Analysing and Visualising COVID-19 pandemic
Astha Malhotra
10/06/2020
A pneumonia of unknown cause detected in Wuhan, China was first reported to the WHO Country Office in China on 31 December 2019. Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus.
Most people infected with the COVID-19 virus will experience mild to moderate respiratory illness and recover without requiring special treatment. Older people, and those with underlying medical problems like cardiovascular disease, diabetes, chronic respiratory disease, and cancer are more likely to develop serious illness.
The outbreak was declared a Public Health Emergency of International Concern on 30 January 2020.
On 11 February 2020, WHO announced a name for the new coronavirus disease: COVID-19.
To get the latest data on covid 19, we will use the covid19.analytics package.
library(covid19.analytics)
#Data
ag <- covid19.data(case = "aggregated")## Data being read from JHU/CCSE repository## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~## Reading data from https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_daily_reports/06-12-2020.csvIf we observe the last line of the output, we see that the data has been updated as of 9th June 2020, which is the latest data as of the date of this project.
#Lets look at the time series data of confirmed cases
time_series_confirmed <- covid19.data(case = "ts-confirmed")## Data being read from JHU/CCSE repository## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~## Reading data from https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv## Data retrieved on 2020-06-13 11:43:23 || Range of dates on data: 2020-01-22--2020-06-12 | Nbr of records: 266## --------------------------------------------------------------------------------We have time series data from 22nd January 2020 to 9th June 2020.
For Summary report.
report.summary(Nentries = 10,
graphical.output = T)## Data being read from JHU/CCSE repository## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~## Reading data from https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv## Data retrieved on 2020-06-13 11:43:23 || Range of dates on data: 2020-01-22--2020-06-12 | Nbr of records: 266## --------------------------------------------------------------------------------## >>> checking data integrity...## No critical issues have been found.## >>> checking data consistency...## Warning in consistency.check(data, n0, nf, datasetName, details): Inconsistency
## of type.II in ts-confirmed data detected -- 35 records (out of 266) show
## inconsistencies in the data...## ################################################################################
## ##### TS-CONFIRMED Cases -- Data dated: 2020-06-12 :: 2020-06-13 11:43:23
## ################################################################################
## Number of Countries/Regions reported: 188
## Number of Cities/Provinces reported: 82
## Unique number of distinct geographical locations combined: 266
## --------------------------------------------------------------------------------
## Worldwide ts-confirmed Totals: 7632802
## --------------------------------------------------------------------------------
## Country.Region Province.State Totals GlobalPerc LastDayChange t-2 t-3 t-7 t-14 t-30
## 1 US 2048986 26.84 25396 22888 21003 23043 24202 27460
## 2 Brazil 828810 10.86 25982 30412 32913 27075 33274 13028
## 3 Russia 510761 6.69 8961 8777 8393 8846 8952 9974
## 4 India 297535 3.90 0 10930 10459 10438 8336 3942
## 5 United Kingdom 292950 3.84 1541 1266 1003 1557 1604 3446
## 6 Spain 243209 3.19 502 427 314 332 664 849
## 7 Italy 236305 3.10 163 379 202 270 416 992
## 8 Peru 214788 2.81 0 5965 5087 4358 7386 4298
## 9 France 188918 2.48 564 358 397 529 1800 731
## 10 Germany 187226 2.45 535 169 16 526 267 380
## --------------------------------------------------------------------------------
## Global Perc. Average: 0.38 (sd: 1.89)
## Global Perc. Average in top 10 : 6.62 (sd: 7.57)
## --------------------------------------------------------------------------------
## ================================================================================## Data being read from JHU/CCSE repository## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~## Reading data from https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_global.csv## Data retrieved on 2020-06-13 11:43:24 || Range of dates on data: 2020-01-22--2020-06-12 | Nbr of records: 266## --------------------------------------------------------------------------------## >>> checking data integrity...## No critical issues have been found.## >>> checking data consistency...## Warning in consistency.check(data, n0, nf, datasetName, details): Inconsistency
## of type.II in ts-deaths data detected -- 22 records (out of 266) show
## inconsistencies in the data...
## ################################################################################
## ##### TS-DEATHS Cases -- Data dated: 2020-06-12 :: 2020-06-13 11:43:24
## ################################################################################
## Number of Countries/Regions reported: 188
## Number of Cities/Provinces reported: 82
## Unique number of distinct geographical locations combined: 266
## --------------------------------------------------------------------------------
## Worldwide ts-deaths Totals: 425394
## --------------------------------------------------------------------------------
## Country.Region Province.State Totals Perc LastDayChange t-2 t-3 t-7 t-14 t-30
## 1 US 114669 5.60 846 885 927 707 941 1776
## 2 Brazil 41828 5.05 909 1239 1274 904 956 759
## 3 United Kingdom 41481 14.16 202 151 245 204 215 428
## 4 Italy 34223 14.48 56 53 71 72 111 262
## 5 France 29315 15.52 28 27 23 31 57 349
## 6 Spain 27136 11.16 0 0 0 1 4 217
## 7 Mexico 16448 11.82 504 587 708 341 364 257
## 8 Belgium 9646 16.13 10 7 10 14 23 60
## 9 Germany 8783 4.69 11 20 16 15 26 23
## 10 Iran 8659 4.74 75 78 81 75 57 71
## --------------------------------------------------------------------------------
## --------------------------------------------------------------------------------
## ================================================================================## Data being read from JHU/CCSE repository## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~## Reading data from https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_recovered_global.csv## Data retrieved on 2020-06-13 11:43:24 || Range of dates on data: 2020-01-22--2020-06-12 | Nbr of records: 253## --------------------------------------------------------------------------------## >>> checking data integrity...## No critical issues have been found.## >>> checking data consistency...## Warning in consistency.check(data, n0, nf, datasetName, details): Inconsistency
## of type.II in ts-recovered data detected -- 56 records (out of 253) show
## inconsistencies in the data...
## ################################################################################
## ##### TS-RECOVERED Cases -- Data dated: 2020-06-12 :: 2020-06-13 11:43:25
## ################################################################################
## Number of Countries/Regions reported: 188
## Number of Cities/Provinces reported: 68
## Unique number of distinct geographical locations combined: 253
## --------------------------------------------------------------------------------
## Worldwide ts-recovered Totals: 3613277
## --------------------------------------------------------------------------------
## Country.Region Province.State Totals LastDayChange t-2 t-3 t-7 t-14 t-30
## 1 US 547386 7094 6788 8649 9143 10015 2984
## 2 Brazil 445123 15158 16049 17179 10209 11416 1055
## 3 Russia 268862 8213 8354 10378 8698 8212 5527
## 4 Italy 173085 1747 1399 1293 1297 2789 2747
## 5 Germany 171535 574 331 501 478 663 1600
## 6 Spain 150376 0 0 0 0 0 2551
## 7 Turkey 149102 1242 1021 2241 1922 1021 2315
## 8 India 147195 0 11989 536 5462 4309 1569
## 9 Iran 144649 1986 2073 2133 2297 1896 1111
## 10 Chile 131358 4914 4664 4419 4459 1833 790
## --------------------------------------------------------------------------------
## --------------------------------------------------------------------------------
## ================================================================================## Data being read from JHU/CCSE repository## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~## Reading data from https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_daily_reports/06-12-2020.csv
## ############################################################################################################################################
## ##### AGGREGATED Data -- ORDERED BY CONFIRMED Cases -- Data dated: 2020-06-13 :: 2020-06-13 11:43:25
## ############################################################################################################################################
## Number of Countries/Regions reported: 188
## Number of Cities/Provinces reported: 549
## Unique number of distinct geographical locations combined: 3738
## --------------------------------------------------------------------------------------------------------------------------------------------
## Location Confirmed Perc.Confirmed Deaths Perc.Deaths Recovered Perc.Recovered Active Perc.Active
## 1 New York City, New York, US 208954 2.74 22043 10.55 0 0.00 186911 89.45
## 2 Moscow, Russia 202935 2.66 3187 1.57 118024 58.16 81724 40.27
## 3 France 188918 2.48 29315 15.52 69578 36.83 90025 47.65
## 4 Iran 182525 2.39 8659 4.74 144649 79.25 29217 16.01
## 5 Turkey 175218 2.30 4778 2.73 149102 85.10 21338 12.18
## 6 Sao Paulo, Brazil 167900 2.20 10368 6.18 49295 29.36 108237 64.47
## 7 England, United Kingdom 156410 2.05 37069 23.70 0 0.00 119341 76.30
## 8 Metropolitana, Chile 129694 1.70 2468 1.90 0 0.00 127226 98.10
## 9 Lima, Peru 125640 1.65 2675 2.13 0 0.00 122965 97.87
## 10 Saudi Arabia 119942 1.57 893 0.74 81029 67.56 38020 31.70
## ============================================================================================================================================## ############################################################################################################################################
## ##### AGGREGATED Data -- ORDERED BY DEATHS Cases -- Data dated: 2020-06-13 :: 2020-06-13 11:43:25
## ############################################################################################################################################
## Number of Countries/Regions reported: 188
## Number of Cities/Provinces reported: 549
## Unique number of distinct geographical locations combined: 3738
## --------------------------------------------------------------------------------------------------------------------------------------------
## Location Confirmed Perc.Confirmed Deaths Perc.Deaths Recovered Perc.Recovered Active Perc.Active
## 1 England, United Kingdom 156410 2.05 37069 23.70 0 0.00 119341 76.30
## 2 France 188918 2.48 29315 15.52 69578 36.83 90025 47.65
## 3 New York City, New York, US 208954 2.74 22043 10.55 0 0.00 186911 89.45
## 4 Lombardia, Italy 91204 1.19 16405 17.99 57775 63.35 17024 18.67
## 5 Sao Paulo, Brazil 167900 2.20 10368 6.18 49295 29.36 108237 64.47
## 6 Belgium 59819 0.78 9646 16.13 16498 27.58 33675 56.29
## 7 Madrid, Spain 70231 0.92 8691 12.37 40736 58.00 20804 29.62
## 8 Iran 182525 2.39 8659 4.74 144649 79.25 29217 16.01
## 9 Rio de Janeiro, Brazil 77784 1.02 7417 9.54 61690 79.31 8677 11.16
## 10 Netherlands 48461 0.63 6053 12.49 0 0.00 42408 87.51
## ============================================================================================================================================## ############################################################################################################################################
## ##### AGGREGATED Data -- ORDERED BY RECOVERED Cases -- Data dated: 2020-06-13 :: 2020-06-13 11:43:25
## ############################################################################################################################################
## Number of Countries/Regions reported: 188
## Number of Cities/Provinces reported: 549
## Unique number of distinct geographical locations combined: 3738
## --------------------------------------------------------------------------------------------------------------------------------------------
## Location Confirmed Perc.Confirmed Deaths Perc.Deaths Recovered Perc.Recovered Active Perc.Active
## 1 Recovered, US 0 0.00 0 NaN 547386 Inf -621891 -Inf
## 2 Turkey 175218 2.30 4778 2.73 149102 85.10 21338 12.18
## 3 Iran 182525 2.39 8659 4.74 144649 79.25 29217 16.01
## 4 Unknown, Chile 0 0.00 0 NaN 131358 Inf -131358 -Inf
## 5 Moscow, Russia 202935 2.66 3187 1.57 118024 58.16 81724 40.27
## 6 Unknown, Peru 0 0.00 0 NaN 107133 Inf -107133 -Inf
## 7 Saudi Arabia 119942 1.57 893 0.74 81029 67.56 38020 31.70
## 8 France 188918 2.48 29315 15.52 69578 36.83 90025 47.65
## 9 Hubei, China 68135 0.89 4512 6.62 63623 93.38 0 0.00
## 10 Rio de Janeiro, Brazil 77784 1.02 7417 9.54 61690 79.31 8677 11.16
## ============================================================================================================================================## ############################################################################################################################################
## ##### AGGREGATED Data -- ORDERED BY ACTIVE Cases -- Data dated: 2020-06-13 :: 2020-06-13 11:43:25
## ############################################################################################################################################
## Number of Countries/Regions reported: 188
## Number of Cities/Provinces reported: 549
## Unique number of distinct geographical locations combined: 3738
## --------------------------------------------------------------------------------------------------------------------------------------------
## Location Confirmed Perc.Confirmed Deaths Perc.Deaths Recovered Perc.Recovered Active Perc.Active
## 1 New York City, New York, US 208954 2.74 22043 10.55 0 0.00 186911 89.45
## 2 Metropolitana, Chile 129694 1.70 2468 1.90 0 0.00 127226 98.10
## 3 Lima, Peru 125640 1.65 2675 2.13 0 0.00 122965 97.87
## 4 England, United Kingdom 156410 2.05 37069 23.70 0 0.00 119341 76.30
## 5 Sao Paulo, Brazil 167900 2.20 10368 6.18 49295 29.36 108237 64.47
## 6 Unknown, United Kingdom 101335 1.33 0 0.00 0 0.00 101335 100.00
## 7 France 188918 2.48 29315 15.52 69578 36.83 90025 47.65
## 8 Moscow, Russia 202935 2.66 3187 1.57 118024 58.16 81724 40.27
## 9 Cook, Illinois, US 84249 1.10 4162 4.94 0 0.00 80087 95.06
## 10 Los Angeles, California, US 70529 0.92 2834 4.02 0 0.00 67695 95.98
## ============================================================================================================================================## Confirmed Deaths Recovered Active
## Totals
## 7632802 425394 3613277 3519626
## Average
## 2041.95 113.8 966.63 941.58
## Standard Deviation
## 10897.86 1014.92 10934.14 12504.68
##
##
## * Statistical estimators computed considering 3738 independent reported entries## >>> checking data integrity...## No critical issues have been found.
##
##
## ********************************************************************************
## ******************************** OVERALL SUMMARY********************************
## ********************************************************************************
## **** Time Series Worldwide TOTS ****
## ts-confirmed ts-deaths ts-recovered
## 7632802 425394 3613277
## 5.57% 47.34%
## **** Time Series Worldwide AVGS ****
## ts-confirmed ts-deaths ts-recovered
## 28694.74 1599.23 14281.73
## 5.57% 49.77%
## **** Time Series Worldwide SDS ****
## ts-confirmed ts-deaths ts-recovered
## 144504.97 8594.52 54130.29
## 5.95% 37.46%
##
##
## * Statistical estimators computed considering 266/266/253 independent reported entries per case-type
## ********************************************************************************We see that we get data from all the categories.
#Totals per location
tots.per.location(time_series_confirmed, geo.loc = "US")## US -- 2048986
## =============================== running models...===============================
## Linear Regression (lm):
##
## Call:
## lm(formula = y.var ~ x.var)
##
## Residuals:
## Min 1Q Median 3Q Max
## -429077 -220285 32196 204523 511391
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -527364.0 43298.4 -12.18 <2e-16 ***
## x.var 15973.6 521.7 30.62 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 257500 on 141 degrees of freedom
## Multiple R-squared: 0.8693, Adjusted R-squared: 0.8683
## F-statistic: 937.5 on 1 and 141 DF, p-value: < 2.2e-16
##
## --------------------------------------------------------------------------------
## Linear Regression (lm):
##
## Call:
## lm(formula = y.var ~ x.var)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.1779 -1.4400 -0.2985 1.6499 2.8887
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.222693 0.301682 4.053 8.32e-05 ***
## x.var 0.115301 0.003635 31.720 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.794 on 141 degrees of freedom
## Multiple R-squared: 0.8771, Adjusted R-squared: 0.8762
## F-statistic: 1006 on 1 and 141 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
## -615.8 -369.6 -229.0 242.9 436.9
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 9.968e+00 4.805e-04 20743 <2e-16 ***
## x.var 3.473e-02 4.051e-06 8575 <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: 131296912 on 142 degrees of freedom
## Residual deviance: 16501482 on 141 degrees of freedom
## AIC: 16503107
##
## Number of Fisher Scoring iterations: 6
##
## --------------------------------------------------------------------------------## Warning: glm.fit: algorithm did not converge## GLM using Family Family: Gamma Link function: log :
##
## Call:
## glm(formula = y.var ~ x.var, family = family)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.9352 -1.9039 -1.0962 0.1839 2.1351
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.686337 0.248373 6.79 2.89e-10 ***
## x.var 0.126918 0.002993 42.41 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Gamma family taken to be 2.182327)
##
## Null deviance: 1102.96 on 142 degrees of freedom
## Residual deviance: 382.96 on 141 degrees of freedom
## AIC: 3321.9
##
## Number of Fisher Scoring iterations: 25
##
## --------------------------------------------------------------------------------
We see that there are 3 different models fitted on to the data.
The most interesting seems to be the non-linear model. We see a convex pattern, showing an increasing trend and then we see a concave pattern signifying a decreasing trend.
Lets analyse the growth rate for USA
#Growth rate
growth.rate(time_series_confirmed, geo.loc = "US")## Processing... US## Loading required package: pheatmap## Loading required package: gplots##
## Attaching package: 'gplots'## The following object is masked from 'package:stats':
##
## lowess
## $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 0 0 2 1 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 0 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 6 23 20
## 2020-03-04 2020-03-05 2020-03-06 2020-03-07 2020-03-08 2020-03-09 2020-03-10
## 1 31 70 48 115 114 68 192
## 2020-03-11 2020-03-12 2020-03-13 2020-03-14 2020-03-15 2020-03-16 2020-03-17
## 1 398 451 589 710 96 1383 1776
## 2020-03-18 2020-03-19 2020-03-20 2020-03-21 2020-03-22 2020-03-23 2020-03-24
## 1 2760 5224 5312 6323 7927 10060 10239
## 2020-03-25 2020-03-26 2020-03-27 2020-03-28 2020-03-29 2020-03-30 2020-03-31
## 1 11913 18021 18147 19774 19115 21456 25980
## 2020-04-01 2020-04-02 2020-04-03 2020-04-04 2020-04-05 2020-04-06 2020-04-07
## 1 25427 30362 31904 33131 27834 29588 30707
## 2020-04-08 2020-04-09 2020-04-10 2020-04-11 2020-04-12 2020-04-13 2020-04-14
## 1 31638 34693 33449 29965 28515 25245 26981
## 2020-04-15 2020-04-16 2020-04-17 2020-04-18 2020-04-19 2020-04-20 2020-04-21
## 1 29085 31226 32679 28283 26034 27281 25440
## 2020-04-22 2020-04-23 2020-04-24 2020-04-25 2020-04-26 2020-04-27 2020-04-28
## 1 28144 34092 36176 32870 27641 22414 24445
## 2020-04-29 2020-04-30 2020-05-01 2020-05-02 2020-05-03 2020-05-04 2020-05-05
## 1 27332 29622 34093 29146 25558 22363 24080
## 2020-05-06 2020-05-07 2020-05-08 2020-05-09 2020-05-10 2020-05-11 2020-05-12
## 1 25160 27774 27040 25663 19735 18703 21789
## 2020-05-13 2020-05-14 2020-05-15 2020-05-16 2020-05-17 2020-05-18 2020-05-19
## 1 21009 27460 25154 25055 18960 21589 20323
## 2020-05-20 2020-05-21 2020-05-22 2020-05-23 2020-05-24 2020-05-25 2020-05-26
## 1 23414 25372 23985 21776 20754 18946 18718
## 2020-05-27 2020-05-28 2020-05-29 2020-05-30 2020-05-31 2020-06-01 2020-06-02
## 1 18252 22718 24378 24202 20071 17272 20778
## 2020-06-03 2020-06-04 2020-06-05 2020-06-06 2020-06-07 2020-06-08 2020-06-09
## 1 19768 21179 30005 23043 18135 17633 18078
## 2020-06-10 2020-06-11 2020-06-12
## 1 21003 22888 25396
##
## $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 NaN
## 2020-01-30 2020-01-31 2020-02-01 2020-02-02 2020-02-03 2020-02-04 2020-02-05
## 1 NaN NA 0.5 0 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 NaN NaN 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 0.75 3.833333 0.8695652 1.55
## 2020-03-05 2020-03-06 2020-03-07 2020-03-08 2020-03-09 2020-03-10 2020-03-11
## 1 2.258065 0.6857143 2.395833 0.9913043 0.5964912 2.823529 2.072917
## 2020-03-12 2020-03-13 2020-03-14 2020-03-15 2020-03-16 2020-03-17 2020-03-18
## 1 1.133166 1.305987 1.205433 0.1352113 14.40625 1.284165 1.554054
## 2020-03-19 2020-03-20 2020-03-21 2020-03-22 2020-03-23 2020-03-24 2020-03-25
## 1 1.892754 1.016845 1.190324 1.253677 1.26908 1.017793 1.163493
## 2020-03-26 2020-03-27 2020-03-28 2020-03-29 2020-03-30 2020-03-31 2020-04-01
## 1 1.512717 1.006992 1.089657 0.9666734 1.122469 1.21085 0.9787144
## 2020-04-02 2020-04-03 2020-04-04 2020-04-05 2020-04-06 2020-04-07 2020-04-08
## 1 1.194085 1.050787 1.038459 0.8401195 1.063016 1.037819 1.030319
## 2020-04-09 2020-04-10 2020-04-11 2020-04-12 2020-04-13 2020-04-14 2020-04-15
## 1 1.096561 0.9641426 0.8958414 0.9516102 0.8853235 1.068766 1.077981
## 2020-04-16 2020-04-17 2020-04-18 2020-04-19 2020-04-20 2020-04-21 2020-04-22
## 1 1.073612 1.046532 0.8654794 0.9204823 1.047899 0.9325171 1.106289
## 2020-04-23 2020-04-24 2020-04-25 2020-04-26 2020-04-27 2020-04-28 2020-04-29
## 1 1.211342 1.061129 0.9086134 0.8409188 0.8108969 1.090613 1.118102
## 2020-04-30 2020-05-01 2020-05-02 2020-05-03 2020-05-04 2020-05-05 2020-05-06
## 1 1.083785 1.150935 0.8548969 0.8768956 0.8749902 1.076779 1.04485
## 2020-05-07 2020-05-08 2020-05-09 2020-05-10 2020-05-11 2020-05-12 2020-05-13
## 1 1.103895 0.9735724 0.9490754 0.769006 0.9477071 1.165 0.9642021
## 2020-05-14 2020-05-15 2020-05-16 2020-05-17 2020-05-18 2020-05-19 2020-05-20
## 1 1.307059 0.9160233 0.9960642 0.7567352 1.13866 0.941359 1.152094
## 2020-05-21 2020-05-22 2020-05-23 2020-05-24 2020-05-25 2020-05-26 2020-05-27
## 1 1.083625 0.9453334 0.9079008 0.9530676 0.9128843 0.9879658 0.9751042
## 2020-05-28 2020-05-29 2020-05-30 2020-05-31 2020-06-01 2020-06-02 2020-06-03
## 1 1.244686 1.07307 0.9927804 0.8293116 0.8605451 1.202987 0.9513909
## 2020-06-04 2020-06-05 2020-06-06 2020-06-07 2020-06-08 2020-06-09 2020-06-10
## 1 1.071378 1.416734 0.767972 0.7870069 0.9723187 1.025237 1.161799
## 2020-06-11 2020-06-12 NA
## 1 1.089749 1.109577 NAThis plot has 2 y axis- the first axis shows changes on a regular scale, the second axis is in a log scale. The graph on the top shows the log cases while the one on the bottom is for the regular scale.
The number of changes are hovering around 30,000 at present and we can see a slight downward trend in the graph towards the end signifying stabilization and the decline in the number of new cases.
Let’s import all time series data-
time_series_all <- covid19.data(case = 'ts-ALL')## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------
## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## --------------------------------------------------------------------------------#We will use the all data for a totals plot
totals.plt(time_series_all)## Warning: `arrange_()` is deprecated as of dplyr 0.7.0.
## Please use `arrange()` instead.
## See vignette('programming') for more help
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.
One of the models that is being used by the researchers is the SIR model. In this mode, people are grouped into 3 categories healthy but susceptible - ‘S’, Infected - ‘I’, Recovered - ‘R’
generate.SIR.model(time_series_confirmed, "US", tot.population = 32820000)## ################################################################################## This is an experimental feature, being currently under active development!## Please check the development version of the package for the latest updates on it## ################################################################################
## Processing... US
## [1] 1 1 2 2 5 5 5 5 5
## [10] 7 8 8 11 11 11 11 11 11
## [19] 11 11 12 12 13 13 13 13 13
## [28] 13 13 13 15 15 15 15 15 15
## [37] 16 16 24 30 53 73 104 174 222
## [46] 337 451 519 711 1109 1560 2149 2859 2955
## [55] 4338 6114 8874 14098 19410 25733 33660 43720 53959
## [64] 65872 83893 102040 121814 140929 162385 188365 213792 244154
## [73] 276058 309189 337023 366611 397318 428956 463649 497098 527063
## [82] 555578 580823 607804 636889 668115 700794 729077 755111 782392
## [91] 807832 835976 870068 906244 939114 966755 989169 1013614 1040946
## [100] 1070568 1104661 1133807 1159365 1181728 1205808 1230968 1258742 1285782
## [109] 1311445 1331180 1349883 1371672 1392681 1420141 1445295 1470350 1489310
## [118] 1510899 1531222 1554636 1580008 1603993 1625769 1646523 1665469 1684187
## [127] 1702439 1725157 1749535 1773737 1793808 1811080 1831858 1851626 1872805
## [136] 1902810 1925853 1943988 1961621 1979699 2000702 2023590 2048986
## [1] 40
## [1] 30 53 73 104 174 222 337 451 519 711 1109 1560
## [13] 2149 2859 2955 4338 6114 8874 14098 19410 25733 33660 43720 53959
## [25] 65872 83893
## ------------------------ 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: 32820000
## --------------------------------------------------------------------------------## Loading required package: deSolve## [1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
## beta gamma
## 0.6608945 0.3391055
## R0 = 1.9489344224675
## Max of infecteded: 4728217.28 ( 14.41 %)
## Max nbr of casualties, assuming 2% fatality rate: 94564.35
## Max reached at day : 44 ==> 2020-04-15
## ================================================================================## Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE): 1 y value
## <= 0 omitted from logarithmic plot
## $Infected
## [1] 30 53 73 104 174 222 337 451 519 711 1109 1560
## [13] 2149 2859 2955 4338 6114 8874 14098 19410 25733 33660 43720 53959
## [25] 65872 83893
##
## $model
## time S I R
## 1 1 32819970 3.000000e+01 0.000000e+00
## 2 2 32819947 4.138777e+01 1.200062e+01
## 3 3 32819914 5.709823e+01 2.855658e+01
## 4 4 32819870 7.877219e+01 5.139705e+01
## 5 5 32819808 1.086733e+02 8.290755e+01
## 6 6 32819724 1.499243e+02 1.263790e+02
## 7 7 32819607 2.068332e+02 1.863517e+02
## 8 8 32819446 2.853431e+02 2.690890e+02
## 9 9 32819223 3.936524e+02 3.832315e+02
## 10 10 32818916 5.430704e+02 5.406994e+02
## 11 11 32818493 7.491972e+02 7.579362e+02
## 12 12 32817909 1.033551e+03 1.057626e+03
## 13 13 32817103 1.425809e+03 1.471058e+03
## 14 14 32815992 1.966902e+03 2.041392e+03
## 15 15 32814459 2.713268e+03 2.828157e+03
## 16 16 32812344 3.742714e+03 3.913450e+03
## 17 17 32809427 5.162487e+03 5.410479e+03
## 18 18 32805404 7.120346e+03 7.475324e+03
## 19 19 32799857 9.819780e+03 1.032312e+04
## 20 20 32792209 1.354083e+04 1.425030e+04
## 21 21 32781666 1.866851e+04 1.966513e+04
## 22 22 32767139 2.573153e+04 2.712953e+04
## 23 23 32747129 3.545453e+04 3.741623e+04
## 24 24 32719585 4.882830e+04 5.158653e+04
## 25 25 32681702 6.720286e+04 7.109561e+04
## 26 26 32629657 9.240891e+04 9.793411e+04
## 27 27 32558271 1.269125e+05 1.348162e+05
## 28 28 32460568 1.740050e+05 1.854266e+05
## 29 29 32327242 2.380216e+05 2.547365e+05
## 30 30 32146035 3.245681e+05 3.493966e+05
## 31 31 31901097 4.407019e+05 4.782008e+05
## 32 32 31572443 5.949658e+05 6.525907e+05
## 33 33 31135779 7.970984e+05 8.871224e+05
## 34 34 30563098 1.057158e+06 1.199744e+06
## 35 35 29824621 1.383745e+06 1.611634e+06
## 36 36 28892664 1.781091e+06 2.146245e+06
## 37 37 27747680 2.245143e+06 2.827177e+06
## 38 38 26385795 2.759532e+06 3.674673e+06
## 39 39 24825770 3.293269e+06 4.700962e+06
## 40 40 23112107 3.802441e+06 5.905453e+06
## 41 41 21311441 4.237173e+06 7.271386e+06
## 42 42 19501955 4.552459e+06 8.765586e+06
## 43 43 17759198 4.718809e+06 1.034199e+07
## 44 44 16143669 4.728217e+06 1.194811e+07
## 45 45 14694168 4.593461e+06 1.353237e+07
## 46 46 13427642 4.342111e+06 1.505025e+07
## 47 47 12343488 4.008562e+06 1.646795e+07
## 48 48 11429481 3.627026e+06 1.776349e+07
## 49 49 10667234 3.226991e+06 1.892577e+07
## 50 50 10036242 2.831181e+06 1.995258e+07
## 51 51 9516418 2.455384e+06 2.084820e+07
## 52 52 9089448 2.109327e+06 2.162123e+07
## 53 53 8739335 1.797964e+06 2.228270e+07
## 54 54 8452478 1.522797e+06 2.284472e+07
## 55 55 8217511 1.283006e+06 2.331948e+07
## 56 56 8025030 1.076348e+06 2.371862e+07
## 57 57 7867311 8.998090e+05 2.405288e+07
## 58 58 7738027 7.500619e+05 2.433191e+07
## 59 59 7632009 6.237613e+05 2.456423e+07
## 60 60 7545033 5.177243e+05 2.475724e+07
## 61 61 7473653 4.290308e+05 2.491732e+07
## 62 62 7415052 3.550683e+05 2.504988e+07
## 63 63 7366926 2.935420e+05 2.515953e+07
## 64 64 7327393 2.424636e+05 2.525014e+07
## 65 65 7294911 2.001284e+05 2.532496e+07
## 66 66 7268217 1.650871e+05 2.538670e+07
## 67 67 7246275 1.361149e+05 2.543761e+07
## 68 68 7228238 1.121822e+05 2.547958e+07
## 69 69 7213408 9.242699e+04 2.551416e+07
## 70 70 7201215 7.613002e+04 2.554266e+07
## 71 71 7191188 6.269259e+04 2.556612e+07
## 72 72 7182942 5.161749e+04 2.558544e+07
## 73 73 7176160 4.249247e+04 2.560135e+07
## 74 74 7170582 3.497625e+04 2.561444e+07
## 75 75 7165995 2.878659e+04 2.562522e+07
## 76 76 7162222 2.369030e+04 2.563409e+07
## 77 77 7159118 1.949491e+04 2.564139e+07
## 78 78 7156565 1.604157e+04 2.564739e+07
## 79 79 7154465 1.319935e+04 2.565234e+07
## 80 80 7152737 1.086029e+04 2.565640e+07
## 81 81 7151316 8.935454e+03 2.565975e+07
## 82 82 7150147 7.351576e+03 2.566250e+07
## 83 83 7149186 6.048324e+03 2.566477e+07
## 84 84 7148395 4.976018e+03 2.566663e+07
## 85 85 7147744 4.093762e+03 2.566816e+07
## 86 86 7147209 3.367892e+03 2.566942e+07
## 87 87 7146769 2.770699e+03 2.567046e+07
## 88 88 7146406 2.279382e+03 2.567131e+07
## 89 89 7146108 1.875176e+03 2.567202e+07
## 90 90 7145863 1.542639e+03 2.567259e+07Analysis: The y-axis are the number of people who are affected vs no of days on the x axis.(based on 1st 25 days of data). The second plot is the same except that the number of infected have been converted to log scale. This semi-log plot or log linear plot. The model fits the data well The third plot gives us the break up according to the three categories ‘S I R’ The number of people infected (red line)reached a peak around day 45 whereas the recovered(green line) peaked at around day 60. We can see that the things are stabilizing pretty much from this plot. The same is echoed by the 4th plot which is the log of the third plot.
Lets look at UK as well-
generate.SIR.model(time_series_confirmed, "United Kingdom", tot.population = 67886004)## ################################################################################## This is an experimental feature, being currently under active development!## Please check the development version of the package for the latest updates on it## ################################################################################
## Processing... UNITED KINGDOM
## [1] 0 0 0 0 0 0 0 0 0 2
## [11] 2 2 2 2 2 2 3 3 3 8
## [21] 8 9 9 9 9 9 9 9 9 9
## [31] 9 9 9 13 13 13 15 20 23 36
## [41] 40 51 86 116 164 207 274 322 384 459
## [51] 459 802 1144 1145 1551 1960 2642 2716 4014 5067
## [61] 5745 6726 8164 9640 11812 14745 17312 19780 22453 25481
## [71] 29865 34173 38689 42477 48436 52279 55949 61474 65872 74605
## [81] 79874 85206 89570 94845 99483 104145 109769 115314 121172 125856
## [91] 130172 134638 139246 144640 149569 154037 158348 162350 166441 172481
## [101] 178685 183500 187842 191832 196243 202359 207977 212629 216525 220449
## [111] 224332 227741 230985 234440 238004 241461 244995 247709 250138 249619
## [121] 252246 255544 258504 260916 262547 266599 268619 270508 272607 274219
## [131] 276156 277736 279392 281270 283079 284734 286294 287621 288834 290581
## [141] 291588 292860 294402
## [1] 39
## [1] 23 36 40 51 86 116 164 207 274 322 384 459 459 802 1144
## [16] 1145 1551 1960 2642 2716 4014 5067 5745 6726 8164 9640
## ------------------------ Parameters used to create model ------------------------
## Region: UNITED KINGDOM
## Time interval to consider: t0=39 - t1= ; tfinal=90
## t0: 2020-03-01 -- t1:
## Number of days considered for initial guess: 26
## Fatality rate: 0.02
## Population of the region: 67886004
## --------------------------------------------------------------------------------
## [1] "ERROR: ABNORMAL_TERMINATION_IN_LNSRCH"
## beta gamma
## 0.6228167 0.3771834
## R0 = 1.6512303058082
## Max of infecteded: 6140682.72 ( 9.05 %)
## Max nbr of casualties, assuming 2% fatality rate: 122813.65
## Max reached at day : 59 ==> 2020-04-29
## ================================================================================## Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE): 1 y value
## <= 0 omitted from logarithmic plot
## $Infected
## [1] 23 36 40 51 86 116 164 207 274 322 384 459 459 802 1144
## [16] 1145 1551 1960 2642 2716 4014 5067 5745 6726 8164 9640
##
## $model
## time S I R
## 1 1 67885981 2.300000e+01 0.000000e+00
## 2 2 67885965 2.940390e+01 9.833547e+00
## 3 3 67885944 3.759083e+01 2.240505e+01
## 4 4 67885917 4.805724e+01 3.847685e+01
## 5 5 67885884 6.143780e+01 5.902352e+01
## 6 6 67885840 7.854388e+01 8.529099e+01
## 7 7 67885785 1.004127e+02 1.188720e+02
## 8 8 67885714 1.283704e+02 1.618030e+02
## 9 9 67885623 1.641122e+02 2.166872e+02
## 10 10 67885507 2.098053e+02 2.868526e+02
## 11 11 67885359 2.682202e+02 3.765538e+02
## 12 12 67885170 3.428986e+02 4.912298e+02
## 13 13 67884928 4.383684e+02 6.378341e+02
## 14 14 67884618 5.604174e+02 8.252557e+02
## 15 15 67884223 7.164446e+02 1.064858e+03
## 16 16 67883717 9.159079e+02 1.371168e+03
## 17 17 67883070 1.170897e+03 1.762757e+03
## 18 18 67882244 1.496865e+03 2.263361e+03
## 19 19 67881187 1.913564e+03 2.903328e+03
## 20 20 67879836 2.446237e+03 3.721444e+03
## 21 21 67878110 3.127144e+03 4.767289e+03
## 22 22 67875902 3.997509e+03 6.104232e+03
## 23 23 67873081 5.110003e+03 7.813262e+03
## 24 24 67869474 6.531907e+03 9.997876e+03
## 25 25 67864865 8.349156e+03 1.279033e+04
## 26 26 67858973 1.067147e+04 1.635958e+04
## 27 27 67851444 1.363891e+04 2.092149e+04
## 28 28 67841822 1.743013e+04 2.675170e+04
## 29 29 67829529 2.227299e+04 3.420217e+04
## 30 30 67813824 2.845776e+04 4.372210e+04
## 31 31 67793765 3.635398e+04 5.588454e+04
## 32 32 67768152 4.643150e+04 7.142008e+04
## 33 33 67735458 5.928679e+04 9.125953e+04
## 34 34 67693741 7.567555e+04 1.165875e+05
## 35 35 67640541 9.655283e+04 1.489100e+05
## 36 36 67572744 1.231217e+05 1.901381e+05
## 37 37 67486420 1.568912e+05 2.426927e+05
## 38 38 67376628 1.997439e+05 3.096317e+05
## 39 39 67237186 2.540120e+05 3.948058e+05
## 40 40 67060403 3.225581e+05 5.030426e+05
## 41 41 66836789 4.088532e+05 6.403617e+05
## 42 42 66554747 5.170394e+05 8.142172e+05
## 43 43 66200293 6.519540e+05 1.033757e+06
## 44 44 65756846 8.190807e+05 1.310078e+06
## 45 45 65205182 1.024379e+06 1.656443e+06
## 46 46 64523673 1.273930e+06 2.088401e+06
## 47 47 63688955 1.573323e+06 2.623726e+06
## 48 48 62677216 1.926723e+06 3.282065e+06
## 49 49 61466222 2.335606e+06 4.084175e+06
## 50 50 60038157 2.797223e+06 5.050624e+06
## 51 51 58383067 3.303041e+06 6.199895e+06
## 52 52 56502484 3.837552e+06 7.545968e+06
## 53 53 54412409 4.378003e+06 9.095592e+06
## 54 54 52144710 4.895568e+06 1.084573e+07
## 55 55 49746107 5.358165e+06 1.278173e+07
## 56 56 47274468 5.734640e+06 1.487690e+07
## 57 57 44792944 5.999395e+06 1.709366e+07
## 58 58 42363213 6.136280e+06 1.938651e+07
## 59 59 40039358 6.140683e+06 2.170596e+07
## 60 60 37863622 6.019386e+06 2.400300e+07
## 61 61 35864556 5.788465e+06 2.623298e+07
## 62 62 34057377 5.470017e+06 2.835861e+07
## 63 63 32445865 5.088659e+06 3.035148e+07
## 64 64 31025012 4.668526e+06 3.219247e+07
## 65 65 29783758 4.231138e+06 3.387111e+07
## 66 66 28707410 3.794223e+06 3.538437e+07
## 67 67 27779553 3.371330e+06 3.673512e+07
## 68 68 26983423 2.972013e+06 3.793057e+07
## 69 69 26302820 2.602337e+06 3.898085e+07
## 70 70 25722651 2.265528e+06 3.989783e+07
## 71 71 25229206 1.962641e+06 4.069416e+07
## 72 72 24810262 1.693161e+06 4.138258e+07
## 73 73 24455061 1.455516e+06 4.197543e+07
## 74 74 24154233 1.247473e+06 4.248430e+07
## 75 75 23899673 1.066453e+06 4.291988e+07
## 76 76 23684411 9.097423e+05 4.329185e+07
## 77 77 23502479 7.746501e+05 4.360888e+07
## 78 78 23348782 6.586059e+05 4.387862e+07
## 79 79 23218985 5.592194e+05 4.410780e+07
## 80 80 23109401 4.743109e+05 4.430229e+07
## 81 81 23016904 4.019225e+05 4.446718e+07
## 82 82 22938844 3.403161e+05 4.460684e+07
## 83 83 22872978 2.879630e+05 4.472506e+07
## 84 84 22817408 2.435284e+05 4.482507e+07
## 85 85 22770528 2.058538e+05 4.490962e+07
## 86 86 22730984 1.739387e+05 4.498108e+07
## 87 87 22697630 1.469227e+05 4.504145e+07
## 88 88 22669499 1.240679e+05 4.509244e+07
## 89 89 22645773 1.047434e+05 4.513549e+07
## 90 90 22625765 8.841116e+04 4.517183e+07Here we see the infected peak at around day 60 and a recovered peak at around day 75.
Now we will look at India
generate.SIR.model(time_series_confirmed, "India", tot.population = 1349217956)## ################################################################################## This is an experimental feature, being currently under active development!## Please check the development version of the package for the latest updates on it## ################################################################################
## Processing... INDIA
## [1] 0 0 0 0 0 0 0 0 1 1
## [11] 1 2 3 3 3 3 3 3 3 3
## [21] 3 3 3 3 3 3 3 3 3 3
## [31] 3 3 3 3 3 3 3 3 3 3
## [41] 5 5 28 30 31 34 39 43 56 62
## [51] 73 82 102 113 119 142 156 194 244 330
## [61] 396 499 536 657 727 887 987 1024 1251 1397
## [71] 1998 2543 2567 3082 3588 4778 5311 5916 6725 7598
## [81] 8446 9205 10453 11487 12322 13430 14352 15722 17615 18539
## [91] 20080 21370 23077 24530 26283 27890 29451 31324 33062 34863
## [101] 37257 39699 42505 46437 49400 52987 56351 59695 62808 67161
## [111] 70768 74292 78055 81997 85784 90648 95698 100328 106475 112028
## [121] 118226 124794 131423 138536 144950 150793 158086 165386 173491 181827
## [131] 190609 198370 207191 216824 226713 236184 246622 257486 265928 276146
## [141] 286605 297535 297535
## [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: 1349217956
## --------------------------------------------------------------------------------
## [1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
## beta gamma
## 0.6081878 0.3918122
## R0 = 1.5522432706608
## Max of infecteded: 97822176.53 ( 7.25 %)
## Max nbr of casualties, assuming 2% fatality rate: 1956443.53
## Max reached at day : 86 ==> 2020-05-29
## ================================================================================## Warning in xy.coords(x, y, xlabel, ylabel, log = log, recycle = TRUE): 1 y value
## <= 0 omitted from logarithmic plot
## $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 1349217951 5.000000e+00 0.000000e+00
## 2 2 1349217948 6.207843e+00 2.187158e+00
## 3 3 1349217943 7.707465e+00 4.902667e+00
## 4 4 1349217938 9.569346e+00 8.274155e+00
## 5 5 1349217932 1.188100e+01 1.246009e+01
## 6 6 1349217924 1.475108e+01 1.765722e+01
## 7 7 1349217914 1.831449e+01 2.410983e+01
## 8 8 1349217901 2.273869e+01 3.212116e+01
## 9 9 1349217886 2.823165e+01 4.206778e+01
## 10 10 1349217867 3.505153e+01 5.441721e+01
## 11 11 1349217843 4.351889e+01 6.974987e+01
## 12 12 1349217813 5.403170e+01 8.878642e+01
## 13 13 1349217776 6.708407e+01 1.124216e+02
## 14 14 1349217731 8.328948e+01 1.417663e+02
## 15 15 1349217674 1.034096e+02 1.781998e+02
## 16 16 1349217604 1.283901e+02 2.234345e+02
## 17 17 1349217517 1.594052e+02 2.795964e+02
## 18 18 1349217409 1.979124e+02 3.493253e+02
## 19 19 1349217274 2.457219e+02 4.358985e+02
## 20 20 1349217108 3.050805e+02 5.433851e+02
## 21 21 1349216900 3.787783e+02 6.768370e+02
## 22 22 1349216643 4.702791e+02 8.425267e+02
## 23 23 1349216324 5.838835e+02 1.048242e+03
## 24 24 1349215927 7.249309e+02 1.303651e+03
## 25 25 1349215435 9.000507e+02 1.620759e+03
## 26 26 1349214824 1.117474e+03 2.014469e+03
## 27 27 1349214065 1.387418e+03 2.503288e+03
## 28 28 1349213123 1.722572e+03 3.110188e+03
## 29 29 1349211954 2.138686e+03 3.863695e+03
## 30 30 1349210501 2.655318e+03 4.799223e+03
## 31 31 1349208699 3.296748e+03 5.960742e+03
## 32 32 1349206460 4.093121e+03 7.402842e+03
## 33 33 1349203681 5.081862e+03 9.193298e+03
## 34 34 1349200230 6.309436e+03 1.141626e+04
## 35 35 1349195946 7.833529e+03 1.417620e+04
## 36 36 1349190627 9.725758e+03 1.760281e+04
## 37 37 1349184024 1.207503e+04 2.185714e+04
## 38 38 1349175825 1.499173e+04 2.713910e+04
## 39 39 1349165646 1.861287e+04 3.369689e+04
## 40 40 1349153009 2.310855e+04 4.183865e+04
## 41 41 1349137319 2.868991e+04 5.194690e+04
## 42 42 1349117840 3.561906e+04 6.449653e+04
## 43 43 1349093658 4.422129e+04 8.007705e+04
## 44 44 1349063635 5.490034e+04 9.942025e+04
## 45 45 1349026364 6.815725e+04 1.234345e+05
## 46 46 1348980095 8.461376e+04 1.532472e+05
## 47 47 1348922657 1.050412e+05 1.902577e+05
## 48 48 1348851357 1.303966e+05 2.362027e+05
## 49 49 1348762852 1.618664e+05 2.932371e+05
## 50 50 1348652999 2.009223e+05 3.640345e+05
## 51 51 1348516656 2.493880e+05 4.519119e+05
## 52 52 1348347450 3.095231e+05 5.609829e+05
## 53 53 1348137482 3.841259e+05 6.963485e+05
## 54 54 1347876965 4.766595e+05 8.643317e+05
## 55 55 1347553782 5.914064e+05 1.072767e+06
## 56 56 1347152940 7.336572e+05 1.331359e+06
## 57 57 1346655898 9.099401e+05 1.652118e+06
## 58 58 1346039760 1.128298e+06 2.049898e+06
## 59 59 1345276277 1.398622e+06 2.543057e+06
## 60 60 1344330657 1.733046e+06 3.154253e+06
## 61 61 1343160130 2.146415e+06 3.911411e+06
## 62 62 1341712247 2.656818e+06 4.848892e+06
## 63 63 1339922878 3.286201e+06 6.008877e+06
## 64 64 1337713911 4.061033e+06 7.443012e+06
## 65 65 1334990644 5.013001e+06 9.214311e+06
## 66 66 1331638932 6.179687e+06 1.139934e+07
## 67 67 1327522199 7.605129e+06 1.409063e+07
## 68 68 1322478526 9.340129e+06 1.739930e+07
## 69 69 1316318170 1.144210e+07 2.145768e+07
## 70 70 1308822027 1.397416e+07 2.642176e+07
## 71 71 1299741809 1.700308e+07 3.247307e+07
## 72 72 1288802932 2.059560e+07 3.981942e+07
## 73 73 1275711340 2.481270e+07 4.869391e+07
## 74 74 1260165587 2.970130e+07 5.935107e+07
## 75 75 1241875333 3.528332e+07 7.205930e+07
## 76 76 1220586812 4.154253e+07 8.708861e+07
## 77 77 1196114611 4.841050e+07 1.046928e+08
## 78 78 1168377259 5.575400e+07 1.250867e+08
## 79 79 1137431900 6.336743e+07 1.484186e+08
## 80 80 1103501340 7.097424e+07 1.747424e+08
## 81 81 1066985961 7.824054e+07 2.039915e+08
## 82 82 1028454370 8.480209e+07 2.359615e+08
## 83 83 988610448 9.030197e+07 2.703055e+08
## 84 84 948239994 9.443287e+07 3.065451e+08
## 85 85 908145489 9.697508e+07 3.440974e+08
## 86 86 869080639 9.782218e+07 3.823151e+08
## 87 87 831695877 9.698885e+07 4.205332e+08
## 88 88 796502559 9.460084e+07 4.581146e+08
## 89 89 763858118 9.087057e+07 4.944893e+08
## 90 90 733970085 8.606532e+07 5.291825e+08This model seems to suggest that the peak will be around 90 days for Infected rate.