Data 698 Spring 2021: Final Project
COVID-19 Cases & Unemployment Claims Analysis
Aaron Zalki
Abstract
COVID-19 has spread on a global scale and caused many lives and jobs to be lost. With that in mind, the purpose of this project was to ultimately answer two questions: 1) Can we create SIR Models for different population (i.e India vs. USA) and compare the results? 2) Is it possible to predict unemployment claims based on COVID-19 cases?
The methodology for addressing these questions consisted of different processes: Data Exploration, Data Preparation, SIR Model Simulation, Regression Modeling, and Forecasting. I created multiple visualizations using different data sets. After merging daily COVID data and weekly unemployment data, I was able to run a simple linear regression. Next, I converted the data into time series in order to successfully forecast. Overall, there are a number of factors that impact unemployment claims such as the industry of the occupation.
Key Words: SIR Modeling, Epidemic Model, Forecasting, Time Series, Interactive Visualization
Introduction
The Problem
In May 2019 Bill Gates made a claim that “In terms of the death toll, a pandemic would rival even the gigantic wars of the past. The economy will shut down, the cost to humanity will be unbelievable, and no country will be immune from the problem this will create.” This statement would surprisingly come to be accurate as in 2020, the United States recorded nearly 400,000 deaths due to COVID-19 and 3,000,000 worldwide. In 2002, SARS was introduced as a new corona virus that spread around the world, killing hundreds. According to the LA Times, there was an initial concern in February 2020 with the emergence of a new virus. The World Health Organization director, Lawrence Gostin, said “it’s affecting hundreds of thousands of people. and potentially a lot more going forward. It’s really hard to contain once you’ve got that kind of saturation, this is a much bigger challenge that SARS.” SARS was much more deadly which made it harder for the virus to spread.
As stated in the LA Times article, SARS was nowhere as impactful in comparison to SARS – COV – 2 which causes the disease COVID-19. SARS- COV – 2 is one of seven coronaviruses known to infect humans. It has become famous this past year, as are SARS and MERS. 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. The contagious disease, COVID-19, has dramatically impacted the labor force in the United States. In addition to the thousands of lives that have been lost, the unemployment rate reached an all-time worst since the Great Depression era in 1932. According to Washington Post, on May 8, 2020 the Labor Department said “20.5 million people abruptly lost their jobs.”
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.
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.
COVID Data Summary
## State Number of Cases
## 5 California 1655086
## 43 Texas 1513359
## 9 Florida 1143786
## 13 Illinois 865261
## 32 New York 799551
## 35 Ohio 579357
## 10 Georgia 534646
## 38 Pennsylvania 515009
## 22 Michigan 477613
## 49 Wisconsin 475340
## 42 Tennessee 460454
## 33 North Carolina 447303
## 14 Indiana 437513
## 3 Arizona 427233
## 30 New Jersey 411313
## 23 Minnesota 384223
## 25 Missouri 370869
## 21 Massachusetts 305917
## 1 Alabama 301533
## 6 Colorado 295558
## 46 Virginia 288309
## 18 Louisiana 273155
## 40 South Carolina 257320
## 15 Iowa 256902
## 36 Oklahoma 241991
## 20 Maryland 239694
## 44 Utah 237787
## 17 Kentucky 231287
## 47 Washington 214085
## 16 Kansas 193555
## 28 Nevada 192109
## 4 Arkansas 189598
## 24 Mississippi 183300
## 7 Connecticut 155489
## 27 Nebraska 151228
## 12 Idaho 124288
## 31 New Mexico 122557
## 37 Oregon 96093
## 41 South Dakota 91699
## 34 North Dakota 88436
## 39 Rhode Island 75367
## 26 Montana 74160
## 48 West Virginia 65708
## 8 Delaware 47185
## 2 Alaska 41650
## 50 Wyoming 40072
## 29 New Hampshire 32545
## 11 Hawaii 19546
## 19 Maine 16760
## 45 Vermont 5923
Unemployment Data Summary
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 unemployment claims are: California, New York, Texas, Georgia, and Florida.
## State Number of Initial Claims
## 5 California 13265290
## 32 New York 5583284
## 43 Texas 5147481
## 10 Georgia 4777436
## 9 Florida 4749123
## 13 Illinois 3702843
## 35 Ohio 3340524
## 38 Pennsylvania 3142618
## 22 Michigan 2549657
## 47 Washington 2393225
## 30 New Jersey 2195795
## 21 Massachusetts 2182318
## 33 North Carolina 1714082
## 46 Virginia 1633145
## 17 Kentucky 1556222
## 14 Indiana 1462752
## 49 Wisconsin 1452753
## 23 Minnesota 1392997
## 18 Louisiana 1340415
## 20 Maryland 1306551
## 25 Missouri 1201081
## 42 Tennessee 1175119
## 3 Arizona 1173389
## 1 Alabama 1115823
## 36 Oklahoma 1112313
## 28 Nevada 964597
## 6 Colorado 945946
## 40 South Carolina 922581
## 37 Oregon 907708
## 7 Connecticut 772348
## 16 Kansas 713925
## 15 Iowa 655707
## 24 Mississippi 653594
## 4 Arkansas 523542
## 11 Hawaii 495989
## 39 Rhode Island 419295
## 31 New Mexico 384981
## 12 Idaho 371138
## 29 New Hampshire 349549
## 44 Utah 336125
## 2 Alaska 332151
## 48 West Virginia 321331
## 27 Nebraska 281442
## 19 Maine 265923
## 26 Montana 240140
## 8 Delaware 214553
## 34 North Dakota 135464
## 45 Vermont 132087
## 50 Wyoming 101012
## 41 South Dakota 83808
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[1:482]
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: 2021-05-17 :: 2021-05-18 17:47:34
## ################################################################################
## Number of Countries/Regions reported: 192
## Number of Cities/Provinces reported: 87
## Unique number of distinct geographical locations combined: 275
## --------------------------------------------------------------------------------
## Worldwide ts-confirmed Totals: 163609594
## --------------------------------------------------------------------------------
## Country.Region Province.State Totals GlobalPerc LastDayChange t-2 t-3 t-7 t-14 t-30
## 1 US 32969480 20.15 28634 16864 28813 33651 40733 42018
## 2 India 25228996 15.42 263533 281386 311170 348421 382146 273802
## --------------------------------------------------------------------------------
## Global Perc. Average: 0.36 (sd: 1.69)
## Global Perc. Average in top 2 : 17.78 (sd: 3.34)
## --------------------------------------------------------------------------------
## ================================================================================
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------
## ################################################################################
## ##### TS-DEATHS Cases -- Data dated: 2021-05-17 :: 2021-05-18 17:47:35
## ################################################################################
## Number of Countries/Regions reported: 192
## Number of Cities/Provinces reported: 87
## Unique number of distinct geographical locations combined: 275
## --------------------------------------------------------------------------------
## Worldwide ts-deaths Totals: 3389992
## --------------------------------------------------------------------------------
## Country.Region Province.State Totals Perc LastDayChange t-2 t-3 t-7 t-14 t-30
## 1 US 586362 1.78 392 262 476 671 874 332
## 2 Brazil 436537 2.79 786 1036 2087 2311 2966 1657
## --------------------------------------------------------------------------------
## --------------------------------------------------------------------------------
## ================================================================================
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------
## ################################################################################
## ##### TS-RECOVERED Cases -- Data dated: 2021-05-17 :: 2021-05-18 17:47:36
## ################################################################################
## Number of Countries/Regions reported: 192
## Number of Cities/Provinces reported: 71
## Unique number of distinct geographical locations combined: 260
## --------------------------------------------------------------------------------
## Worldwide ts-recovered Totals: 99808931
## --------------------------------------------------------------------------------
## Country.Region Province.State Totals LastDayChange t-2 t-3 t-7 t-14 t-30
## 1 India 21596512 422436 378741 362437 355338 338229 144179
## 2 Brazil 13856731 92211 53698 7542 111401 35418 90648
## --------------------------------------------------------------------------------
## --------------------------------------------------------------------------------
## ================================================================================
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## ############################################################################################################################################
## ##### AGGREGATED Data -- ORDERED BY CONFIRMED Cases -- Data dated: 2021-05-18 :: 2021-05-18 17:47:37
## ############################################################################################################################################
## Number of Countries/Regions reported: 192
## Number of Cities/Provinces reported: 577
## Unique number of distinct geographical locations combined: 3979
## --------------------------------------------------------------------------------------------------------------------------------------------
## Location Confirmed Perc.Confirmed Deaths Perc.Deaths Recovered Perc.Recovered Active Perc.Active
## 1 France 5829009 3.56 107041 1.84 321874 5.52 5400094 92.64
## 2 Maharashtra, India 5405068 3.30 82486 1.53 4874582 90.19 448000 8.29
## ============================================================================================================================================## ############################################################################################################################################
## ##### AGGREGATED Data -- ORDERED BY DEATHS Cases -- Data dated: 2021-05-18 :: 2021-05-18 17:47:37
## ############################################################################################################################################
## Number of Countries/Regions reported: 192
## Number of Cities/Provinces reported: 577
## Unique number of distinct geographical locations combined: 3979
## --------------------------------------------------------------------------------------------------------------------------------------------
## Location Confirmed Perc.Confirmed Deaths Perc.Deaths Recovered Perc.Recovered Active Perc.Active
## 1 England, United Kingdom 3889132 2.38 112310 2.89 0 0.00 3776822 97.11
## 2 France 5829009 3.56 107041 1.84 321874 5.52 5400094 92.64
## ============================================================================================================================================## ############################################################################################################################################
## ##### AGGREGATED Data -- ORDERED BY RECOVERED Cases -- Data dated: 2021-05-18 :: 2021-05-18 17:47:37
## ############################################################################################################################################
## Number of Countries/Regions reported: 192
## Number of Cities/Provinces reported: 577
## Unique number of distinct geographical locations combined: 3979
## --------------------------------------------------------------------------------------------------------------------------------------------
## Location Confirmed Perc.Confirmed Deaths Perc.Deaths Recovered Perc.Recovered Active Perc.Active
## 1 Turkey 5127548 3.13 44983 0.88 4961120 96.75 121445 2.37
## 2 Maharashtra, India 5405068 3.30 82486 1.53 4874582 90.19 448000 8.29
## ============================================================================================================================================## ############################################################################################################################################
## ##### AGGREGATED Data -- ORDERED BY ACTIVE Cases -- Data dated: 2021-05-18 :: 2021-05-18 17:47:37
## ############################################################################################################################################
## Number of Countries/Regions reported: 192
## Number of Cities/Provinces reported: 577
## Unique number of distinct geographical locations combined: 3979
## --------------------------------------------------------------------------------------------------------------------------------------------
## Location Confirmed Perc.Confirmed Deaths Perc.Deaths Recovered Perc.Recovered Active Perc.Active
## 1 France 5829009 3.56 107041 1.84 321874 5.52 5400094 92.64
## 2 England, United Kingdom 3889132 2.38 112310 2.89 0 0.00 3776822 97.11
## ============================================================================================================================================
## Confirmed Deaths Recovered Active
## Totals
## 163585478 3364960 NA NA
## Average
## 41112.21 845.68 NA NA
## Standard Deviation
## 227789.54 4772.67 NA NA
##
##
## * Statistical estimators computed considering 3979 independent reported entries
##
##
## ********************************************************************************
## ******************************** OVERALL SUMMARY********************************
## ********************************************************************************
## **** Time Series Worldwide TOTS ****
## ts-confirmed ts-deaths ts-recovered
## 163609594 3389992 99808931
## 2.07% 61%
## **** Time Series Worldwide AVGS ****
## ts-confirmed ts-deaths ts-recovered
## 594943.98 12327.24 383880.5
## 2.07% 64.52%
## **** Time Series Worldwide SDS ****
## ts-confirmed ts-deaths ts-recovered
## 2768007.87 51802.96 1703725.81
## 1.87% 61.55%
##
##
## * Statistical estimators computed considering 275/275/260 independent reported entries per case-type
## ********************************************************************************Totals Per Location
## US -- 32969480
## =============================== running models...===============================
## Linear Regression (lm):
##
## Call:
## lm(formula = y.var ~ x.var)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5970422 -3357741 295689 3351581 7357643
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7436977 342163 -21.73 <2e-16 ***
## x.var 79334 1228 64.62 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3750000 on 480 degrees of freedom
## Multiple R-squared: 0.8969, Adjusted R-squared: 0.8967
## F-statistic: 4176 on 1 and 480 DF, p-value: < 2.2e-16
##
## --------------------------------------------------------------------------------
## Linear Regression (lm):
##
## Call:
## lm(formula = y.var ~ x.var)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.9928 -1.2270 0.5376 2.1732 2.9158
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.6389576 0.2412135 35.81 <2e-16 ***
## x.var 0.0234774 0.0008654 27.13 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.644 on 480 degrees of freedom
## Multiple R-squared: 0.6052, Adjusted R-squared: 0.6044
## F-statistic: 735.9 on 1 and 480 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
## -2351.92 -861.36 9.67 280.79 1461.74
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.362e+01 5.154e-05 264294 <2e-16 ***
## x.var 8.452e-03 1.337e-07 63240 <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: 5983404352 on 481 degrees of freedom
## Residual deviance: 420730183 on 480 degrees of freedom
## AIC: 420737965
##
## 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
## -4.7463 -0.5696 0.1157 0.4653 0.6772
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.224e+01 5.165e-02 236.92 <2e-16 ***
## x.var 1.296e-02 1.853e-04 69.92 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Gamma family taken to be 0.3205193)
##
## Null deviance: 1908.2 on 481 degrees of freedom
## Residual deviance: 1031.2 on 480 degrees of freedom
## AIC: 15680
##
## Number of Fisher Scoring iterations: 17
##
## --------------------------------------------------------------------------------
## INDIA -- 25228996
## =============================== running models...===============================
## Linear Regression (lm):
##
## Call:
## lm(formula = y.var ~ x.var)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2444658 -1507809 -267184 515751 9540246
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3673211.8 187240.5 -19.62 <2e-16 ***
## x.var 40170.0 671.8 59.80 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2052000 on 480 degrees of freedom
## Multiple R-squared: 0.8816, Adjusted R-squared: 0.8814
## F-statistic: 3575 on 1 and 480 DF, p-value: < 2.2e-16
##
## --------------------------------------------------------------------------------
## Linear Regression (lm):
##
## Call:
## lm(formula = y.var ~ x.var)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.2721 -1.9416 0.7319 2.3395 2.7752
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.0414641 0.2343020 25.79 <2e-16 ***
## x.var 0.0288284 0.0008406 34.29 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.568 on 480 degrees of freedom
## Multiple R-squared: 0.7101, Adjusted R-squared: 0.7095
## F-statistic: 1176 on 1 and 480 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
## -1332.4 -1121.3 -547.4 698.7 1441.9
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.303e+01 7.066e-05 184411 <2e-16 ***
## x.var 8.252e-03 1.840e-07 44846 <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: 3251585302 on 481 degrees of freedom
## Residual deviance: 488623284 on 480 degrees of freedom
## AIC: 488630418
##
## 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 32259 32232 32295 32390 29877 31393 30769
## 2020-04-08 2020-04-09 2020-04-10 2020-04-11 2020-04-12 2020-04-13 2020-04-14
## 1 31215 35936 34414 29102 27257 26940 28825
## 2020-04-15 2020-04-16 2020-04-17 2020-04-18 2020-04-19 2020-04-20 2020-04-21
## 1 25406 30015 33030 27932 26096 29828 25917
## 2020-04-22 2020-04-23 2020-04-24 2020-04-25 2020-04-26 2020-04-27 2020-04-28
## 1 28859 33570 32327 30396 26501 23703 24577
## 2020-04-29 2020-04-30 2020-05-01 2020-05-02 2020-05-03 2020-05-04 2020-05-05
## 1 26438 29220 34926 27350 24297 24085 24531
## 2020-05-06 2020-05-07 2020-05-08 2020-05-09 2020-05-10 2020-05-11 2020-05-12
## 1 24560 27411 26839 25136 18867 19271 22948
## 2020-05-13 2020-05-14 2020-05-15 2020-05-16 2020-05-17 2020-05-18 2020-05-19
## 1 20408 26818 24747 24159 18363 22390 21007
## 2020-05-20 2020-05-21 2020-05-22 2020-05-23 2020-05-24 2020-05-25 2020-05-26
## 1 22697 25766 23657 21111 20067 18673 19650
## 2020-05-27 2020-05-28 2020-05-29 2020-05-30 2020-05-31 2020-06-01 2020-06-02
## 1 18549 22322 24473 23633 18987 17436 21502
## 2020-06-03 2020-06-04 2020-06-05 2020-06-06 2020-06-07 2020-06-08 2020-06-09
## 1 19855 21639 25400 21160 17916 17637 18384
## 2020-06-10 2020-06-11 2020-06-12 2020-06-13 2020-06-14 2020-06-15 2020-06-16
## 1 21110 23133 24866 25208 18948 19819 23670
## 2020-06-17 2020-06-18 2020-06-19 2020-06-20 2020-06-21 2020-06-22 2020-06-23
## 1 27064 28526 31562 32270 25148 32152 37075
## 2020-06-24 2020-06-25 2020-06-26 2020-06-27 2020-06-28 2020-06-29 2020-06-30
## 1 35876 40317 45994 41346 40730 41283 46430
## 2020-07-01 2020-07-02 2020-07-03 2020-07-04 2020-07-05 2020-07-06 2020-07-07
## 1 51819 56629 51361 45681 50768 43085 60654
## 2020-07-08 2020-07-09 2020-07-10 2020-07-11 2020-07-12 2020-07-13 2020-07-14
## 1 60119 62496 68055 60033 58438 58896 68036
## 2020-07-15 2020-07-16 2020-07-17 2020-07-18 2020-07-19 2020-07-20 2020-07-21
## 1 68120 75820 72261 62535 60476 62090 64520
## 2020-07-22 2020-07-23 2020-07-24 2020-07-25 2020-07-26 2020-07-27 2020-07-28
## 1 70564 68440 73323 64915 54775 56851 66457
## 2020-07-29 2020-07-30 2020-07-31 2020-08-01 2020-08-02 2020-08-03 2020-08-04
## 1 71853 67457 68719 56184 45545 45529 58801
## 2020-08-05 2020-08-06 2020-08-07 2020-08-08 2020-08-09 2020-08-10 2020-08-11
## 1 54457 59357 59297 54119 45754 47624 48001
## 2020-08-12 2020-08-13 2020-08-14 2020-08-15 2020-08-16 2020-08-17 2020-08-18
## 1 56049 51314 65340 46921 39192 36676 45034
## 2020-08-19 2020-08-20 2020-08-21 2020-08-22 2020-08-23 2020-08-24 2020-08-25
## 1 47359 44040 48829 43045 34232 36522 40360
## 2020-08-26 2020-08-27 2020-08-28 2020-08-29 2020-08-30 2020-08-31 2020-09-01
## 1 45166 45380 46848 42731 34381 35388 41864
## 2020-09-02 2020-09-03 2020-09-04 2020-09-05 2020-09-06 2020-09-07 2020-09-08
## 1 41014 44210 50393 43088 31169 23567 27393
## 2020-09-09 2020-09-10 2020-09-11 2020-09-12 2020-09-13 2020-09-14 2020-09-15
## 1 34057 36073 47778 41062 34351 34428 39507
## 2020-09-16 2020-09-17 2020-09-18 2020-09-19 2020-09-20 2020-09-21 2020-09-22
## 1 39018 45137 49284 42159 38415 51972 39862
## 2020-09-23 2020-09-24 2020-09-25 2020-09-26 2020-09-27 2020-09-28 2020-09-29
## 1 39062 47111 48282 44652 37508 33235 43448
## 2020-09-30 2020-10-01 2020-10-02 2020-10-03 2020-10-04 2020-10-05 2020-10-06
## 1 39434 45653 54962 48535 35715 39449 45256
## 2020-10-07 2020-10-08 2020-10-09 2020-10-10 2020-10-11 2020-10-12 2020-10-13
## 1 51062 58593 56381 54918 45941 41842 52248
## 2020-10-14 2020-10-15 2020-10-16 2020-10-17 2020-10-18 2020-10-19 2020-10-20
## 1 59765 64888 69146 56736 49340 67752 61971
## 2020-10-21 2020-10-22 2020-10-23 2020-10-24 2020-10-25 2020-10-26 2020-10-27
## 1 63283 76300 81949 82729 62140 67403 76843
## 2020-10-28 2020-10-29 2020-10-30 2020-10-31 2020-11-01 2020-11-02 2020-11-03
## 1 79404 91052 99240 89695 104848 85308 127116
## 2020-11-04 2020-11-05 2020-11-06 2020-11-07 2020-11-08 2020-11-09 2020-11-10
## 1 104608 129354 128005 127450 115072 120573 140496
## 2020-11-11 2020-11-12 2020-11-13 2020-11-14 2020-11-15 2020-11-16 2020-11-17
## 1 146626 164839 180389 167761 136224 162945 163922
## 2020-11-18 2020-11-19 2020-11-20 2020-11-21 2020-11-22 2020-11-23 2020-11-24
## 1 173177 191548 198297 179274 146784 174449 175514
## 2020-11-25 2020-11-26 2020-11-27 2020-11-28 2020-11-29 2020-11-30 2020-12-01
## 1 183287 112322 208188 155533 140234 160570 188219
## 2020-12-02 2020-12-03 2020-12-04 2020-12-05 2020-12-06 2020-12-07 2020-12-08
## 1 202557 223613 232785 215542 181012 194858 224492
## 2020-12-09 2020-12-10 2020-12-11 2020-12-12 2020-12-13 2020-12-14 2020-12-15
## 1 222539 231515 239977 217585 187703 194821 209006
## 2020-12-16 2020-12-17 2020-12-18 2020-12-19 2020-12-20 2020-12-21 2020-12-22
## 1 246700 239725 251969 191906 187819 199049 198011
## 2020-12-23 2020-12-24 2020-12-25 2020-12-26 2020-12-27 2020-12-28 2020-12-29
## 1 229618 194204 97646 226288 155635 174634 200252
## 2020-12-30 2020-12-31 2021-01-01 2021-01-02 2021-01-03 2021-01-04 2021-01-05
## 1 233684 235667 153628 300310 208746 184282 235111
## 2021-01-06 2021-01-07 2021-01-08 2021-01-09 2021-01-10 2021-01-11 2021-01-12
## 1 255444 278290 295215 260695 213248 214994 226920
## 2021-01-13 2021-01-14 2021-01-15 2021-01-16 2021-01-17 2021-01-18 2021-01-19
## 1 230362 235707 242731 201680 177782 143416 176706
## 2021-01-20 2021-01-21 2021-01-22 2021-01-23 2021-01-24 2021-01-25 2021-01-26
## 1 183236 193818 190753 170613 131062 151969 147540
## 2021-01-27 2021-01-28 2021-01-29 2021-01-30 2021-01-31 2021-02-01 2021-02-02
## 1 153945 168610 166568 142312 111997 135202 115333
## 2021-02-03 2021-02-04 2021-02-05 2021-02-06 2021-02-07 2021-02-08 2021-02-09
## 1 121641 123975 134397 103987 89648 90315 95632
## 2021-02-10 2021-02-11 2021-02-12 2021-02-13 2021-02-14 2021-02-15 2021-02-16
## 1 95177 105760 99638 87122 65021 54186 62719
## 2021-02-17 2021-02-18 2021-02-19 2021-02-20 2021-02-21 2021-02-22 2021-02-23
## 1 70118 69924 79297 71525 57080 56220 72263
## 2021-02-24 2021-02-25 2021-02-26 2021-02-27 2021-02-28 2021-03-01 2021-03-02
## 1 74732 77501 77346 64575 51357 58229 57060
## 2021-03-03 2021-03-04 2021-03-05 2021-03-06 2021-03-07 2021-03-08 2021-03-09
## 1 67193 68051 66451 58203 41007 45036 57642
## 2021-03-10 2021-03-11 2021-03-12 2021-03-13 2021-03-14 2021-03-15 2021-03-16
## 1 57920 62474 61523 52932 38221 56666 53957
## 2021-03-17 2021-03-18 2021-03-19 2021-03-20 2021-03-21 2021-03-22 2021-03-23
## 1 59136 60538 61629 55374 33768 51593 53603
## 2021-03-24 2021-03-25 2021-03-26 2021-03-27 2021-03-28 2021-03-29 2021-03-30
## 1 86960 67465 77321 62700 43097 69429 61249
## 2021-03-31 2021-04-01 2021-04-02 2021-04-03 2021-04-04 2021-04-05 2021-04-06
## 1 67039 79045 69831 63067 34972 77679 60544
## 2021-04-07 2021-04-08 2021-04-09 2021-04-10 2021-04-11 2021-04-12 2021-04-13
## 1 75038 79878 82698 66535 46380 70230 77878
## 2021-04-14 2021-04-15 2021-04-16 2021-04-17 2021-04-18 2021-04-19 2021-04-20
## 1 75375 74289 79991 52373 42018 67933 61273
## 2021-04-21 2021-04-22 2021-04-23 2021-04-24 2021-04-25 2021-04-26 2021-04-27
## 1 62857 67257 62399 53363 32065 47691 50856
## 2021-04-28 2021-04-29 2021-04-30 2021-05-01 2021-05-02 2021-05-03 2021-05-04
## 1 55125 58199 57922 45303 29367 50560 40733
## 2021-05-05 2021-05-06 2021-05-07 2021-05-08 2021-05-09 2021-05-10 2021-05-11
## 1 44735 47514 47289 34493 21392 36898 33651
## 2021-05-12 2021-05-13 2021-05-14 2021-05-15 2021-05-16 2021-05-17
## 1 35878 38087 42298 28813 16864 28634
##
## $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 1.225925
## 2020-04-02 2020-04-03 2020-04-04 2020-04-05 2020-04-06 2020-04-07 2020-04-08
## 1 0.999163 1.001955 1.002942 0.9224143 1.050741 0.980123 1.014495
## 2020-04-09 2020-04-10 2020-04-11 2020-04-12 2020-04-13 2020-04-14 2020-04-15
## 1 1.151241 0.9576469 0.8456442 0.9366023 0.98837 1.06997 0.8813877
## 2020-04-16 2020-04-17 2020-04-18 2020-04-19 2020-04-20 2020-04-21 2020-04-22
## 1 1.181414 1.10045 0.8456555 0.9342689 1.14301 0.8688816 1.113516
## 2020-04-23 2020-04-24 2020-04-25 2020-04-26 2020-04-27 2020-04-28 2020-04-29
## 1 1.163242 0.9629729 0.9402667 0.8718581 0.8944191 1.036873 1.075721
## 2020-04-30 2020-05-01 2020-05-02 2020-05-03 2020-05-04 2020-05-05 2020-05-06
## 1 1.105227 1.195277 0.7830842 0.8883729 0.9912746 1.018518 1.001182
## 2020-05-07 2020-05-08 2020-05-09 2020-05-10 2020-05-11 2020-05-12 2020-05-13
## 1 1.116083 0.9791325 0.9365476 0.7505968 1.021413 1.190805 0.889315
## 2020-05-14 2020-05-15 2020-05-16 2020-05-17 2020-05-18 2020-05-19 2020-05-20
## 1 1.314093 0.9227757 0.9762395 0.7600894 1.2193 0.9382314 1.080449
## 2020-05-21 2020-05-22 2020-05-23 2020-05-24 2020-05-25 2020-05-26 2020-05-27
## 1 1.135216 0.9181479 0.8923786 0.9505471 0.9305327 1.052322 0.9439695
## 2020-05-28 2020-05-29 2020-05-30 2020-05-31 2020-06-01 2020-06-02 2020-06-03
## 1 1.203407 1.096362 0.9656765 0.8034105 0.9183125 1.233196 0.9234025
## 2020-06-04 2020-06-05 2020-06-06 2020-06-07 2020-06-08 2020-06-09 2020-06-10
## 1 1.089851 1.173807 0.8330709 0.8466919 0.9844273 1.042354 1.148281
## 2020-06-11 2020-06-12 2020-06-13 2020-06-14 2020-06-15 2020-06-16 2020-06-17
## 1 1.095831 1.074915 1.013754 0.7516661 1.045968 1.194308 1.143388
## 2020-06-18 2020-06-19 2020-06-20 2020-06-21 2020-06-22 2020-06-23 2020-06-24
## 1 1.05402 1.106429 1.022432 0.7792997 1.278511 1.153116 0.9676601
## 2020-06-25 2020-06-26 2020-06-27 2020-06-28 2020-06-29 2020-06-30 2020-07-01
## 1 1.123787 1.140809 0.8989433 0.9851013 1.013577 1.124676 1.116067
## 2020-07-02 2020-07-03 2020-07-04 2020-07-05 2020-07-06 2020-07-07 2020-07-08
## 1 1.092823 0.9069735 0.8894103 1.111359 0.8486645 1.407775 0.9911795
## 2020-07-09 2020-07-10 2020-07-11 2020-07-12 2020-07-13 2020-07-14 2020-07-15
## 1 1.039538 1.08895 0.8821248 0.9734313 1.007837 1.155189 1.001235
## 2020-07-16 2020-07-17 2020-07-18 2020-07-19 2020-07-20 2020-07-21 2020-07-22
## 1 1.113036 0.9530599 0.8654046 0.9670744 1.026688 1.039137 1.093676
## 2020-07-23 2020-07-24 2020-07-25 2020-07-26 2020-07-27 2020-07-28 2020-07-29
## 1 0.9698997 1.071347 0.8853293 0.8437957 1.037901 1.168968 1.081195
## 2020-07-30 2020-07-31 2020-08-01 2020-08-02 2020-08-03 2020-08-04 2020-08-05
## 1 0.9388195 1.018708 0.8175905 0.81064 0.9996487 1.291507 0.9261237
## 2020-08-06 2020-08-07 2020-08-08 2020-08-09 2020-08-10 2020-08-11 2020-08-12
## 1 1.089979 0.9989892 0.9126769 0.8454332 1.040871 1.007916 1.167663
## 2020-08-13 2020-08-14 2020-08-15 2020-08-16 2020-08-17 2020-08-18 2020-08-19
## 1 0.9155203 1.273337 0.7181053 0.8352763 0.9358032 1.227887 1.051628
## 2020-08-20 2020-08-21 2020-08-22 2020-08-23 2020-08-24 2020-08-25 2020-08-26
## 1 0.9299183 1.108742 0.8815458 0.7952608 1.066896 1.105087 1.119078
## 2020-08-27 2020-08-28 2020-08-29 2020-08-30 2020-08-31 2020-09-01 2020-09-02
## 1 1.004738 1.032349 0.91212 0.8045915 1.029289 1.183 0.9796962
## 2020-09-03 2020-09-04 2020-09-05 2020-09-06 2020-09-07 2020-09-08 2020-09-09
## 1 1.077925 1.139855 0.8550394 0.7233801 0.7561038 1.162346 1.243274
## 2020-09-10 2020-09-11 2020-09-12 2020-09-13 2020-09-14 2020-09-15 2020-09-16
## 1 1.059195 1.324481 0.8594332 0.8365642 1.002242 1.147525 0.9876224
## 2020-09-17 2020-09-18 2020-09-19 2020-09-20 2020-09-21 2020-09-22 2020-09-23
## 1 1.156825 1.091876 0.8554298 0.9111933 1.352909 0.7669899 0.9799308
## 2020-09-24 2020-09-25 2020-09-26 2020-09-27 2020-09-28 2020-09-29 2020-09-30
## 1 1.206057 1.024856 0.9248167 0.8400072 0.8860776 1.307297 0.9076137
## 2020-10-01 2020-10-02 2020-10-03 2020-10-04 2020-10-05 2020-10-06 2020-10-07
## 1 1.157707 1.203908 0.8830647 0.7358607 1.10455 1.147203 1.128292
## 2020-10-08 2020-10-09 2020-10-10 2020-10-11 2020-10-12 2020-10-13 2020-10-14
## 1 1.147487 0.9622481 0.9740515 0.8365381 0.9107769 1.248697 1.143872
## 2020-10-15 2020-10-16 2020-10-17 2020-10-18 2020-10-19 2020-10-20 2020-10-21
## 1 1.085719 1.065621 0.8205247 0.8696418 1.373166 0.9146741 1.021171
## 2020-10-22 2020-10-23 2020-10-24 2020-10-25 2020-10-26 2020-10-27 2020-10-28
## 1 1.205695 1.074037 1.009518 0.7511272 1.084696 1.140053 1.033328
## 2020-10-29 2020-10-30 2020-10-31 2020-11-01 2020-11-02 2020-11-03 2020-11-04
## 1 1.146693 1.089927 0.903819 1.168939 0.813635 1.490083 0.8229334
## 2020-11-05 2020-11-06 2020-11-07 2020-11-08 2020-11-09 2020-11-10 2020-11-11
## 1 1.236559 0.9895713 0.9956642 0.9028796 1.047805 1.165236 1.043631
## 2020-11-12 2020-11-13 2020-11-14 2020-11-15 2020-11-16 2020-11-17 2020-11-18
## 1 1.124214 1.094334 0.9299957 0.8120123 1.196155 1.005996 1.05646
## 2020-11-19 2020-11-20 2020-11-21 2020-11-22 2020-11-23 2020-11-24 2020-11-25
## 1 1.106082 1.035234 0.9040681 0.818769 1.188474 1.006105 1.044287
## 2020-11-26 2020-11-27 2020-11-28 2020-11-29 2020-11-30 2020-12-01 2020-12-02
## 1 0.6128203 1.853493 0.7470796 0.901635 1.145015 1.172193 1.076177
## 2020-12-03 2020-12-04 2020-12-05 2020-12-06 2020-12-07 2020-12-08 2020-12-09
## 1 1.103951 1.041017 0.9259274 0.8397992 1.076492 1.15208 0.9913004
## 2020-12-10 2020-12-11 2020-12-12 2020-12-13 2020-12-14 2020-12-15 2020-12-16
## 1 1.040335 1.036551 0.9066911 0.8626652 1.037922 1.07281 1.180349
## 2020-12-17 2020-12-18 2020-12-19 2020-12-20 2020-12-21 2020-12-22 2020-12-23
## 1 0.9717268 1.051075 0.7616254 0.9787031 1.059792 0.9947852 1.159622
## 2020-12-24 2020-12-25 2020-12-26 2020-12-27 2020-12-28 2020-12-29 2020-12-30
## 1 0.8457699 0.5028012 2.317432 0.687774 1.122074 1.146695 1.16695
## 2020-12-31 2021-01-01 2021-01-02 2021-01-03 2021-01-04 2021-01-05 2021-01-06
## 1 1.008486 0.6518859 1.954787 0.6951017 0.8828049 1.275822 1.086483
## 2021-01-07 2021-01-08 2021-01-09 2021-01-10 2021-01-11 2021-01-12 2021-01-13
## 1 1.089436 1.060818 0.8830683 0.817998 1.008188 1.055471 1.015168
## 2021-01-14 2021-01-15 2021-01-16 2021-01-17 2021-01-18 2021-01-19 2021-01-20
## 1 1.023203 1.0298 0.8308786 0.8815054 0.8066958 1.232122 1.036954
## 2021-01-21 2021-01-22 2021-01-23 2021-01-24 2021-01-25 2021-01-26 2021-01-27
## 1 1.057751 0.9841862 0.8944184 0.768183 1.15952 0.9708559 1.043412
## 2021-01-28 2021-01-29 2021-01-30 2021-01-31 2021-02-01 2021-02-02 2021-02-03
## 1 1.095261 0.9878892 0.8543778 0.7869821 1.207193 0.8530421 1.054694
## 2021-02-04 2021-02-05 2021-02-06 2021-02-07 2021-02-08 2021-02-09 2021-02-10
## 1 1.019188 1.084065 0.7737301 0.8621078 1.00744 1.058872 0.9952422
## 2021-02-11 2021-02-12 2021-02-13 2021-02-14 2021-02-15 2021-02-16 2021-02-17
## 1 1.111193 0.9421142 0.8743853 0.7463213 0.8333615 1.157476 1.117971
## 2021-02-18 2021-02-19 2021-02-20 2021-02-21 2021-02-22 2021-02-23 2021-02-24
## 1 0.9972332 1.134046 0.9019887 0.7980426 0.9849334 1.285361 1.034167
## 2021-02-25 2021-02-26 2021-02-27 2021-02-28 2021-03-01 2021-03-02 2021-03-03
## 1 1.037052 0.998 0.8348848 0.7953078 1.133808 0.9799241 1.177585
## 2021-03-04 2021-03-05 2021-03-06 2021-03-07 2021-03-08 2021-03-09 2021-03-10
## 1 1.012769 0.9764882 0.8758785 0.7045513 1.098252 1.279909 1.004823
## 2021-03-11 2021-03-12 2021-03-13 2021-03-14 2021-03-15 2021-03-16 2021-03-17
## 1 1.078626 0.9847777 0.8603612 0.7220774 1.482588 0.9521936 1.095984
## 2021-03-18 2021-03-19 2021-03-20 2021-03-21 2021-03-22 2021-03-23 2021-03-24
## 1 1.023708 1.018022 0.8985056 0.6098169 1.527867 1.038959 1.622297
## 2021-03-25 2021-03-26 2021-03-27 2021-03-28 2021-03-29 2021-03-30 2021-03-31
## 1 0.7758165 1.146091 0.8109052 0.6873525 1.610994 0.8821818 1.094532
## 2021-04-01 2021-04-02 2021-04-03 2021-04-04 2021-04-05 2021-04-06 2021-04-07
## 1 1.17909 0.8834335 0.9031376 0.5545214 2.221177 0.7794127 1.239396
## 2021-04-08 2021-04-09 2021-04-10 2021-04-11 2021-04-12 2021-04-13 2021-04-14
## 1 1.064501 1.035304 0.8045539 0.6970767 1.51423 1.108899 0.96786
## 2021-04-15 2021-04-16 2021-04-17 2021-04-18 2021-04-19 2021-04-20 2021-04-21
## 1 0.985592 1.076754 0.6547362 0.8022836 1.616759 0.9019622 1.025852
## 2021-04-22 2021-04-23 2021-04-24 2021-04-25 2021-04-26 2021-04-27 2021-04-28
## 1 1.07 0.9277696 0.85519 0.6008845 1.487323 1.066365 1.083943
## 2021-04-29 2021-04-30 2021-05-01 2021-05-02 2021-05-03 2021-05-04 2021-05-05
## 1 1.055764 0.9952405 0.782138 0.6482352 1.72166 0.8056369 1.09825
## 2021-05-06 2021-05-07 2021-05-08 2021-05-09 2021-05-10 2021-05-11 2021-05-12
## 1 1.062121 0.9952646 0.7294085 0.6201838 1.72485 0.9120007 1.066179
## 2021-05-13 2021-05-14 2021-05-15 2021-05-16 2021-05-17 NA
## 1 1.06157 1.110563 0.6811906 0.5852914 1.697936 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 224560 256792
## [73] 289087 321477 351354 382747 413516 444731 480667 515081
## [81] 544183 571440 598380 627205 652611 682626 715656 743588
## [89] 769684 799512 825429 854288 887858 920185 950581 977082
## [97] 1000785 1025362 1051800 1081020 1115946 1143296 1167593 1191678
## [105] 1216209 1240769 1268180 1295019 1320155 1339022 1358293 1381241
## [113] 1401649 1428467 1453214 1477373 1495736 1518126 1539133 1561830
## [121] 1587596 1611253 1632364 1652431 1671104 1690754 1709303 1731625
## [129] 1756098 1779731 1798718 1816154 1837656 1857511 1879150 1904550
## [137] 1925710 1943626 1961263 1979647 2000757 2023890 2048756 2073964
## [145] 2092912 2112731 2136401 2163465 2191991 2223553 2255823 2280971
## [153] 2313123 2350198 2386074 2426391 2472385 2513731 2554461 2595744
## [161] 2642174 2693993 2750622 2801983 2847664 2898432 2941517 3002171
## [169] 3062290 3124786 3192841 3252874 3311312 3370208 3438244 3506364
## [177] 3582184 3654445 3716980 3777456 3839546 3904066 3974630 4043070
## [185] 4116393 4181308 4236083 4292934 4359391 4431244 4498701 4567420
## [193] 4623604 4669149 4714678 4773479 4827936 4887293 4946590 5000709
## [201] 5046463 5094087 5142088 5198137 5249451 5314791 5361712 5400904
## [209] 5437580 5482614 5529973 5574013 5622842 5665887 5700119 5736641
## [217] 5777001 5822167 5867547 5914395 5957126 5991507 6026895 6068759
## [225] 6109773 6153983 6204376 6247464 6278633 6302200 6329593 6363650
## [233] 6399723 6447501 6488563 6522914 6557342 6596849 6635867 6681004
## [241] 6730288 6772447 6810862 6862834 6902696 6941758 6988869 7037151
## [249] 7081803 7119311 7152546 7195994 7235428 7281081 7336043 7384578
## [257] 7420293 7459742 7504998 7556060 7614653 7671034 7725952 7771893
## [265] 7813735 7865983 7925748 7990636 8059782 8116518 8165858 8233610
## [273] 8295581 8358864 8435164 8517113 8599842 8661982 8729385 8806228
## [281] 8885632 8976684 9075924 9165619 9270467 9355775 9482891 9587499
## [289] 9716853 9844858 9972308 10087380 10207953 10348449 10495075 10659914
## [297] 10840303 11008064 11144288 11307233 11471155 11644332 11835880 12034177
## [305] 12213451 12360235 12534684 12710198 12893485 13005807 13213995 13369528
## [313] 13509762 13670332 13858551 14061108 14284721 14517506 14733048 14914060
## [321] 15108918 15333410 15555949 15787464 16027441 16245026 16432729 16627550
## [329] 16836556 17083256 17322981 17574950 17766856 17954675 18153724 18351735
## [337] 18581353 18775557 18873203 19099491 19255126 19429760 19630012 19863696
## [345] 20099363 20252991 20553301 20762047 20946329 21181440 21436884 21715174
## [353] 22010389 22271084 22484332 22699326 22926246 23156608 23392315 23635046
## [361] 23836726 24014508 24157924 24334630 24517866 24711684 24902437 25073050
## [369] 25204112 25356081 25503621 25657566 25826176 25992744 26135056 26247053
## [377] 26382255 26497588 26619229 26743204 26877601 26981588 27071236 27161551
## [385] 27257183 27352360 27458120 27557758 27644880 27709901 27764087 27826806
## [393] 27896924 27966848 28046145 28117670 28174750 28230970 28303233 28377965
## [401] 28455466 28532812 28597387 28648744 28706973 28764033 28831226 28899277
## [409] 28965728 29023931 29064938 29109974 29167616 29225536 29288010 29349533
## [417] 29402465 29440686 29497352 29551309 29610445 29670983 29732612 29787986
## [425] 29821754 29873347 29926950 30013910 30081375 30158696 30221396 30264493
## [433] 30333922 30395171 30462210 30541255 30611086 30674153 30709125 30786804
## [441] 30847348 30922386 31002264 31084962 31151497 31197877 31268107 31345985
## [449] 31421360 31495649 31575640 31628013 31670031 31737964 31799237 31862094
## [457] 31929351 31991750 32045113 32077178 32124869 32175725 32230850 32289049
## [465] 32346971 32392274 32421641 32472201 32512934 32557669 32605183 32652472
## [473] 32686965 32708357 32745255 32778906 32814784 32852871 32895169 32923982
## [481] 32940846 32969480
## [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] 10266674 10286709 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
## [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