#My model to describe the number of Corona cases in Germany, from data in March 2020 #Comparison with the data from JHU github #Gerald Schuller, April 2020 import numpy as np import matplotlib.pyplot as plt def logistic(K, valueondate, factorincrease, t): #logistic function for exponential growth with saturation at population size K #starting from a value on a given date "valueondate" #factor for the increase from day to day is "factorincrease" #prediction for the number of days "t" after the given day, #prediction before the given date is obtained by using negative values for t return K/(1+ ((K-valueondate)/valueondate)*np.exp(-np.log(factorincrease)*t )) #Read data from github: import urllib.request import pandas as pd Retrievedata=False #Cases if Retrievedata: url = 'https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv' urllib.request.urlretrieve(url, './corona_cases.csv') #('./corona_cases.csv', ) df = pd.read_csv('./corona_cases.csv') #df.head() df=df.drop(['Lat','Long','Province/State'], axis=1) df=df.set_index('Country/Region') countries = ['Italy', 'Germany', 'Spain', 'Brazil', 'US', 'Russia','Korea, South'] print("countries=", countries) data=df.loc[countries,: ] #data #starting MARCH 1: data.iloc[0,37:] #detected cases Italy #Germanycases = data.iloc[1,37:].reset_index(drop=True) Germanycases = data.loc['Germany','2/29/20':'3/31/20'].reset_index(drop=True) Germanycases= np.array(Germanycases) print("Cases March:", data.loc['Germany','2/29/20':'3/31/20']) #detected cases Germany #print("Germany cases", Germanycases) #Recovered if Retrievedata: url = 'https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_recovered_global.csv' urllib.request.urlretrieve(url, './corona_recovered.csv') df_recovered = pd.read_csv('./corona_recovered.csv') df_recovered=df_recovered.drop(['Lat','Long','Province/State'], axis=1) df_recovered=df_recovered.set_index('Country/Region') data_recovered=df_recovered.loc[countries,: ] Germanyrecovered=data_recovered.loc['Germany','2/29/20':'3/31/20'].reset_index(drop=True) #print("data_recovered March", data_recovered.iloc[1,39:]) print("Germanyrecovered", data_recovered.loc['Germany','2/29/20':'3/31/20']) #Deaths if Retrievedata: url = 'https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_global.csv' urllib.request.urlretrieve(url, './corona_deaths.csv') df_deaths = pd.read_csv('./corona_deaths.csv') df_deaths=df_deaths.drop(['Lat','Long','Province/State'], axis=1) df_deaths=df_deaths.set_index('Country/Region') data_deaths=df_deaths.loc[countries,: ] Germanydeaths=data_deaths.loc['Germany','2/29/20':'3/31/20'].reset_index(drop=True) Germanydeaths=np.array(Germanydeaths) #print("data_deaths March", data_deaths.iloc[1,39:]) print("Germanydeaths", data_deaths.loc['Germany','2/29/20':'3/31/20']) #Model for Corona cases: #639 cases on March 6th, 25% increase per day #639*(1.25**3) #Days since March 6 factorincrease=1.25 #1.25increase factor day to day valueondate=639 #639 value on a given day dayofvalue=6 #the given day of the month of the value K=83e6 #Population of Germany timetorecovery=11.5#16 #days from dicovering to recovery #Plot range in days: t=np.arange(1,32) #prediction for this range of days of the month. For the next month, use day numbers larger that 30. plt.plot(t, logistic(K, valueondate, factorincrease, t-dayofvalue) ) plt.plot(t, Germanycases[t]) plt.plot(t, logistic(K, valueondate, factorincrease, t-timetorecovery-dayofvalue) ) #estimated recovered plt.plot(t, Germanyrecovered[t]) #plt.plot(t, valueondate*(factorincrease**(t-dayofvalue))) plt.xlabel('Day after beginning of March') plt.ylabel('Corona Cases') plt.legend(('Predicted Cases', 'Detected Cases', 'Predicted Recovered Cases', 'Detected Recovered')) plt.grid() plt.title('Corona Cases in Germany, from logistic model') plt.show() #Plot of currently sick patients #Difference cases minus recovered plt.plot(t, logistic(K, valueondate, factorincrease, t-dayofvalue) -logistic(K, valueondate, factorincrease, t-timetorecovery-dayofvalue) ) plt.xlabel('Day after beginning of March') plt.ylabel('Current Corona Cases') plt.grid() plt.title('Currently Sick Cases in Germany, from logistic model') plt.show() #Death cases: 2 on march 9, 5 on March 13. #20 days back for cases: 18% death rate, compensation for the undiscovered cases #2*(1.25**4) #todesfaelle, tage seit 9.3. #valueondate=2 #value on a given day #dayofvalue=9 #the given day of the month of the value #plt.plot(t, valueondate*(factorincrease**(t-dayofvalue))) plt.plot(t,logistic(K, valueondate, factorincrease, t-timetorecovery-dayofvalue)*0.048) #0.07 early, 0.02 long term plt.plot(t, Germanydeaths[t]) plt.xlabel('Day of March') plt.ylabel('Accumulated Corona Death Cases') plt.grid() plt.legend(('Predicted Deaths', 'Detected Deaths')) plt.title('Corona Death Cases in Germany, from logistic model') plt.show() #Factor of increase to previous day: plt.plot(t, Germanycases[t]/Germanycases[t-1]) plt.plot(t, Germanydeaths[t]/(Germanydeaths[t-1])) plt.xlabel('Day of March') plt.ylabel('Factor of increase') plt.grid() plt.legend(('Factor for deteced cases','Factor for deaths')) plt.title('Factor of increase to previous day') #plt.axis([1,31,0, 2]) plt.show() countrycases=data.loc[countries,'2/29/20':'3/31/20'].reset_index(drop=True) countrycases=np.array(countrycases) factorsofincrease=countrycases[:,1:]/countrycases[:,:-1] #factor of increase f for each country plt.plot(factorsofincrease.T) plt.legend(countries) plt.xlabel('Day of March') plt.ylabel('Factor of increase') plt.grid() plt.title('Factor of increase to previous day internationally') #plt.axis([1,31,0, 2]) plt.show()