="Sim. Infections")
plot = sns.lineplot(day_range, x_pred_infections_4days, label="Sim. Infections (Based on last 4 days)")
plot = sns.lineplot(days, df_inf['infected'], label="Confirmed Infections")
plt.ylabel('Infected', fontsize=14)
plt.xlabel('Days since first case', fontsize=14)
plot.set_title("Cumulative Infections in Italy")
Text(0.5, 1.0, 'Cumulative Infections in Italy')
Plotting the new cases
df_growth = df.copy()
df_growth['new_cases'] = df_growth['totale_casi'].diff()
df_growth['days'] = range(df_growth.shape[0])
fig, ax = plt.subplots(figsize=(10,6))
plot = sns.barplot(y="new_cases", x="days", data=df_growth, label="New Cases", palette="Blues")
plt.ylabel('New Cases', fontsize=14)
plt.xlabel('Days since first case', fontsize=14)
plot.set_title("New Cases each Day in Italy")
Text(0.5, 1.0, 'New Cases each Day in Italy')
Fitting a logistic model
In real life we almost never observe an exponential growth, but instead the exponential curve is just the beginning of a logistic curve.
from scipy.optimize import curve_fit, fsolve
import datetime as dt
def logistic_model(x,a,b,c):
return c/(1+np.exp(-(x-b)/a))
x_pred = [logistic_model(x,5,50,20) for x in range(0,100)]
plot = sns.lineplot(range(0,100), x_pred, label="Logistic Model")
plot.set_title("A simple logistic model")
Text(0.5, 1.0, 'A simple logistic model')
Preprocessing
df_log = pd.read_csv(url, error_bad_lines=False)
df_log = df_log.loc[:,['data','totale_casi']]
FMT = '%Y-%m-%dT%H:%M:%S'
date = df_log['data']
df_log['day_of_year'] = date.map(lambda x : (datetime.strptime(x, FMT) - datetime.strptime("2020-01-01T00:00:00", FMT)).days )
Fitting the model
x = list(df_log.iloc[:,2])
y = list(df_log.iloc[:,1])
fit = curve_fit(logistic_model, x, y, p0=[2,100,20000],maxfev=2000)
The result gives us three values:
a: the infection speed
b: day of year with maximum new infections
c: total number of recorded infected people at the end of the epidemic
a = fit[0][0]
b = fit[0][1]
c = fit[0][2]
print("a=", a, " b=", b, " c=", c)
a= 5.4378699133809265 b= 82.14669060053295 c= 129862.49170271672
B will be the inflection point, i.e. the point where new infections on a day will be less than on the previous day
date = dt.date(2020,1,1) + dt.timedelta(int(b))
print(date)
2020-03-23
We can compute the end of the epidemic according to the model by solving the equation of the model
sol = int(fsolve(lambda x : logistic_model(x,a,b,c) - int(c),b))
date = dt.date(2020,1,1) + dt.timedelta(sol)
print(date)
2020-05-30
Plotting the logistic curve
fig, ax = plt.subplots(figsize=(10,6))
# logistic model
x_pred_log = [logistic_model(x,a,b,c) for x in range(54,120)]
y_pred_log = [dt.date(2020,1,1) + dt.timedelta(i) for i in range(54,120)]
# exponential model
x_pred_infections = [np.exp(a_exp + b_exp * x) for x in range(35)]
y_pred_exp = [dt.date(2020,1,1) + dt.timedelta(i) for i in range(54,89)]
plot = sns.lineplot(df_inf['date'], df_inf['infected'], label="Confirmed Infections")
plot = sns.lineplot(y_pred_log, x_pred_log, label="Logistic Model")
plot = sns.lineplot(y_pred_exp, x_pred_infections, label="Exponential Model")
plt.xticks(rotation=70)
ax.xaxis.set_major_locator(mdates.AutoDateLocator())
ax.xaxis.set_major_formatter(mdates.DateFormatter('%m.%d'))
plt.ylabel('Total Infections', fontsize=14)
plt.xlabel('Date', fontsize=14)
plot.set_title("Comparison of total infection models")
Text(0.5, 1.0, 'Comparison of total infection models')
