# An estimate of vaccination duration using linear regression 
# Inputs: 
#       pop - population size  (default 5466000)
#       vac - percentage of vacctination (default 60)
#       dose - number of doses (default 2)
#       data - from 06.01.2021 to 11.02.2021
#       region - Slovakia, EU, UK, World
#      
#       Slovakia population: 5466000
#       [(6,6618),(13,46243),(20,85957),(27,121245),(34,178442),(42,268844)]
#       EU population: 445561000
#       Data= [(1,1477853),(7,4093497),(14,7141406),(20,10762226),(27,14888339), (42,19628190)]

#       UK population: 67969000

#       Data= [(10,2677971),(17,4514802),(24,7044048),(31,9790576),(38,12806587), (47,16499549)]

#       World population: 7809575000
#       [(6,16326929),(13,35780021),(20,54315120),(27,82980899),(34,115614565),(42,160070774)]
#       Note: input data can be modificated
#       Source: https://github.com/owid/covid-19-data/blob/master/public/data/vaccinations/vaccinations.csv
#       linear regression: https://www.oxfordreference.com/view/10.1093/oi/authority.20110803100107226
#       Algorithm: based on input data application of a linear regression model 

# The program can also be run at: https://sagecell.sagemath.org/
# To run - paste the source code into the Sagecell box
#
# February 24, 2021 Peter Szabó, Miroslava Ferencová - updated

# auxiliary function for calculating the date 
def den(i):
    # calculating the date, valid only in January and February 2021,
    if (i<32): s=str(i)+"th January 2021"
    if (i>31) and (i<59): s=str(i-31)+"th February 2021"
    return s

# the main program
@interact
def imunita(
    pop = input_box(default=5466000, label="Population" ),
    vac = slider(vmin=1, vmax=100, step_size=1, default=60, label="Percentage"),
    dose = ("two doses", true),
    data = input_box(default =[(6,6618),(13,46243),(20,85957),(27,121245),(34,178442),(42,268844),(47,322162),(54,394790)], label="Vaccinated"),
    reg = selector(['Slovakia', 'European Union', 'United Kingdom','World'],buttons=True,  label="Region" )):
    
    if reg == 'European Union':
       data =  [(1,1477853),(7,4093497),(14,7141406),(20,10762226),(27,14888339),(42,19628190), (47,23113359), (54,28262415)]
       pop = 445561000

    
    if reg == 'United Kingdom':
       data = [(10,2677971),(17,4514802),(24,7044048),(31,9790576),(38,12806587), (47,16499549), (53,18558969)]     
       pop = 67969000

   
    if reg == 'World':
       data =  [(6,16326929),(13,35780021),(20,54315120),(27,82980899),(34,115614565),(42,160070774),(47,184585643),(54,216167273)]
       pop = 7809575000
        
    # Linear regression
    # x - days, y - the number of vaccinated
    var("a,b")
    model(x) = a*x+b
    a1=find_fit(data,model)[0].rhs()
    b1=find_fit(data,model)[1].rhs()
    n = len(data)-1
    
    # input data and linear regression
   
    p = scatter_plot(data,frame=True, gridlines=True)
    p += plot(a1*x+b1, (x,data[0][0],data[n][0]), color = "blue", thickness = 2, axes_labels =[ "Days","Vaccinated"], 
              title="Regression analysis - Calculation of vaccination time") 
    p.show() 
    
    # Estimation of vaccination time , calculation of vaccination
    poc=pop*vac/100
    if dose : poc=2*poc
    
    # Number of days(x) based on regression line y= a1*x+b1, x=(y-b1)/a1   
    dni=round((poc-b1)/a1)
    
    # Calculation of vaccination percentage
    perc=(data[n][1]/pop)*100
    if dose : perc=perc/2
        
    print("For the",vac,"% vaccination of the population is still needed ", dni,"days (",(dni/365).n(12)," years).")
    print("On the date",den(data[n][0]), "percentage of vacctination is ",perc.n(20),"%.") 
    # print("y=",round(a1),"x + ",round(b1)," - is the regression line ")