Key Words: SIR Modeling, Epidemic Model, Forecasting, Time Series, Interactive Visualization
Dr. Edward Parker used John Hopkins Center for Systems Science and Engineering data to build a Shiny COVID-19 tracker that allows the user to visualize global changes of either COVID-19 or SARS outbreak at a daily rate. The visualization also highlights the number of new cases and number of deaths for a given country.
Objectives
- create SIR Model based on the COVID data that has been collected till May 2021.
In Data 604 (Simulation and Modeling Techniques), I was introduced to developing models of an epidemic as it spreads in a susceptible population. I will use the covid19.analytics library.
- create several visualizations to analyze COVID-19 data
I was inspired by Dr. Parker’s tracker and Dr. Rai’s research. Data 608 (Visual Analytics) also helped prepare me to create animated and interactive visualizations.
- Is it possible to predict unemployment claims based on number of COVID-19 cases?
In Data 624 (Predictive Analytics), I used ARIMA Models to forecast the total international visitors to Australia. I will also utilize the prophet library.
Data
In order to successfully complete these objectives, I will utilize the data sets in the following Github.
Global COVID-19 data from January 2020 - March 2020
The US Department of Labor’s Unemployment Insurance Weekly Claim data for each US state from 1967-2021
New York Times Daily COVID confirmed cases data.
Latest COVID-19 Data from the
covid19.analyticslibrary in R .
Methodology
When COVID-19 was first discovered, the below global data from January 2020 - March 2020 was collected. The data includes age, symptoms, whether the patient lives in Wuhan, travel history etc. For our analysis, we are interested in visualizing the cases by US county. This information is helpful to understand where cases can spread. Leaflet library can help achieve this.
Load Data
# early COVID data - leaflet map of US
# group data by the city/county
early_data <- read.csv("/Users/aaronzalki/Downloads/latestdata.csv", header = T)
usa <- early_data %>% filter(country == 'United States')
usa <- usa %>% group_by(city, province, longitude, latitude) %>%
summarise(count = n()) %>%
arrange(desc(count))
#the below commented code will tabulate the usa dataframe
#kable(usa) %>%
#kable_styling(bootstrap_options = "bordered") %>%
#row_spec(0, bold = T, color = "black", background = "#7fcdbb")
glimpse(usa)## Rows: 1,322
## Columns: 5
## Groups: city, province, longitude [1,322]
## $ city <chr> "", "New York City", "", "", "Westchester County", "Nassau …
## $ province <chr> "New York", "New York", "New Jersey", "California", "New Yo…
## $ longitude <dbl> -75.64646, -73.94400, -74.67120, -119.67788, -73.75697, -73…
## $ latitude <dbl> 43.01409, 40.66100, 40.20301, 37.38020, 41.16249, 40.73995,…
## $ count <int> 23708, 17373, 6306, 5074, 4679, 3241, 2921, 2058, 2000, 166…Early Data Visualization
County
We can also add a filter to concentrate on fewer states.
New York & New Jersey
The below toggle can hide/unhide the States that the user selects/deselects.
Interactive Toggle
Cluster Counties
Animation Plots
We can see an exponential growth in March.
Exploratory Data Analysis
For this analysis, we will be referring to unemployment claims data by US State and daily COVID confirmed cases data. This COVID data is more up to date than the above used for the County Map and Animated Visualizations.
Load Data
# Unemployment data - USA
df <- read.csv("https://raw.githubusercontent.com/aaronzalkisps/data698/main/state_claims.csv", header = T)
glimpse(df)## Rows: 3,604
## Columns: 7
## $ State <chr> "Alabama", "Alabama", "Alabama", "Alabama",…
## $ week <dbl> 43834, 43841, 43848, 43855, 43862, 43869, 4…
## $ Initial.Claims <dbl> 4578, 3629, 2483, 2129, 2170, 2176, 1981, 1…
## $ Reflecting.Week.Ended <chr> "12/28/19", "1/4/20", "1/11/20", "1/18/20",…
## $ Continued.Claims <dbl> 18523, 21143, 17402, 18390, 17284, 16745, 1…
## $ Covered.Employment <dbl> 1923741, 1923741, 1923741, 1923741, 1923741…
## $ Insured.Unemployment.Rate <dbl> 0.96, 1.10, 0.90, 0.96, 0.90, 0.87, 0.86, 0…# COVID data - USA
df2 <- read.csv("https://raw.githubusercontent.com/aaronzalkisps/data698/main/coronavirus_states.csv", header = T)
glimpse(df2)## Rows: 15,854
## Columns: 15
## $ State <chr> "Washington", "Washington", "Washington", "Illinoi…
## $ date <chr> "1/21/20", "1/22/20", "1/23/20", "1/24/20", "1/24/…
## $ week <dbl> 43855, 43855, 43855, 43855, 43855, 43855, 43855, 4…
## $ fips <int> 53, 53, 53, 17, 53, 6, 17, 53, 4, 6, 17, 53, 4, 6,…
## $ cases <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1,…
## $ deaths <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ population <int> 6724540, 6724540, 6724540, 12830632, 6724540, 3725…
## $ new_cases <int> 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,…
## $ new_deaths <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ days_since_death10 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ days_since_case100 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ per100k <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ newper100k <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ deathsper100k <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ newdeathsper100k <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…Merge Data
The two data frames are joined by week and State. This will provide how many COVID confirmed cases and unemployment claims occurred for a State in a given week. After pivoting the data, we can conclude that from the weeks 01/26/20 - 12/21/20 the top 5 states to record the most COVID cases are: California, Texas, Florida, Illinois and New York.
Data Preparation
#group total claims
subset2 <- no_zero[c(2,3,5)]
#remove duplicates
distinct_subset2<-unique(subset2)
df_join <- df4 %>% full_join(distinct_subset2, by=c("week", "State"))
#date format
dpm<- as.Date(df_join$week)
dpm <- dpm %m-% years(70)
dpm_df <- as.data.frame(dpm)
final_df <- cbind(dpm_df, df_join)
conditions <- filter (final_df, !State %in% c("Virgin Islands", "Puerto Rico", "Northern Mariana Islands", "Guam", "District of Columbia"))
#the below commented code will tabulate the merged dataframe
#kable(conditions) %>%
#kable_styling(bootstrap_options = "bordered") %>%
#row_spec(0, bold = T, color = "black", background = "#7fcdbb")
#pivot data
weekly_ue <- conditions %>%
group_by(dpm)%>%
summarise(claim_sum=sum(Initial.Claims))
names (weekly_ue) <- c("Week","Unemployment Claim")
#the below commented code will tabulate the unemployment claims data
#kable(weekly_ue) %>%
#kable_styling(bootstrap_options = "bordered") %>%
#row_spec(0, bold = T, color = "black", background = "#7fcdbb")
weekly_covid <- conditions %>%
group_by(dpm)%>%
summarise(case_sum=sum(case_sum))
names (weekly_covid) <- c("Week","Confirmed COVID Case")
#the below commented code will tabulate the confirmed COVID case data
#kable(weekly_covid) %>%
#kable_styling(bootstrap_options = "bordered") %>%
#row_spec(0, bold = T, color = "black", background = "#7fcdbb")
final_df2 <- cbind(weekly_ue, weekly_covid)
final_df <-final_df2[c(1,2,4)]
kable(final_df) %>%
kable_styling(bootstrap_options = "bordered") %>%
row_spec(0, bold = T, color = "black", background = "#7fcdbb")| Week | Unemployment Claim | Confirmed COVID Case |
|---|---|---|
| 2020-01-26 | 63430 | 3 |
| 2020-02-02 | 62131 | 5 |
| 2020-02-09 | 46971 | 4 |
| 2020-02-16 | 56235 | 3 |
| 2020-02-23 | 47519 | 15 |
| 2020-03-02 | 74443 | 40 |
| 2020-03-09 | 163864 | 357 |
| 2020-03-16 | 248557 | 2450 |
| 2020-03-23 | 2879374 | 21532 |
| 2020-03-30 | 5920274 | 99075 |
| 2020-04-06 | 6079352 | 187414 |
| 2020-04-13 | 4845813 | 216899 |
| 2020-04-20 | 4186423 | 199967 |
| 2020-04-27 | 3442164 | 210581 |
| 2020-05-04 | 2763201 | 193264 |
| 2020-05-11 | 2305713 | 175582 |
| 2020-05-18 | 2147410 | 156877 |
| 2020-05-25 | 1884090 | 155246 |
| 2020-06-01 | 1600893 | 145901 |
| 2020-06-08 | 1544311 | 154389 |
| 2020-06-15 | 1445887 | 151283 |
| 2020-06-22 | 1434831 | 180497 |
| 2020-06-29 | 1413477 | 257028 |
| 2020-07-06 | 1377025 | 339063 |
| 2020-07-13 | 1501234 | 392431 |
| 2020-07-20 | 1363059 | 459774 |
| 2020-07-27 | 1192803 | 463854 |
| 2020-08-03 | 979257 | 434245 |
| 2020-08-10 | 823559 | 375297 |
| 2020-08-17 | 874349 | 362902 |
| 2020-08-24 | 810445 | 301250 |
| 2020-08-31 | 823605 | 289983 |
| 2020-09-07 | 854702 | 292244 |
| 2020-09-14 | 783005 | 239009 |
| 2020-09-21 | 812885 | 280328 |
| 2020-09-28 | 729914 | 307852 |
| 2020-10-05 | 720812 | 302546 |
| 2020-10-12 | 818784 | 356551 |
| 2020-10-19 | 756140 | 391420 |
| 2020-10-26 | 729733 | 471458 |
| 2020-11-02 | 734824 | 559425 |
| 2020-11-09 | 718174 | 742361 |
| 2020-11-16 | 706824 | 1015006 |
| 2020-11-23 | 825781 | 1187417 |
| 2020-11-30 | 709284 | 1131896 |
| 2020-12-07 | 943572 | 1338682 |
| 2020-12-14 | 925470 | 1520834 |
| 2020-12-21 | 851448 | 584482 |
Linear Regression
COVID cases as the predictor
Unemployment claim as the output
Forecasting
Unemployment
Auto ARIMA chose the model ARIMA(1,0,2)
#date handling
weekly_ue$Week <- as.Date(weekly_ue$Week)
#convert to timeseries
data_ts_ue <- xts(weekly_ue$`Unemployment Claim`, weekly_ue$Week)
#ARIMA
aa_austa<-auto.arima(data_ts_ue)
summary(aa_austa)## Series: data_ts_ue
## ARIMA(1,0,2) with non-zero mean
##
## Coefficients:
## ar1 ma1 ma2 mean
## 0.6898 1.2677 0.4765 1308430.3
## s.e. 0.1222 0.1838 0.1786 490132.1
##
## sigma^2 estimated as 1.797e+11: log likelihood=-689.96
## AIC=1389.92 AICc=1391.35 BIC=1399.28
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 13382.1 405866 208666 -41.66823 53.16551 0.7719208 0.004131897Check Residuals
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,0,2) with non-zero mean
## Q* = 1.6415, df = 6, p-value = 0.9496
##
## Model df: 4. Total lags used: 10
COVID-19
#date handling
weekly_covid$Week <- as.Date(weekly_covid$Week)
#convert to timeseries
data_ts_covid <- xts(weekly_covid$`Confirmed COVID Case`, weekly_ue$Week)
#ARIMA
ab_austa<-auto.arima(data_ts_covid)
summary(ab_austa)## Series: data_ts_covid
## ARIMA(0,1,0)
##
## sigma^2 estimated as 2.474e+10: log likelihood=-629.08
## AIC=1260.17 AICc=1260.26 BIC=1262.02
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 12176.65 155642.1 66718.52 10.87979 25.32519 0.9791667 -0.01591221Check Residuals
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,0)
## Q* = 5.7173, df = 10, p-value = 0.8384
##
## Model df: 0. Total lags used: 10
Forecasting via Prophet
The following code will get confirmed cases data from the covid19.analytics library. I have saved the object as ‘tsc’ which stands for time series confirmed. I will filter for United States and will transpose the dataframe.
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------tsc <- tsc %>% filter(Country.Region == 'US')
tsc <- data.frame(t(tsc))
tsc <- cbind(rownames(tsc), data.frame(tsc, row.names = NULL))
#change column name
colnames(tsc) <- c('Date', 'Confirmed')
#lubridate library
tsc$Date <- ymd(tsc$Date)
tsc$Confirmed <- as.numeric(tsc$Confirmed)
ds <- tsc$Date
y <- tsc$Confirmed
#create dataframe with date and confirmed cases
df <- data.frame(ds, y)Forecast for the next 4 weeks or 28 days
#remove NA in first four rows
N <- 4
df <- tail(df, -N)
fore_cast_case <- prophet(df)
# Prediction
future <- make_future_dataframe(fore_cast_case, periods = 28)
forecast <- predict(fore_cast_case, future)
Model performance seems to be strong.
#Model performance
pred <- forecast$yhat[1:546]
actual <- fore_cast_case$history$y
plot(actual, pred)
Results
The following code will get COVID cases data from the covid19.analytics library.
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------Top Two Countries Report
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------
## ################################################################################
## ##### TS-CONFIRMED Cases -- Data dated: 2021-07-20 :: 2021-07-21 13:11:50
## ################################################################################
## Number of Countries/Regions reported: 195
## Number of Cities/Provinces reported: 88
## Unique number of distinct geographical locations combined: 279
## --------------------------------------------------------------------------------
## Worldwide ts-confirmed Totals: 191445502
## --------------------------------------------------------------------------------
## Country.Region Province.State Totals GlobalPerc LastDayChange t-2 t-3 t-7 t-14 t-30
## 1 US 34174774 17.85 42703 52111 12048 31845 22931 12334
## 2 India 31216337 16.31 42015 30093 38164 41733 45892 42640
## --------------------------------------------------------------------------------
## Global Perc. Average: 0.36 (sd: 1.63)
## Global Perc. Average in top 2 : 17.08 (sd: 1.09)
## --------------------------------------------------------------------------------
## ================================================================================
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------
## ################################################################################
## ##### TS-DEATHS Cases -- Data dated: 2021-07-20 :: 2021-07-21 13:11:52
## ################################################################################
## Number of Countries/Regions reported: 195
## Number of Cities/Provinces reported: 88
## Unique number of distinct geographical locations combined: 279
## --------------------------------------------------------------------------------
## Worldwide ts-deaths Totals: 4118391
## --------------------------------------------------------------------------------
## Country.Region Province.State Totals Perc LastDayChange t-2 t-3 t-7 t-14 t-30
## 1 US 609529 1.78 298 212 135 331 292 274
## 2 Brazil 544180 2.80 1424 542 948 1556 1648 761
## --------------------------------------------------------------------------------
## --------------------------------------------------------------------------------
## ================================================================================
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------
## ################################################################################
## ##### TS-RECOVERED Cases -- Data dated: 2021-07-20 :: 2021-07-21 13:11:53
## ################################################################################
## Number of Countries/Regions reported: 195
## Number of Cities/Provinces reported: 72
## Unique number of distinct geographical locations combined: 264
## --------------------------------------------------------------------------------
## Worldwide ts-recovered Totals: 126000293
## --------------------------------------------------------------------------------
## Country.Region Province.State Totals LastDayChange t-2 t-3 t-7 t-14 t-30
## 1 India 30390687 36977 45254 38660 39191 44291 81839
## 2 Brazil 17371065 51736 14515 50485 91402 23386 74301
## --------------------------------------------------------------------------------
## --------------------------------------------------------------------------------
## ================================================================================
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## ############################################################################################################################################
## ##### AGGREGATED Data -- ORDERED BY CONFIRMED Cases -- Data dated: 2021-07-21 :: 2021-07-21 13:11:53
## ############################################################################################################################################
## Number of Countries/Regions reported: 195
## Number of Cities/Provinces reported: 576
## Unique number of distinct geographical locations combined: 3982
## --------------------------------------------------------------------------------------------------------------------------------------------
## Location Confirmed Perc.Confirmed Deaths Perc.Deaths Recovered Perc.Recovered Active Perc.Active
## 1 Maharashtra, India 6229596 3.25 130753 2.1 6000911 96.33 97932 1.57
## 2 France 5814442 3.04 110548 1.9 340769 5.86 5363125 92.24
## ============================================================================================================================================## ############################################################################################################################################
## ##### AGGREGATED Data -- ORDERED BY DEATHS Cases -- Data dated: 2021-07-21 :: 2021-07-21 13:11:53
## ############################################################################################################################################
## Number of Countries/Regions reported: 195
## Number of Cities/Provinces reported: 576
## Unique number of distinct geographical locations combined: 3982
## --------------------------------------------------------------------------------------------------------------------------------------------
## Location Confirmed Perc.Confirmed Deaths Perc.Deaths Recovered Perc.Recovered Active Perc.Active
## 1 Sao Paulo, Brazil 3947574 2.06 135490 3.43 3608391 91.41 203693 5.16
## 2 Maharashtra, India 6229596 3.25 130753 2.10 6000911 96.33 97932 1.57
## ============================================================================================================================================## ############################################################################################################################################
## ##### AGGREGATED Data -- ORDERED BY RECOVERED Cases -- Data dated: 2021-07-21 :: 2021-07-21 13:11:53
## ############################################################################################################################################
## Number of Countries/Regions reported: 195
## Number of Cities/Provinces reported: 576
## Unique number of distinct geographical locations combined: 3982
## --------------------------------------------------------------------------------------------------------------------------------------------
## Location Confirmed Perc.Confirmed Deaths Perc.Deaths Recovered Perc.Recovered Active Perc.Active
## 1 Maharashtra, India 6229596 3.25 130753 2.10 6000911 96.33 97932 1.57
## 2 Turkey 5546166 2.90 50650 0.91 5395300 97.28 100216 1.81
## ============================================================================================================================================## ############################################################################################################################################
## ##### AGGREGATED Data -- ORDERED BY ACTIVE Cases -- Data dated: 2021-07-21 :: 2021-07-21 13:11:53
## ############################################################################################################################################
## Number of Countries/Regions reported: 195
## Number of Cities/Provinces reported: 576
## Unique number of distinct geographical locations combined: 3982
## --------------------------------------------------------------------------------------------------------------------------------------------
## Location Confirmed Perc.Confirmed Deaths Perc.Deaths Recovered Perc.Recovered Active Perc.Active
## 1 France 5814442 3.04 110548 1.90 340769 5.86 5363125 92.24
## 2 England, United Kingdom 4812460 2.51 113257 2.35 0 0.00 4699203 97.65
## ============================================================================================================================================
## Confirmed Deaths Recovered Active
## Totals
## 191408767 4092735 NA NA
## Average
## 48068.5 1027.81 NA NA
## Standard Deviation
## 270133.08 5938.14 NA NA
##
##
## * Statistical estimators computed considering 3982 independent reported entries
##
##
## ********************************************************************************
## ******************************** OVERALL SUMMARY********************************
## ********************************************************************************
## **** Time Series Worldwide TOTS ****
## ts-confirmed ts-deaths ts-recovered
## 191445502 4118391 126000293
## 2.15% 65.82%
## **** Time Series Worldwide AVGS ****
## ts-confirmed ts-deaths ts-recovered
## 686184.59 14761.26 477273.84
## 2.15% 69.55%
## **** Time Series Worldwide SDS ****
## ts-confirmed ts-deaths ts-recovered
## 3115192.63 60694.51 2270930.13
## 1.95% 72.9%
##
##
## * Statistical estimators computed considering 279/279/264 independent reported entries per case-type
## ********************************************************************************Totals Per Location
## US -- 34174774
## =============================== running models...===============================
## Linear Regression (lm):
##
## Call:
## lm(formula = y.var ~ x.var)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5990105 -3116262 213501 3201255 7360408
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7439822 303987 -24.47 <2e-16 ***
## x.var 79415 963 82.47 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3547000 on 544 degrees of freedom
## Multiple R-squared: 0.9259, Adjusted R-squared: 0.9258
## F-statistic: 6801 on 1 and 544 DF, p-value: < 2.2e-16
##
## --------------------------------------------------------------------------------
## Linear Regression (lm):
##
## Call:
## lm(formula = y.var ~ x.var)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.6520 -1.1534 0.8149 2.0636 2.6528
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.3060148 0.2268352 41.02 <2e-16 ***
## x.var 0.0195857 0.0007186 27.26 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.647 on 544 degrees of freedom
## Multiple R-squared: 0.5773, Adjusted R-squared: 0.5765
## F-statistic: 742.9 on 1 and 544 DF, p-value: < 2.2e-16
##
## --------------------------------------------------------------------------------
## GLM using Family [1] "poisson" :
##
## Call:
## glm(formula = y.var ~ x.var, family = family)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2821.7 -1166.4 -112.2 651.9 2053.0
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.414e+01 4.075e-05 346928 <2e-16 ***
## x.var 6.697e-03 9.509e-08 70433 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 7419718377 on 545 degrees of freedom
## Residual deviance: 875882190 on 544 degrees of freedom
## AIC: 875891199
##
## Number of Fisher Scoring iterations: 5
##
## --------------------------------------------------------------------------------
## GLM using Family Family: Gamma Link function: log :
##
## Call:
## glm(formula = y.var ~ x.var, family = family)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -4.8286 -0.6150 0.2612 0.3732 0.6383
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.264e+01 4.751e-02 265.94 <2e-16 ***
## x.var 1.106e-02 1.505e-04 73.51 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Gamma family taken to be 0.3072904)
##
## Null deviance: 1989.1 on 545 degrees of freedom
## Residual deviance: 1101.4 on 544 degrees of freedom
## AIC: 18108
##
## Number of Fisher Scoring iterations: 17
##
## --------------------------------------------------------------------------------
## INDIA -- 31216337
## =============================== running models...===============================
## Linear Regression (lm):
##
## Call:
## lm(formula = y.var ~ x.var)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5375050 -2553630 -1322091 2657408 7991868
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6093658 329481 -18.50 <2e-16 ***
## x.var 54337 1044 52.06 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3844000 on 544 degrees of freedom
## Multiple R-squared: 0.8328, Adjusted R-squared: 0.8325
## F-statistic: 2710 on 1 and 544 DF, p-value: < 2.2e-16
##
## --------------------------------------------------------------------------------
## Linear Regression (lm):
##
## Call:
## lm(formula = y.var ~ x.var)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9626 -1.5168 0.5826 2.3127 2.9084
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.7658180 0.2236107 30.26 <2e-16 ***
## x.var 0.0246034 0.0007084 34.73 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.609 on 544 degrees of freedom
## Multiple R-squared: 0.6892, Adjusted R-squared: 0.6886
## F-statistic: 1206 on 1 and 544 DF, p-value: < 2.2e-16
##
## --------------------------------------------------------------------------------
## GLM using Family [1] "poisson" :
##
## Call:
## glm(formula = y.var ~ x.var, family = family)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1390.6 -1103.7 -379.6 518.7 1405.9
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.314e+01 5.845e-05 224814 <2e-16 ***
## x.var 7.912e-03 1.325e-07 59720 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 5632832606 on 545 degrees of freedom
## Residual deviance: 512291033 on 544 degrees of freedom
## AIC: 512299385
##
## Number of Fisher Scoring iterations: 5
##
## --------------------------------------------------------------------------------
Growth Rate
## Processing... US
## $Changes
## geo.loc 2020-01-23 2020-01-24 2020-01-25 2020-01-26 2020-01-27 2020-01-28
## 1 US 0 1 0 3 0 0
## 2020-01-29 2020-01-30 2020-01-31 2020-02-01 2020-02-02 2020-02-03 2020-02-04
## 1 1 0 2 0 0 3 0
## 2020-02-05 2020-02-06 2020-02-07 2020-02-08 2020-02-09 2020-02-10 2020-02-11
## 1 0 1 0 0 0 0 1
## 2020-02-12 2020-02-13 2020-02-14 2020-02-15 2020-02-16 2020-02-17 2020-02-18
## 1 0 1 0 0 0 0 0
## 2020-02-19 2020-02-20 2020-02-21 2020-02-22 2020-02-23 2020-02-24 2020-02-25
## 1 0 0 2 0 0 0 0
## 2020-02-26 2020-02-27 2020-02-28 2020-02-29 2020-03-01 2020-03-02 2020-03-03
## 1 0 1 0 8 7 23 19
## 2020-03-04 2020-03-05 2020-03-06 2020-03-07 2020-03-08 2020-03-09 2020-03-10
## 1 33 77 53 166 116 75 188
## 2020-03-11 2020-03-12 2020-03-13 2020-03-14 2020-03-15 2020-03-16 2020-03-17
## 1 365 439 633 759 234 1467 1833
## 2020-03-18 2020-03-19 2020-03-20 2020-03-21 2020-03-22 2020-03-23 2020-03-24
## 1 2657 4494 6367 5995 8873 11238 10619
## 2020-03-25 2020-03-26 2020-03-27 2020-03-28 2020-03-29 2020-03-30 2020-03-31
## 1 12082 17856 18690 19630 18899 22075 26314
## 2020-04-01 2020-04-02 2020-04-03 2020-04-04 2020-04-05 2020-04-06 2020-04-07
## 1 32286 32222 32307 32386 29895 31390 30779
## 2020-04-08 2020-04-09 2020-04-10 2020-04-11 2020-04-12 2020-04-13 2020-04-14
## 1 31235 35942 34403 29083 27256 26939 28818
## 2020-04-15 2020-04-16 2020-04-17 2020-04-18 2020-04-19 2020-04-20 2020-04-21
## 1 25408 30002 33066 27907 26062 29820 25926
## 2020-04-22 2020-04-23 2020-04-24 2020-04-25 2020-04-26 2020-04-27 2020-04-28
## 1 28911 33612 32327 30380 26488 23715 24575
## 2020-04-29 2020-04-30 2020-05-01 2020-05-02 2020-05-03 2020-05-04 2020-05-05
## 1 26459 29205 34907 27348 24321 24068 24528
## 2020-05-06 2020-05-07 2020-05-08 2020-05-09 2020-05-10 2020-05-11 2020-05-12
## 1 24569 27429 26830 25176 18805 19298 22927
## 2020-05-13 2020-05-14 2020-05-15 2020-05-16 2020-05-17 2020-05-18 2020-05-19
## 1 20433 26817 24733 24135 18388 22389 20979
## 2020-05-20 2020-05-21 2020-05-22 2020-05-23 2020-05-24 2020-05-25 2020-05-26
## 1 22725 25769 23649 21099 20077 18662 19663
## 2020-05-27 2020-05-28 2020-05-29 2020-05-30 2020-05-31 2020-06-01 2020-06-02
## 1 18551 22320 24478 23632 18983 17414 21502
## 2020-06-03 2020-06-04 2020-06-05 2020-06-06 2020-06-07 2020-06-08 2020-06-09
## 1 19857 21658 25403 21142 17928 17616 18383
## 2020-06-10 2020-06-11 2020-06-12 2020-06-13 2020-06-14 2020-06-15 2020-06-16
## 1 21111 23166 24828 25212 18941 19827 23667
## 2020-06-17 2020-06-18 2020-06-19 2020-06-20 2020-06-21 2020-06-22 2020-06-23
## 1 27072 28537 31544 32280 25150 32144 37072
## 2020-06-24 2020-06-25 2020-06-26 2020-06-27 2020-06-28 2020-06-29 2020-06-30
## 1 35878 40326 45999 41330 40734 41299 46420
## 2020-07-01 2020-07-02 2020-07-03 2020-07-04 2020-07-05 2020-07-06 2020-07-07
## 1 51820 56636 51351 45693 50747 43106 60661
## 2020-07-08 2020-07-09 2020-07-10 2020-07-11 2020-07-12 2020-07-13 2020-07-14
## 1 60119 62509 68057 60017 58424 58930 68051
## 2020-07-15 2020-07-16 2020-07-17 2020-07-18 2020-07-19 2020-07-20 2020-07-21
## 1 68090 75866 72236 62536 60456 62107 64461
## 2020-07-22 2020-07-23 2020-07-24 2020-07-25 2020-07-26 2020-07-27 2020-07-28
## 1 70579 68445 73319 64953 54816 56783 66412
## 2020-07-29 2020-07-30 2020-07-31 2020-08-01 2020-08-02 2020-08-03 2020-08-04
## 1 71873 67466 68712 56201 45568 45501 58774
## 2020-08-05 2020-08-06 2020-08-07 2020-08-08 2020-08-09 2020-08-10 2020-08-11
## 1 54466 59349 59303 54134 45769 47606 48003
## 2020-08-12 2020-08-13 2020-08-14 2020-08-15 2020-08-16 2020-08-17 2020-08-18
## 1 56040 51316 65336 46951 39212 36652 45033
## 2020-08-19 2020-08-20 2020-08-21 2020-08-22 2020-08-23 2020-08-24 2020-08-25
## 1 47320 44041 48843 43064 34247 36482 40354
## 2020-08-26 2020-08-27 2020-08-28 2020-08-29 2020-08-30 2020-08-31 2020-09-01
## 1 45172 45393 46832 42754 34404 35362 41846
## 2020-09-02 2020-09-03 2020-09-04 2020-09-05 2020-09-06 2020-09-07 2020-09-08
## 1 41018 44251 50382 43158 31218 23613 27226
## 2020-09-09 2020-09-10 2020-09-11 2020-09-12 2020-09-13 2020-09-14 2020-09-15
## 1 34049 36056 47769 41101 34372 34423 39492
## 2020-09-16 2020-09-17 2020-09-18 2020-09-19 2020-09-20 2020-09-21 2020-09-22
## 1 39030 45130 49282 42202 38447 51878 39866
## 2020-09-23 2020-09-24 2020-09-25 2020-09-26 2020-09-27 2020-09-28 2020-09-29
## 1 39069 47103 48295 44673 37528 33294 43338
## 2020-09-30 2020-10-01 2020-10-02 2020-10-03 2020-10-04 2020-10-05 2020-10-06
## 1 39443 45650 54950 48577 35738 39376 45289
## 2020-10-07 2020-10-08 2020-10-09 2020-10-10 2020-10-11 2020-10-12 2020-10-13
## 1 51056 58599 56384 54953 45981 41774 52231
## 2020-10-14 2020-10-15 2020-10-16 2020-10-17 2020-10-18 2020-10-19 2020-10-20
## 1 59778 64880 69147 56759 49367 67717 61956
## 2020-10-21 2020-10-22 2020-10-23 2020-10-24 2020-10-25 2020-10-26 2020-10-27
## 1 63301 76310 81933 82767 62204 67310 76838
## 2020-10-28 2020-10-29 2020-10-30 2020-10-31 2020-11-01 2020-11-02 2020-11-03
## 1 79426 91019 99264 89754 104900 85211 127198
## 2020-11-04 2020-11-05 2020-11-06 2020-11-07 2020-11-08 2020-11-09 2020-11-10
## 1 104541 129367 128033 127510 115170 120434 140504
## 2020-11-11 2020-11-12 2020-11-13 2020-11-14 2020-11-15 2020-11-16 2020-11-17
## 1 146750 164750 180398 167926 136356 162624 163958
## 2020-11-18 2020-11-19 2020-11-20 2020-11-21 2020-11-22 2020-11-23 2020-11-24
## 1 173251 191510 198333 179436 146947 174089 175544
## 2020-11-25 2020-11-26 2020-11-27 2020-11-28 2020-11-29 2020-11-30 2020-12-01
## 1 183403 112526 207933 155661 140328 160321 188339
## 2020-12-02 2020-12-03 2020-12-04 2020-12-05 2020-12-06 2020-12-07 2020-12-08
## 1 202894 223421 232644 215811 181253 194409 224452
## 2020-12-09 2020-12-10 2020-12-11 2020-12-12 2020-12-13 2020-12-14 2020-12-15
## 1 222648 231428 240089 217797 187971 194314 208992
## 2020-12-16 2020-12-17 2020-12-18 2020-12-19 2020-12-20 2020-12-21 2020-12-22
## 1 246644 239900 251832 192102 188015 198703 198107
## 2020-12-23 2020-12-24 2020-12-25 2020-12-26 2020-12-27 2020-12-28 2020-12-29
## 1 229624 194155 97880 226416 155845 174152 200408
## 2020-12-30 2020-12-31 2021-01-01 2021-01-02 2021-01-03 2021-01-04 2021-01-05
## 1 233701 235600 153916 300462 208853 184005 235042
## 2021-01-06 2021-01-07 2021-01-08 2021-01-09 2021-01-10 2021-01-11 2021-01-12
## 1 255637 278337 295257 260967 213415 214664 226967
## 2021-01-13 2021-01-14 2021-01-15 2021-01-16 2021-01-17 2021-01-18 2021-01-19
## 1 230301 235766 242780 201858 177931 143598 176216
## 2021-01-20 2021-01-21 2021-01-22 2021-01-23 2021-01-24 2021-01-25 2021-01-26
## 1 183261 193856 190760 170759 131198 151677 147626
## 2021-01-27 2021-01-28 2021-01-29 2021-01-30 2021-01-31 2021-02-01 2021-02-02
## 1 153961 168804 166613 142459 112152 134975 115303
## 2021-02-03 2021-02-04 2021-02-05 2021-02-06 2021-02-07 2021-02-08 2021-02-09
## 1 121691 124006 134422 104176 89746 90438 95265
## 2021-02-10 2021-02-11 2021-02-12 2021-02-13 2021-02-14 2021-02-15 2021-02-16
## 1 95250 105764 99670 87219 65135 54279 62498
## 2021-02-17 2021-02-18 2021-02-19 2021-02-20 2021-02-21 2021-02-22 2021-02-23
## 1 70139 69911 79282 71696 57152 56159 72270
## 2021-02-24 2021-02-25 2021-02-26 2021-02-27 2021-02-28 2021-03-01 2021-03-02
## 1 74749 77504 77349 64626 51422 58098 57098
## 2021-03-03 2021-03-04 2021-03-05 2021-03-06 2021-03-07 2021-03-08 2021-03-09
## 1 67191 68060 66419 58254 41073 44917 57667
## 2021-03-10 2021-03-11 2021-03-12 2021-03-13 2021-03-14 2021-03-15 2021-03-16
## 1 57895 62471 61513 53031 38278 56541 54008
## 2021-03-17 2021-03-18 2021-03-19 2021-03-20 2021-03-21 2021-03-22 2021-03-23
## 1 59280 60375 61651 55519 33822 51436 53688
## 2021-03-24 2021-03-25 2021-03-26 2021-03-27 2021-03-28 2021-03-29 2021-03-30
## 1 86938 67546 77377 62842 43223 69273 61429
## 2021-03-31 2021-04-01 2021-04-02 2021-04-03 2021-04-04 2021-04-05 2021-04-06
## 1 66765 79119 69887 63261 35133 77404 60674
## 2021-04-07 2021-04-08 2021-04-09 2021-04-10 2021-04-11 2021-04-12 2021-04-13
## 1 75021 79894 82710 66687 46509 70075 77966
## 2021-04-14 2021-04-15 2021-04-16 2021-04-17 2021-04-18 2021-04-19 2021-04-20
## 1 75403 74308 80071 52532 42121 68105 60949
## 2021-04-21 2021-04-22 2021-04-23 2021-04-24 2021-04-25 2021-04-26 2021-04-27
## 1 62855 67278 62411 53495 32153 47568 50836
## 2021-04-28 2021-04-29 2021-04-30 2021-05-01 2021-05-02 2021-05-03 2021-05-04
## 1 55150 58251 57919 45391 29403 50491 40723
## 2021-05-05 2021-05-06 2021-05-07 2021-05-08 2021-05-09 2021-05-10 2021-05-11
## 1 44704 47557 48130 33675 21427 36798 33662
## 2021-05-12 2021-05-13 2021-05-14 2021-05-15 2021-05-16 2021-05-17 2021-05-18
## 1 35826 38076 42260 28857 16875 28621 27789
## 2021-05-19 2021-05-20 2021-05-21 2021-05-22 2021-05-23 2021-05-24 2021-05-25
## 1 29301 30206 27946 19798 12868 25815 22739
## 2021-05-26 2021-05-27 2021-05-28 2021-05-29 2021-05-30 2021-05-31 2021-06-01
## 1 23976 27448 21859 12001 6734 5775 22940
## 2021-06-02 2021-06-03 2021-06-04 2021-06-05 2021-06-06 2021-06-07 2021-06-08
## 1 16917 19080 16850 13906 5395 15496 13013
## 2021-06-09 2021-06-10 2021-06-11 2021-06-12 2021-06-13 2021-06-14 2021-06-15
## 1 18647 14545 24699 8228 4777 12730 11305
## 2021-06-16 2021-06-17 2021-06-18 2021-06-19 2021-06-20 2021-06-21 2021-06-22
## 1 12425 10393 20591 8520 3892 12334 10940
## 2021-06-23 2021-06-24 2021-06-25 2021-06-26 2021-06-27 2021-06-28 2021-06-29
## 1 12436 12830 23715 7303 3920 15083 11350
## 2021-06-30 2021-07-01 2021-07-02 2021-07-03 2021-07-04 2021-07-05 2021-07-06
## 1 13118 14463 29892 4739 3697 5528 24224
## 2021-07-07 2021-07-08 2021-07-09 2021-07-10 2021-07-11 2021-07-12 2021-07-13
## 1 22931 20061 48241 9038 6164 35013 26424
## 2021-07-14 2021-07-15 2021-07-16 2021-07-17 2021-07-18 2021-07-19 2021-07-20
## 1 31845 28412 79310 12960 12048 52111 42703
##
## $Growth.Rate
## geo.loc 2020-01-24 2020-01-25 2020-01-26 2020-01-27 2020-01-28 2020-01-29
## 1 US NA 0 NA 0 NaN NA
## 2020-01-30 2020-01-31 2020-02-01 2020-02-02 2020-02-03 2020-02-04 2020-02-05
## 1 0 NA 0 NaN NA 0 NaN
## 2020-02-06 2020-02-07 2020-02-08 2020-02-09 2020-02-10 2020-02-11 2020-02-12
## 1 NA 0 NaN NaN NaN NA 0
## 2020-02-13 2020-02-14 2020-02-15 2020-02-16 2020-02-17 2020-02-18 2020-02-19
## 1 NA 0 NaN NaN NaN NaN NaN
## 2020-02-20 2020-02-21 2020-02-22 2020-02-23 2020-02-24 2020-02-25 2020-02-26
## 1 NaN NA 0 NaN NaN NaN NaN
## 2020-02-27 2020-02-28 2020-02-29 2020-03-01 2020-03-02 2020-03-03 2020-03-04
## 1 NA 0 NA 0.875 3.285714 0.826087 1.736842
## 2020-03-05 2020-03-06 2020-03-07 2020-03-08 2020-03-09 2020-03-10 2020-03-11
## 1 2.333333 0.6883117 3.132075 0.6987952 0.6465517 2.506667 1.941489
## 2020-03-12 2020-03-13 2020-03-14 2020-03-15 2020-03-16 2020-03-17 2020-03-18
## 1 1.20274 1.441913 1.199052 0.3083004 6.269231 1.249489 1.449536
## 2020-03-19 2020-03-20 2020-03-21 2020-03-22 2020-03-23 2020-03-24 2020-03-25
## 1 1.691381 1.416778 0.9415737 1.480067 1.266539 0.944919 1.137772
## 2020-03-26 2020-03-27 2020-03-28 2020-03-29 2020-03-30 2020-03-31 2020-04-01
## 1 1.477901 1.046707 1.050294 0.9627611 1.168051 1.192027 1.226951
## 2020-04-02 2020-04-03 2020-04-04 2020-04-05 2020-04-06 2020-04-07 2020-04-08
## 1 0.9980177 1.002638 1.002445 0.923084 1.050008 0.9805352 1.014815
## 2020-04-09 2020-04-10 2020-04-11 2020-04-12 2020-04-13 2020-04-14 2020-04-15
## 1 1.150696 0.957181 0.8453623 0.9371798 0.9883695 1.06975 0.8816712
## 2020-04-16 2020-04-17 2020-04-18 2020-04-19 2020-04-20 2020-04-21 2020-04-22
## 1 1.180809 1.102127 0.8439787 0.9338876 1.144195 0.8694165 1.115135
## 2020-04-23 2020-04-24 2020-04-25 2020-04-26 2020-04-27 2020-04-28 2020-04-29
## 1 1.162602 0.9617696 0.9397717 0.8718894 0.8953111 1.036264 1.076663
## 2020-04-30 2020-05-01 2020-05-02 2020-05-03 2020-05-04 2020-05-05 2020-05-06
## 1 1.103783 1.195241 0.7834532 0.8893155 0.9895975 1.019113 1.001672
## 2020-05-07 2020-05-08 2020-05-09 2020-05-10 2020-05-11 2020-05-12 2020-05-13
## 1 1.116407 0.9781618 0.9383526 0.7469415 1.026216 1.188051 0.89122
## 2020-05-14 2020-05-15 2020-05-16 2020-05-17 2020-05-18 2020-05-19 2020-05-20
## 1 1.312436 0.9222881 0.9758218 0.7618811 1.217588 0.9370226 1.083226
## 2020-05-21 2020-05-22 2020-05-23 2020-05-24 2020-05-25 2020-05-26 2020-05-27
## 1 1.133949 0.9177306 0.892173 0.9515617 0.9295213 1.053638 0.9434471
## 2020-05-28 2020-05-29 2020-05-30 2020-05-31 2020-06-01 2020-06-02 2020-06-03
## 1 1.20317 1.096685 0.9654384 0.8032752 0.9173471 1.234754 0.9234955
## 2020-06-04 2020-06-05 2020-06-06 2020-06-07 2020-06-08 2020-06-09 2020-06-10
## 1 1.090698 1.172915 0.8322639 0.8479803 0.9825971 1.04354 1.148398
## 2020-06-11 2020-06-12 2020-06-13 2020-06-14 2020-06-15 2020-06-16 2020-06-17
## 1 1.097343 1.071743 1.015466 0.7512692 1.046777 1.193675 1.143871
## 2020-06-18 2020-06-19 2020-06-20 2020-06-21 2020-06-22 2020-06-23 2020-06-24
## 1 1.054115 1.105372 1.023332 0.7791202 1.278091 1.15331 0.9677924
## 2020-06-25 2020-06-26 2020-06-27 2020-06-28 2020-06-29 2020-06-30 2020-07-01
## 1 1.123976 1.140678 0.8984978 0.9855795 1.01387 1.123998 1.116329
## 2020-07-02 2020-07-03 2020-07-04 2020-07-05 2020-07-06 2020-07-07 2020-07-08
## 1 1.092937 0.9066848 0.8898171 1.110608 0.8494295 1.407252 0.9910651
## 2020-07-09 2020-07-10 2020-07-11 2020-07-12 2020-07-13 2020-07-14 2020-07-15
## 1 1.039754 1.088755 0.8818637 0.9734575 1.008661 1.154777 1.000573
## 2020-07-16 2020-07-17 2020-07-18 2020-07-19 2020-07-20 2020-07-21 2020-07-22
## 1 1.114202 0.9521525 0.8657179 0.9667392 1.027309 1.037902 1.09491
## 2020-07-23 2020-07-24 2020-07-25 2020-07-26 2020-07-27 2020-07-28 2020-07-29
## 1 0.9697644 1.07121 0.8858959 0.8439333 1.035884 1.169575 1.082229
## 2020-07-30 2020-07-31 2020-08-01 2020-08-02 2020-08-03 2020-08-04 2020-08-05
## 1 0.9386835 1.018469 0.8179212 0.8108041 0.9985297 1.291708 0.9267023
## 2020-08-06 2020-08-07 2020-08-08 2020-08-09 2020-08-10 2020-08-11 2020-08-12
## 1 1.089652 0.9992249 0.9128375 0.845476 1.040136 1.008339 1.167427
## 2020-08-13 2020-08-14 2020-08-15 2020-08-16 2020-08-17 2020-08-18 2020-08-19
## 1 0.9157031 1.273209 0.7186084 0.8351686 0.9347139 1.228664 1.050785
## 2020-08-20 2020-08-21 2020-08-22 2020-08-23 2020-08-24 2020-08-25 2020-08-26
## 1 0.9307058 1.109035 0.8816821 0.7952582 1.065261 1.106135 1.119393
## 2020-08-27 2020-08-28 2020-08-29 2020-08-30 2020-08-31 2020-09-01 2020-09-02
## 1 1.004892 1.031701 0.9129228 0.8046966 1.027846 1.183361 0.9802132
## 2020-09-03 2020-09-04 2020-09-05 2020-09-06 2020-09-07 2020-09-08 2020-09-09
## 1 1.078819 1.138551 0.8566155 0.7233421 0.7563905 1.153009 1.250606
## 2020-09-10 2020-09-11 2020-09-12 2020-09-13 2020-09-14 2020-09-15 2020-09-16
## 1 1.058944 1.324856 0.8604116 0.8362814 1.001484 1.147256 0.9883014
## 2020-09-17 2020-09-18 2020-09-19 2020-09-20 2020-09-21 2020-09-22 2020-09-23
## 1 1.15629 1.092001 0.856337 0.9110232 1.349338 0.7684568 0.980008
## 2020-09-24 2020-09-25 2020-09-26 2020-09-27 2020-09-28 2020-09-29 2020-09-30
## 1 1.205636 1.025306 0.9250026 0.84006 0.8871776 1.301676 0.9101251
## 2020-10-01 2020-10-02 2020-10-03 2020-10-04 2020-10-05 2020-10-06 2020-10-07
## 1 1.157366 1.203724 0.8840218 0.735698 1.101796 1.150168 1.127338
## 2020-10-08 2020-10-09 2020-10-10 2020-10-11 2020-10-12 2020-10-13 2020-10-14
## 1 1.14774 0.9622007 0.9746205 0.8367332 0.9085057 1.250323 1.144493
## 2020-10-15 2020-10-16 2020-10-17 2020-10-18 2020-10-19 2020-10-20 2020-10-21
## 1 1.085349 1.065768 0.8208454 0.8697651 1.371706 0.9149254 1.021709
## 2020-10-22 2020-10-23 2020-10-24 2020-10-25 2020-10-26 2020-10-27 2020-10-28
## 1 1.20551 1.073686 1.010179 0.7515556 1.082085 1.141554 1.033681
## 2020-10-29 2020-10-30 2020-10-31 2020-11-01 2020-11-02 2020-11-03 2020-11-04
## 1 1.14596 1.090585 0.9041949 1.16875 0.812307 1.492742 0.8218761
## 2020-11-05 2020-11-06 2020-11-07 2020-11-08 2020-11-09 2020-11-10 2020-11-11
## 1 1.237476 0.9896883 0.9959151 0.9032233 1.045706 1.166647 1.044454
## 2020-11-12 2020-11-13 2020-11-14 2020-11-15 2020-11-16 2020-11-17 2020-11-18
## 1 1.122658 1.09498 0.930864 0.8120005 1.192643 1.008203 1.056679
## 2020-11-19 2020-11-20 2020-11-21 2020-11-22 2020-11-23 2020-11-24 2020-11-25
## 1 1.10539 1.035627 0.9047208 0.8189382 1.184706 1.008358 1.044769
## 2020-11-26 2020-11-27 2020-11-28 2020-11-29 2020-11-30 2020-12-01 2020-12-02
## 1 0.613545 1.847866 0.7486113 0.9014975 1.142473 1.174762 1.077281
## 2020-12-03 2020-12-04 2020-12-05 2020-12-06 2020-12-07 2020-12-08 2020-12-09
## 1 1.101171 1.041281 0.9276448 0.8398691 1.072584 1.154535 0.9919626
## 2020-12-10 2020-12-11 2020-12-12 2020-12-13 2020-12-14 2020-12-15 2020-12-16
## 1 1.039434 1.037424 0.9071511 0.863056 1.033745 1.075538 1.18016
## 2020-12-17 2020-12-18 2020-12-19 2020-12-20 2020-12-21 2020-12-22 2020-12-23
## 1 0.9726569 1.049737 0.7628181 0.9787248 1.056847 0.9970005 1.159091
## 2020-12-24 2020-12-25 2020-12-26 2020-12-27 2020-12-28 2020-12-29 2020-12-30
## 1 0.8455344 0.5041333 2.3132 0.6883127 1.117469 1.150765 1.166126
## 2020-12-31 2021-01-01 2021-01-02 2021-01-03 2021-01-04 2021-01-05 2021-01-06
## 1 1.008126 0.6532937 1.952117 0.6951062 0.8810264 1.277367 1.087623
## 2021-01-07 2021-01-08 2021-01-09 2021-01-10 2021-01-11 2021-01-12 2021-01-13
## 1 1.088798 1.06079 0.8838639 0.8177854 1.005852 1.057313 1.014689
## 2021-01-14 2021-01-15 2021-01-16 2021-01-17 2021-01-18 2021-01-19 2021-01-20
## 1 1.02373 1.02975 0.8314441 0.8814662 0.8070432 1.227148 1.039979
## 2021-01-21 2021-01-22 2021-01-23 2021-01-24 2021-01-25 2021-01-26 2021-01-27
## 1 1.057814 0.9840294 0.895151 0.7683226 1.156092 0.9732919 1.042912
## 2021-01-28 2021-01-29 2021-01-30 2021-01-31 2021-02-01 2021-02-02 2021-02-03
## 1 1.096408 0.9870204 0.8550293 0.7872581 1.203501 0.8542545 1.055402
## 2021-02-04 2021-02-05 2021-02-06 2021-02-07 2021-02-08 2021-02-09 2021-02-10
## 1 1.019024 1.083996 0.7749922 0.8614844 1.007711 1.053374 0.9998425
## 2021-02-11 2021-02-12 2021-02-13 2021-02-14 2021-02-15 2021-02-16 2021-02-17
## 1 1.110383 0.9423812 0.8750778 0.7467983 0.8333308 1.151421 1.12226
## 2021-02-18 2021-02-19 2021-02-20 2021-02-21 2021-02-22 2021-02-23 2021-02-24
## 1 0.9967493 1.134042 0.9043162 0.7971435 0.9826253 1.286882 1.034302
## 2021-02-25 2021-02-26 2021-02-27 2021-02-28 2021-03-01 2021-03-02 2021-03-03
## 1 1.036857 0.9980001 0.8355118 0.7956859 1.129828 0.9827877 1.176766
## 2021-03-04 2021-03-05 2021-03-06 2021-03-07 2021-03-08 2021-03-09 2021-03-10
## 1 1.012933 0.9758889 0.8770683 0.7050675 1.093589 1.283857 1.003954
## 2021-03-11 2021-03-12 2021-03-13 2021-03-14 2021-03-15 2021-03-16 2021-03-17
## 1 1.07904 0.9846649 0.8621104 0.7218042 1.477115 0.9552007 1.097615
## 2021-03-18 2021-03-19 2021-03-20 2021-03-21 2021-03-22 2021-03-23 2021-03-24
## 1 1.018472 1.021135 0.9005369 0.6091969 1.520785 1.043783 1.619319
## 2021-03-25 2021-03-26 2021-03-27 2021-03-28 2021-03-29 2021-03-30 2021-03-31
## 1 0.7769445 1.145545 0.8121535 0.6878043 1.602688 0.8867668 1.086865
## 2021-04-01 2021-04-02 2021-04-03 2021-04-04 2021-04-05 2021-04-06 2021-04-07
## 1 1.185037 0.883315 0.9051898 0.5553659 2.203171 0.7838613 1.23646
## 2021-04-08 2021-04-09 2021-04-10 2021-04-11 2021-04-12 2021-04-13 2021-04-14
## 1 1.064955 1.035247 0.8062749 0.6974223 1.506698 1.112608 0.9671267
## 2021-04-15 2021-04-16 2021-04-17 2021-04-18 2021-04-19 2021-04-20 2021-04-21
## 1 0.985478 1.077556 0.6560677 0.801816 1.616889 0.894927 1.031272
## 2021-04-22 2021-04-23 2021-04-24 2021-04-25 2021-04-26 2021-04-27 2021-04-28
## 1 1.070368 0.9276584 0.8571406 0.6010468 1.479426 1.068702 1.084861
## 2021-04-29 2021-04-30 2021-05-01 2021-05-02 2021-05-03 2021-05-04 2021-05-05
## 1 1.056228 0.9943005 0.7836979 0.6477716 1.717206 0.8065398 1.097758
## 2021-05-06 2021-05-07 2021-05-08 2021-05-09 2021-05-10 2021-05-11 2021-05-12
## 1 1.06382 1.012049 0.6996676 0.636288 1.717366 0.914778 1.064286
## 2021-05-13 2021-05-14 2021-05-15 2021-05-16 2021-05-17 2021-05-18 2021-05-19
## 1 1.062804 1.109885 0.6828443 0.5847801 1.696059 0.9709304 1.05441
## 2021-05-20 2021-05-21 2021-05-22 2021-05-23 2021-05-24 2021-05-25 2021-05-26
## 1 1.030886 0.9251804 0.7084377 0.6499646 2.006139 0.8808445 1.0544
## 2021-05-27 2021-05-28 2021-05-29 2021-05-30 2021-05-31 2021-06-01 2021-06-02
## 1 1.144811 0.7963786 0.5490187 0.5611199 0.8575884 3.972294 0.7374455
## 2021-06-03 2021-06-04 2021-06-05 2021-06-06 2021-06-07 2021-06-08 2021-06-09
## 1 1.12786 0.8831237 0.8252819 0.387962 2.872289 0.8397651 1.432952
## 2021-06-10 2021-06-11 2021-06-12 2021-06-13 2021-06-14 2021-06-15 2021-06-16
## 1 0.7800182 1.698109 0.3331309 0.5805785 2.664852 0.8880597 1.099071
## 2021-06-17 2021-06-18 2021-06-19 2021-06-20 2021-06-21 2021-06-22 2021-06-23
## 1 0.8364588 1.981237 0.413773 0.4568075 3.169065 0.8869791 1.136746
## 2021-06-24 2021-06-25 2021-06-26 2021-06-27 2021-06-28 2021-06-29 2021-06-30
## 1 1.031682 1.848402 0.3079486 0.5367657 3.847704 0.7525028 1.155771
## 2021-07-01 2021-07-02 2021-07-03 2021-07-04 2021-07-05 2021-07-06 2021-07-07
## 1 1.102531 2.066791 0.1585374 0.7801224 1.495266 4.382055 0.9466232
## 2021-07-08 2021-07-09 2021-07-10 2021-07-11 2021-07-12 2021-07-13 2021-07-14
## 1 0.8748419 2.404716 0.187351 0.6820093 5.68024 0.7546911 1.205154
## 2021-07-15 2021-07-16 2021-07-17 2021-07-18 2021-07-19 2021-07-20 NA
## 1 0.8921966 2.791426 0.1634094 0.9296296 4.325282 0.8194623 NATotals Plot
World Map
In a SIR Model, we assume the population consists of three types of individuals, whose numbers are denoted by the letters Susceptibles,Infected and Recovered. They are all functions of time and change according to a system of differential equations.
\(\gamma\) represents recovery rate.
\(\beta\) represents contact rate.
SIR US Model
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------## ################################################################################
## ################################################################################
## Processing... US
## [1] 1 1 2 2 5 5 5 6
## [9] 6 8 8 8 11 11 11 12
## [17] 12 12 12 12 13 13 14 14
## [25] 14 14 14 14 14 14 16 16
## [33] 16 16 16 16 17 17 25 32
## [41] 55 74 107 184 237 403 519 594
## [49] 782 1147 1586 2219 2978 3212 4679 6512
## [57] 9169 13663 20030 26025 34898 46136 56755 68837
## [65] 86693 105383 125013 143912 165987 192301 224587 256809
## [73] 289116 321502 351397 382787 413566 444801 480743 515146
## [81] 544229 571485 598424 627242 652650 682652 715718 743625
## [89] 769687 799507 825433 854344 887956 920283 950663 977151
## [97] 1000866 1025441 1051900 1081105 1116012 1143360 1167681 1191749
## [105] 1216277 1240846 1268275 1295105 1320281 1339086 1358384 1381311
## [113] 1401744 1428561 1453294 1477429 1495817 1518206 1539185 1561910
## [121] 1587679 1611328 1632427 1652504 1671166 1690829 1709380 1731700
## [129] 1756178 1779810 1798793 1816207 1837709 1857566 1879224 1904627
## [137] 1925769 1943697 1961313 1979696 2000807 2023973 2048801 2074013
## [145] 2092954 2112781 2136448 2163520 2192057 2223601 2255881 2281031
## [153] 2313175 2350247 2386125 2426451 2472450 2513780 2554514 2595813
## [161] 2642233 2694053 2750689 2802040 2847733 2898480 2941586 3002247
## [169] 3062366 3124875 3192932 3252949 3311373 3370303 3438354 3506444
## [177] 3582310 3654546 3717082 3777538 3839645 3904106 3974685 4043130
## [185] 4116449 4181402 4236218 4293001 4359413 4431286 4498752 4567464
## [193] 4623665 4669233 4714734 4773508 4827974 4887323 4946626 5000760
## [201] 5046529 5094135 5142138 5198178 5249494 5314830 5361781 5400993
## [209] 5437645 5482678 5529998 5574039 5622882 5665946 5700193 5736675
## [217] 5777029 5822201 5867594 5914426 5957180 5991584 6026946 6068792
## [225] 6109810 6154061 6204443 6247601 6278819 6302432 6329658 6363707
## [233] 6399763 6447532 6488633 6523005 6557428 6596920 6635950 6681080
## [241] 6730362 6772564 6811011 6862889 6902755 6941824 6988927 7037222
## [249] 7081895 7119423 7152717 7196055 7235498 7281148 7336098 7384675
## [257] 7420413 7459789 7505078 7556134 7614733 7671117 7726070 7772051
## [265] 7813825 7866056 7925834 7990714 8059861 8116620 8165987 8233704
## [273] 8295660 8358961 8435271 8517204 8599971 8662175 8729485 8806323
## [281] 8885749 8976768 9076032 9165786 9270686 9355897 9483095 9587636
## [289] 9717003 9845036 9972546 10087716 10208150 10348654 10495404 10660154
## [297] 10840552 11008478 11144834 11307458 11471416 11644667 11836177 12034510
## [305] 12213946 12360893 12534982 12710526 12893929 13006455 13214388 13370049
## [313] 13510377 13670698 13859037 14061931 14285352 14517996 14733807 14915060
## [321] 15109469 15333921 15556569 15787997 16028086 16245883 16433854 16628168
## [329] 16837160 17083804 17323704 17575536 17767638 17955653 18154356 18352463
## [337] 18582087 18776242 18874122 19100538 19256383 19430535 19630943 19864644
## [345] 20100244 20254160 20554622 20763475 20947480 21182522 21438159 21716496
## [353] 22011753 22272720 22486135 22700799 22927766 23158067 23393833 23636613
## [361] 23838471 24016402 24160000 24336216 24519477 24713333 24904093 25074852
## [369] 25206050 25357727 25505353 25659314 25828118 25994731 26137190 26249342
## [377] 26384317 26499620 26621311 26745317 26879739 26983915 27073661 27164099
## [385] 27259364 27354614 27460378 27560048 27647267 27712402 27766681 27829179
## [393] 27899318 27969229 28048511 28120207 28177359 28233518 28305788 28380537
## [401] 28458041 28535390 28600016 28651438 28709536 28766634 28833825 28901885
## [409] 28968304 29026558 29067631 29112548 29170215 29228110 29290581 29352094
## [417] 29405125 29443403 29499944 29553952 29613232 29673607 29735258 29790777
## [425] 29824599 29876035 29929723 30016661 30084207 30161584 30224426 30267649
## [433] 30336922 30398351 30465116 30544235 30614122 30677383 30712516 30789920
## [441] 30850594 30925615 31005509 31088219 31154906 31201415 31271490 31349456
## [449] 31424859 31499167 31579238 31631770 31673891 31741996 31802945 31865800
## [457] 31933078 31995489 32048984 32081137 32128705 32179541 32234691 32292942
## [465] 32350861 32396252 32425655 32476146 32516869 32561573 32609130 32657260
## [473] 32690935 32712362 32749160 32782822 32818648 32856724 32898984 32927841
## [481] 32944716 32973337 33001126 33030427 33060633 33088579 33108377 33121245
## [489] 33147060 33169799 33193775 33221223 33243082 33255083 33261817 33267592
## [497] 33290532 33307449 33326529 33343379 33357285 33362680 33378176 33391189
## [505] 33409836 33424381 33449080 33457308 33462085 33474815 33486120 33498545
## [513] 33508938 33529529 33538049 33541941 33554275 33565215 33577651 33590481
## [521] 33614196 33621499 33625419 33640502 33651852 33664970 33679433 33709325
## [529] 33714064 33717761 33723289 33747513 33770444 33790505 33838746 33847784
## [537] 33853948 33888961 33915385 33947230 33975642 34054952 34067912 34079960
## [545] 34132071 34174774
## [1] 40
## [1] 32 55 74 107 184 237 403 519 594 782 1147 1586
## [13] 2219 2978 3212 4679 6512 9169 13663 20030 26025 34898 46136 56755
## [25] 68837 86693
## ------------------------ Parameters used to create model ------------------------
## Region: US
## Time interval to consider: t0=40 - t1= ; tfinal=90
## t0: 2020-03-02 -- t1:
## Number of days considered for initial guess: 26
## Fatality rate: 0.02
## Population of the region: 328200000
## --------------------------------------------------------------------------------
## [1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
## beta gamma
## 0.6601855 0.3398147
## R0 = 1.94278096379885
## Max nbr of infected: 47008795.32 ( 14.32 %)
## Max nbr of casualties, assuming 2% fatality rate: 940175.91
## Max reached at day : 51 ==> 2020-04-22
## ================================================================================
## $Infected
## [1] 32 55 74 107 184 237 403 519 594 782 1147 1586
## [13] 2219 2978 3212 4679 6512 9169 13663 20030 26025 34898 46136 56755
## [25] 68837 86693
##
## $model
## time S I R
## 1 1 328199968 3.200000e+01 0.000000e+00
## 2 2 328199943 4.408443e+01 1.281786e+01
## 3 3 328199909 6.073240e+01 3.047623e+01
## 4 4 328199862 8.366729e+01 5.480310e+01
## 5 5 328199796 1.152633e+02 8.831672e+01
## 6 6 328199707 1.587910e+02 1.344863e+02
## 7 7 328199583 2.187565e+02 1.980914e+02
## 8 8 328199413 3.013672e+02 2.857161e+02
## 9 9 328199178 4.151746e+02 4.064312e+02
## 10 10 328198855 5.719595e+02 5.727327e+02
## 11 11 328198410 7.879515e+02 8.018356e+02
## 12 12 328197797 1.085509e+03 1.117456e+03
## 13 13 328196952 1.495431e+03 1.552264e+03
## 14 14 328195789 2.060149e+03 2.151269e+03
## 15 15 328194185 2.838113e+03 2.976475e+03
## 16 16 328191977 3.909840e+03 4.113297e+03
## 17 17 328188934 5.386246e+03 5.679402e+03
## 18 18 328184743 7.420106e+03 7.836880e+03
## 19 19 328178969 1.022186e+04 1.080901e+04
## 20 20 328171015 1.408133e+04 1.490336e+04
## 21 21 328160059 1.939765e+04 2.054356e+04
## 22 22 328144966 2.672042e+04 2.831309e+04
## 23 23 328124178 3.680629e+04 3.901548e+04
## 24 24 328095546 5.069666e+04 5.375722e+04
## 25 25 328056114 6.982439e+04 7.406168e+04
## 26 26 328001814 9.615999e+04 1.020257e+05
## 27 27 327927054 1.324115e+05 1.405343e+05
## 28 28 327824147 1.822972e+05 1.935557e+05
## 29 29 327682540 2.509161e+05 2.665439e+05
## 30 30 327487763 3.452481e+05 3.669888e+05
## 31 31 327220011 4.748250e+05 5.051641e+05
## 32 32 326852241 6.526204e+05 6.951386e+05
## 33 33 326347656 8.962097e+05 9.561339e+05
## 34 34 325656418 1.229251e+06 1.314332e+06
## 35 35 324711459 1.683303e+06 1.805238e+06
## 36 36 323423339 2.299938e+06 2.476723e+06
## 37 37 321674255 3.132947e+06 3.392799e+06
## 38 38 319311726 4.250172e+06 4.638103e+06
## 39 39 316143157 5.734024e+06 6.322819e+06
## 40 40 311933603 7.679066e+06 8.587331e+06
## 41 41 306410575 1.018421e+07 1.160522e+07
## 42 42 299281276 1.333647e+07 1.558226e+07
## 43 43 290267992 1.718391e+07 2.074810e+07
## 44 44 279164700 2.169836e+07 2.733694e+07
## 45 45 265909706 2.673558e+07 3.555472e+07
## 46 46 250655886 3.200954e+07 4.553457e+07
## 47 47 233807861 3.710296e+07 5.728918e+07
## 48 48 215996458 4.152848e+07 7.067506e+07
## 49 49 197983597 4.483101e+07 8.538539e+07
## 50 50 180525770 4.669453e+07 1.009797e+08
## 51 51 164247149 4.700880e+07 1.169441e+08
## 52 52 149564873 4.587184e+07 1.327633e+08
## 53 53 136678453 4.353754e+07 1.479840e+08
## 54 54 125606698 4.033857e+07 1.622547e+08
## 55 55 116244643 3.661529e+07 1.753401e+08
## 56 56 108418547 3.266712e+07 1.871143e+08
## 57 57 101927999 2.872900e+07 1.975430e+08
## 58 58 96573158 2.496723e+07 2.066596e+08
## 59 59 92169761 2.148673e+07 2.145435e+08
## 60 60 88555668 1.834338e+07 2.213010e+08
## 61 61 85592320 1.555695e+07 2.270507e+08
## 62 62 83163471 1.312267e+07 2.319139e+08
## 63 63 81172729 1.102036e+07 2.360069e+08
## 64 64 79540720 9.221297e+06 2.394380e+08
## 65 65 78202362 7.692989e+06 2.423046e+08
## 66 66 77104401 6.402322e+06 2.446933e+08
## 67 67 76203309 5.317525e+06 2.466792e+08
## 68 68 75463514 4.409275e+06 2.483272e+08
## 69 69 74855937 3.651222e+06 2.496928e+08
## 70 70 74356798 3.020143e+06 2.508231e+08
## 71 71 73946632 2.495863e+06 2.517575e+08
## 72 72 73609503 2.061051e+06 2.525294e+08
## 73 73 73332351 1.700941e+06 2.531667e+08
## 74 74 73104467 1.403039e+06 2.536925e+08
## 75 75 72917066 1.156830e+06 2.541261e+08
## 76 76 72762939 9.534997e+05 2.544836e+08
## 77 77 72636165 7.856865e+05 2.547781e+08
## 78 78 72531881 6.472580e+05 2.550209e+08
## 79 79 72446091 5.331174e+05 2.552208e+08
## 80 80 72375511 4.390360e+05 2.553855e+08
## 81 81 72317442 3.615109e+05 2.555210e+08
## 82 82 72269665 2.976436e+05 2.556327e+08
## 83 83 72230354 2.450383e+05 2.557246e+08
## 84 84 72198007 2.017158e+05 2.558003e+08
## 85 85 72171392 1.660429e+05 2.558626e+08
## 86 86 72149491 1.366720e+05 2.559138e+08
## 87 87 72131469 1.124920e+05 2.559560e+08
## 88 88 72116639 9.258682e+04 2.559908e+08
## 89 89 72104436 7.620176e+04 2.560194e+08
## 90 90 72094394 6.271496e+04 2.560429e+08
##
## $params
## $params$beta
## beta
## 0.6601855
##
## $params$gamma
## gamma
## 0.3398147
##
## $params$R0
## R0
## 1.942781SIR India Model
## ################################################################################
## ################################################################################
## Processing... INDIA
## [1] 0 0 0 0 0 0 0 0
## [9] 1 1 1 2 3 3 3 3
## [17] 3 3 3 3 3 3 3 3
## [25] 3 3 3 3 3 3 3 3
## [33] 3 3 3 3 3 3 3 3
## [41] 5 5 28 30 31 34 39 43
## [49] 56 62 73 82 102 113 119 142
## [57] 156 194 244 330 396 499 536 657
## [65] 727 887 987 1024 1251 1397 1998 2543
## [73] 2567 3082 3588 4778 5311 5916 6725 7598
## [81] 8446 9205 10453 11487 12322 13430 14352 15722
## [89] 17615 18539 20080 21370 23077 24530 26283 27890
## [97] 29451 31324 33062 34863 37257 39699 42505 46437
## [105] 49400 52987 56351 59695 62808 67161 70768 74292
## [113] 78055 81997 85784 90648 95698 100328 106475 112028
## [121] 118226 124794 131423 138536 144950 150793 158086 165386
## [129] 173491 181827 190609 198370 207191 216824 226713 236184
## [137] 246622 257486 265928 276146 286605 297535 308993 320922
## [145] 332424 343091 354065 366946 380532 395048 410451 425282
## [153] 440215 456183 473105 490401 508953 528859 548318 566840
## [161] 585481 604641 625544 648315 673165 697413 719664 742417
## [169] 767296 793802 820916 849522 878254 906752 936181 968857
## [177] 1003832 1039084 1077781 1118206 1155338 1193078 1238798 1288108
## [185] 1337024 1385635 1435616 1480073 1531669 1581963 1634746 1695988
## [193] 1750723 1803695 1855745 1908254 1964536 2027074 2088611 2153010
## [201] 2215074 2268675 2329638 2396637 2461190 2525922 2589952 2647663
## [209] 2702681 2767253 2836925 2905825 2975701 3044940 3106348 3167323
## [217] 3224547 3310234 3387500 3463972 3542733 3621245 3691166 3769523
## [225] 3853406 3936747 4023179 4113811 4204613 4280422 4370128 4465863
## [233] 4562414 4659984 4754356 4846427 4930236 5020359 5118253 5214677
## [241] 5308014 5400619 5487580 5562663 5646010 5732518 5818570 5903932
## [249] 5992532 6074702 6145291 6225763 6312584 6394068 6473544 6549373
## [257] 6623815 6685082 6757131 6835655 6906151 6979423 7053806 7120538
## [265] 7175880 7239389 7307097 7370468 7432680 7494551 7550273 7597063
## [273] 7651107 7706946 7761312 7814682 7864811 7909959 7946429 7990322
## [281] 8040203 8088851 8137119 8184082 8229313 8267623 8313876 8364086
## [289] 8411724 8462080 8507754 8553657 8591730 8636011 8683916 8728795
## [297] 8773479 8814579 8845127 8874290 8912907 8958483 9004365 9050597
## [305] 9095806 9139865 9177840 9222216 9266705 9309787 9351109 9392919
## [313] 9431691 9462809 9499413 9534964 9571559 9608211 9644222 9677203
## [321] 9703770 9735850 9767371 9796744 9826775 9857029 9884100 9906165
## [329] 9932547 9956557 9979447 10004599 10031223 10055560 10075116 10099066
## [337] 10123778 10146845 10169118 10187850 10207871 10224303 10244852 10266674
## [345] 10286709 10325823 10323965 10340469 10356844 10374932 10395278 10413417
## [353] 10413417 10450284 10466595 10479179 10495147 10512093 10527683 10542841
## [361] 10557985 10571773 10581823 10595639 10610883 10625428 10639684 10654533
## [369] 10667736 10676838 10689527 10701193 10720048 10733130 10746174 10757610
## [377] 10766245 10777284 10790183 10802591 10814304 10826363 10838194 10847304
## [385] 10858371 10871294 10880603 10892746 10904940 10916589 10925710 10937320
## [393] 10950201 10963394 10977387 10991651 11005850 11016434 11030176 11046914
## [401] 11063491 11079979 11096731 11112241 11124527 11139516 11156923 11173761
## [409] 11192045 11210799 11229398 11244786 11262707 11285561 11308846 11333728
## [417] 11359048 11385339 11409831 11438734 11474605 11514331 11555284 11599130
## [425] 11646081 11686796 11734058 11787534 11846652 11908910 11971624 12039644
## [433] 12095855 12149335 12221665 12303131 12392260 12485509 12589067 12686049
## [441] 12801785 12928574 13060542 13205926 13358805 13527717 13689453 13873825
## [449] 14074564 14291917 14526609 14788003 15061805 15320972 15616130 15930774
## [457] 16263695 16610481 16960172 17313163 17636186 17997113 18376421 18762976
## [465] 19164969 19557457 19925517 20282833 20664979 21077410 21491598 21892676
## [473] 22296081 22662575 22992517 23340938 23703665 24046809 24372907 24684077
## [481] 24965463 25228996 25496330 25772440 26031991 26289290 26530132 26752447
## [489] 26948874 27157795 27369093 27555457 27729247 27894800 28047534 28175044
## [497] 28307832 28441986 28574350 28694879 28809339 28909975 28996473 29089069
## [505] 29182532 29274823 29359155 29439989 29510410 29570881 29633105 29700313
## [513] 29762793 29823546 29881772 29935221 29977861 30028709 30082778 30134445
## [521] 30183143 30233183 30279331 30316897 30362848 30411634 30458251 30502362
## [529] 30545433 30585229 30619932 30663665 30709557 30752950 30795716 30837222
## [537] 30874376 30907282 30946147 30987880 31026829 31064908 31106065 31144229
## [545] 31174322 31216337
## [1] 42
## [1] 5 28 30 31 34 39 43 56 62 73 82 102 113 119 142 156 194 244 330
## [20] 396 499 536 657 727 887 987
## ------------------------ Parameters used to create model ------------------------
## Region: INDIA
## Time interval to consider: t0=42 - t1= ; tfinal=90
## t0: 2020-03-04 -- t1:
## Number of days considered for initial guess: 26
## Fatality rate: 0.02
## Population of the region: 1.366e+09
## --------------------------------------------------------------------------------
## [1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
## beta gamma
## 0.6081878 0.3918122
## R0 = 1.55224335206386
## Max nbr of infected: 99036464.33 ( 7.25 %)
## Max nbr of casualties, assuming 2% fatality rate: 1980729.29
## Max reached at day : 86 ==> 2020-05-29
## ================================================================================
## $Infected
## [1] 5 28 30 31 34 39 43 56 62 73 82 102 113 119 142 156 194 244 330
## [20] 396 499 536 657 727 887 987
##
## $model
## time S I R
## 1 1 1365999995 5.000000e+00 0.000000e+00
## 2 2 1365999992 6.207843e+00 2.187158e+00
## 3 3 1365999987 7.707465e+00 4.902667e+00
## 4 4 1365999982 9.569347e+00 8.274155e+00
## 5 5 1365999976 1.188100e+01 1.246009e+01
## 6 6 1365999968 1.475108e+01 1.765722e+01
## 7 7 1365999958 1.831449e+01 2.410983e+01
## 8 8 1365999945 2.273870e+01 3.212116e+01
## 9 9 1365999930 2.823165e+01 4.206778e+01
## 10 10 1365999911 3.505154e+01 5.441721e+01
## 11 11 1365999887 4.351890e+01 6.974988e+01
## 12 12 1365999857 5.403171e+01 8.878643e+01
## 13 13 1365999820 6.708409e+01 1.124216e+02
## 14 14 1365999775 8.328951e+01 1.417664e+02
## 15 15 1365999718 1.034096e+02 1.781998e+02
## 16 16 1365999648 1.283902e+02 2.234345e+02
## 17 17 1365999561 1.594052e+02 2.795965e+02
## 18 18 1365999453 1.979125e+02 3.493254e+02
## 19 19 1365999318 2.457220e+02 4.358987e+02
## 20 20 1365999152 3.050807e+02 5.433853e+02
## 21 21 1365998944 3.787785e+02 6.768373e+02
## 22 22 1365998687 4.702793e+02 8.425271e+02
## 23 23 1365998368 5.838838e+02 1.048242e+03
## 24 24 1365997971 7.249314e+02 1.303652e+03
## 25 25 1365997479 9.000513e+02 1.620760e+03
## 26 26 1365996868 1.117474e+03 2.014470e+03
## 27 27 1365996109 1.387419e+03 2.503289e+03
## 28 28 1365995167 1.722573e+03 3.110190e+03
## 29 29 1365993998 2.138688e+03 3.863698e+03
## 30 30 1365992545 2.655321e+03 4.799227e+03
## 31 31 1365990743 3.296751e+03 5.960747e+03
## 32 32 1365988504 4.093125e+03 7.402848e+03
## 33 33 1365985725 5.081867e+03 9.193306e+03
## 34 34 1365982274 6.309444e+03 1.141627e+04
## 35 35 1365977990 7.833540e+03 1.417621e+04
## 36 36 1365972671 9.725773e+03 1.760283e+04
## 37 37 1365966068 1.207505e+04 2.185717e+04
## 38 38 1365957869 1.499176e+04 2.713913e+04
## 39 39 1365947690 1.861291e+04 3.369694e+04
## 40 40 1365935053 2.310861e+04 4.183871e+04
## 41 41 1365919363 2.869000e+04 5.194699e+04
## 42 42 1365899884 3.561919e+04 6.449667e+04
## 43 43 1365875701 4.422147e+04 8.007725e+04
## 44 44 1365845679 5.490061e+04 9.942054e+04
## 45 45 1365808407 6.815766e+04 1.234349e+05
## 46 46 1365762138 8.461437e+04 1.532478e+05
## 47 47 1365704699 1.050422e+05 1.902587e+05
## 48 48 1365633398 1.303979e+05 2.362041e+05
## 49 49 1365544892 1.618685e+05 2.932391e+05
## 50 50 1365435037 2.009254e+05 3.640375e+05
## 51 51 1365298691 2.493927e+05 4.519164e+05
## 52 52 1365129480 3.095303e+05 5.609897e+05
## 53 53 1364919504 3.841370e+05 6.963589e+05
## 54 54 1364658976 4.766765e+05 8.643476e+05
## 55 55 1364335776 5.914324e+05 1.072792e+06
## 56 56 1363934907 7.336970e+05 1.331396e+06
## 57 57 1363437825 9.100011e+05 1.652174e+06
## 58 58 1362821624 1.128392e+06 2.049984e+06
## 59 59 1362058046 1.398765e+06 2.543189e+06
## 60 60 1361112280 1.733266e+06 3.154454e+06
## 61 61 1359941530 2.146751e+06 3.911720e+06
## 62 62 1358493303 2.657332e+06 4.849365e+06
## 63 63 1356703411 3.286988e+06 6.009601e+06
## 64 64 1354493645 4.062235e+06 7.444120e+06
## 65 65 1351769160 5.014835e+06 9.216005e+06
## 66 66 1348415598 6.182479e+06 1.140192e+07
## 67 67 1344296061 7.609366e+06 1.409457e+07
## 68 68 1339248157 9.346540e+06 1.740530e+07
## 69 69 1333081446 1.145176e+07 2.146679e+07
## 70 70 1325575813 1.398865e+07 2.643554e+07
## 71 71 1316481519 1.702466e+07 3.249382e+07
## 72 72 1305521947 2.062752e+07 3.985053e+07
## 73 73 1292400235 2.485950e+07 4.874027e+07
## 74 74 1276811176 2.976917e+07 5.941965e+07
## 75 75 1258459549 3.538053e+07 7.215992e+07
## 76 76 1237085503 4.167974e+07 8.723476e+07
## 77 77 1212496414 4.860089e+07 1.049027e+08
## 78 78 1184602804 5.601312e+07 1.253841e+08
## 79 79 1153453667 6.371254e+07 1.488338e+08
## 80 80 1119264494 7.142301e+07 1.753125e+08
## 81 81 1082430408 7.880918e+07 2.047604e+08
## 82 82 1043518035 8.550310e+07 2.369789e+08
## 83 83 1003233479 9.114184e+07 2.716247e+08
## 84 84 962369291 9.541027e+07 3.082204e+08
## 85 85 921738808 9.808005e+07 3.461811e+08
## 86 86 882109568 9.903646e+07 3.848540e+08
## 87 87 844147244 9.828750e+07 4.235653e+08
## 88 88 808378201 9.595460e+07 4.616672e+08
## 89 89 775173269 9.224863e+07 4.985781e+08
## 90 90 744750851 8.743797e+07 5.338112e+08
##
## $params
## $params$beta
## beta
## 0.6081878
##
## $params$gamma
## gamma
## 0.3918122
##
## $params$R0
## R0
## 1.552243Appendices
All code used to generate the above visualizations can be found here
The global map gif was created using the following python code
References
Modeling and Simulation in Python, Downey, A.(2017) Chapter 11 Chapter 12
Forecasting: Principles and Practice, Hyndman, R.J., & Athanasopoulos, G. (2018)
Applied Predictive Modeling, Kuhn, M., & Johnson, K. (2013)
Hunter, K., & Kendall, D. (2020). (Rep.). Equitable and Efficient Distribution of a COVID-19 Vaccine
Center on Budget and Policy Priorities. (2020). (Rep.). Center on Budget and Policy Priorities.
World Health Organization. (2006). SARS: How a global epidemic was stopped (pp. 210-217, Rep.). World Health Organization.
https://www.youtube.com/watch?v=ytIZqSaKb3w&list=PL34t5iLfZddtaJ0SB9kfYmytrmXjZLGpD
https://www.youtube.com/watch?v=vLEA8dCfusQ
https://www.youtube.com/watch?v=LQCGeboXZkc
https://in.springboard.com/blog/data-modelling-covid/
https://gisanddata.maps.arcgis.com/apps/dashboards/bda7594740fd40299423467b48e9ecf6