Context

Notes about analyses of COVID-19 data. Inspired by an article on Towards Data Science. This document is an R markdown notebook available from my personal viral2020 GitHub repository.

Worldwide cases and mortalities

Using information made available from the European Centre for Disease Prevention and Control and updated on a daily basis. There are likely other sources that are updated more regularly (e.g. the many sources used by worldometers), but this is a decent starting point.

Worldwide, there were 6,005,018 confirmed cases and 348,480 deaths as this document was generated using the data obtained from the ECDC (HTML document generated 2020-06-02 08:18:47 AST). A total of 208 countries had COVID-19 reported cases, 169 countries had more than 100 reported cases, and 71 countries had more than 100 reported deaths.

Number of new deaths vs. cumulative deaths

Plot the number of new deaths or cases as a function of the cumulative number of deaths or cases and use a log scale on both axes. We do this for the number of deaths in the 10 countries with the most fatalities to date.

Loading required package: ggrepel

Let’s now do the same for another subset of countries.

Progression since 100 confirmed cases

Present the number of cumulative cases starting on the date when 100 or more cases were recorded in each country, and use a logarithmic scale for the y axis.

And do the same for the number of cumulative cases per one million people.

Country-level summaries

How are different countries doing? I am testing a function that takes a country as an argument and fits both an exponential growth and a logistic growth model to the number of cumulative cases.

---
title: "Notebook of COVID-19 analyses"
author: "Daniel Ricard (daniel.ricard@gmail.com)"
date: '`r paste0("Last modified timestap: ", format(Sys.time(), "%Y-%m-%d %H:%M:%S %Z"))`'
output: html_notebook
---

# Context
Notes about analyses of COVID-19 data. Inspired by [an article on Towards Data Science](https://towardsdatascience.com/visualize-the-pandemic-with-r-covid-19-c3443de3b4e4). This document is an R markdown notebook available from my personal [viral2020 GitHub repository](https://github.com/ricardd/viral2020/).

# Worldwide cases and mortalities
Using information made available from the [European Centre for Disease Prevention and Control](https://www.ecdc.europa.eu/en/publications-data/download-todays-data-geographic-distribution-covid-19-cases-worldwide) and updated on a daily basis. There are likely other sources that are updated more regularly (e.g. the many sources used by [worldometers](https://www.worldometers.info/coronavirus/)), but this is a decent starting point.

```{r, include=FALSE}
## this is copied and pasted from the ECDC website

#these libraries need to be loaded
library(utils)
library(httr)

#download the dataset from the ECDC website to a local temporary file
GET("https://opendata.ecdc.europa.eu/covid19/casedistribution/csv", authenticate(":", ":", type="ntlm"), write_disk(tf <- tempfile(fileext = ".csv")))

#read the Dataset sheet into “R”. The dataset will be called "data".
data <- read.csv(tf, stringsAsFactors = FALSE)
names(data)[1] <- "dateRep"
## DR
data$dateRep <- as.Date(data$dateRep, format="%d/%m/%Y") ## DR, incoming data is formatted day/month/year and was not recognised correctly as a date
## compute the cumulative number of cases by country
## compute the cumulative number of fatalities by country
library(dplyr)
df <- data[order(data$countriesAndTerritories, data$dateRep),] %>% group_by(countriesAndTerritories) %>% mutate(cumsum.cases = cumsum(cases)) %>% mutate(cumsum.deaths = cumsum(deaths))
df$death.rate.percent <- 100*(df$cumsum.deaths / df$cumsum.cases)
df$cases.per.e06 <- (df$cumsum.cases / df$popData2018)*1E06
df$deaths.per.e06 <- (df$cumsum.deaths / df$popData2018)*1E06
## make sure that all countries have a 3-letter code so that they can be merged with the other data frame linking each country to a continent
#table(df$countryterritoryCode, exclude=FALSE)
#t.df <- df[df$countryterritoryCode=="",]
#table(t.df$countriesAndTerritories)

df[df$countriesAndTerritories=="Bonaire, Saint Eustatius and Saba","countryterritoryCode"] <- "BES"
df[df$countriesAndTerritories=="Falkland_Islands_(Malvinas)","countryterritoryCode"] <- "FLK"


```

```{r, include=FALSE}
## https://datahub.io/JohnSnowLabs/country-and-continent-codes-list
continent.df <- read.csv("country-and-continent-codes-list-csv_csv.txt")
#head(continent.df)
#df[which(df$countryterritoryCode==""),]
#table(continent.df$Country_Name)
#continent.df[which(continent.df$Country_Name=="Anguilla"),]
df.continent <- merge(df, continent.df, by.x="countryterritoryCode", by.y="Three_Letter_Country_Code")
```

```{r, echo=FALSE}
## a table showing today's number of cases in decreasing order
for.kable <- ungroup(df) %>% filter(dateRep == format(Sys.time(),"%Y-%m-%d")) %>%
 arrange(desc(cumsum.cases))
```

Worldwide, there were `r format(sum(for.kable$cumsum.cases),big.mark=",")` confirmed cases and `r format(sum(for.kable$cumsum.deaths),big.mark=",")` deaths as this document was generated using the data obtained from the ECDC (HTML document generated `r format(Sys.time(), "%Y-%m-%d %H:%M:%S %Z")`). A total of `r nrow(for.kable)` countries had COVID-19 reported cases, `r nrow(for.kable[for.kable$cumsum.cases>100,])` countries had more than 100 reported cases,  and `r nrow(for.kable[for.kable$cumsum.deaths>100,])` countries had more than 100 reported deaths.

## Number of new deaths vs. cumulative deaths

Plot the number of new deaths or cases as a function of the cumulative number of deaths or cases and use a log scale on both axes. We do this for the number of deaths in the 10 countries with the most fatalities to date.

```{r, fig.height=6, fig.width=8, echo=FALSE}
library(dplyr)
#obtain top 20 and 10 country for fatalities
top20.deaths <- ungroup(df) %>% filter(dateRep == format(Sys.time(),"%Y-%m-%d")) %>%
 top_n(n=20, wt=cumsum.deaths) %>%
 arrange(desc(cumsum.deaths))

top10.deaths <- ungroup(df) %>% filter(dateRep == format(Sys.time(),"%Y-%m-%d")) %>%
 top_n(n=10, wt=cumsum.deaths) %>%
 arrange(desc(cumsum.deaths))

library(ggplot2)
require(ggrepel)

g <- 
  ggplot(filter(df, countriesAndTerritories %in% top10.deaths$countriesAndTerritories, deaths>0, cumsum.deaths>=10), aes(cumsum.deaths, deaths)) +
  geom_line(aes(group=countriesAndTerritories, color=countriesAndTerritories)) +
  scale_x_log10() +
  scale_y_log10() +
  xlab("Cumulative number of deaths") +
  ylab("Daily number of deaths") +
  geom_text_repel(aes(label=countriesAndTerritories, color=countriesAndTerritories),
 function(d) d[d$dateRep == format(Sys.time(),"%Y-%m-%d"),]) +
theme_minimal(base_size=14) +
 theme(legend.position = "none") 
#+
#  geom_point(data=filter(df, countriesAndTerritories == "Italy", dateRep=format(Sys.time(),"%Y-%m-%d")))
g
```

Let's now do the same for another subset of countries.

```{r, fig.height=6, fig.width=8, echo=FALSE}
library(dplyr)
my.countries <- c("US","AT","SE","CZ","IT","ES","DE","FR","CA","AU","KR","NZ","DK","BR","EC","CL")

g <- 
  ggplot(filter(df, geoId %in% my.countries, deaths>0, cumsum.deaths>=10), aes(cumsum.deaths, deaths)) +
  geom_line(aes(group=countriesAndTerritories, color=countriesAndTerritories)) +
  scale_x_log10() +
  scale_y_log10() +
  xlab("Cumulative number of deaths") +
  ylab("Daily number of deaths") +
  geom_text_repel(aes(label=countriesAndTerritories, color=countriesAndTerritories),
 function(d) d[d$dateRep == format(Sys.time(),"%Y-%m-%d"),]) +
theme_minimal(base_size=14) +
 theme(legend.position = "none") 
g
```


## Progression since 100 confirmed cases 
Present the number of cumulative cases starting on the date when 100 or more cases were recorded in each country, and use a logarithmic scale for the y axis. 

```{r, fig.height=6, fig.width=8, echo=FALSE}
first.day.100.cases <- aggregate(dateRep~countriesAndTerritories, data=df[which(df$cumsum.cases>=100),],min)
first.day.10.deaths <- aggregate(dateRep~countriesAndTerritories, data=df[which(df$cumsum.deaths>=10),],min)
df2 <- merge(merge(df, first.day.100.cases, by="countriesAndTerritories"), first.day.10.deaths, by="countriesAndTerritories")
names(df2)[c(2,17,18)] <- c("dateRep","date.first.100.cases","date.first.10.deaths")
df2$days.since.100.cases <- df2$dateRep - df2$date.first.100.cases
df2$days.since.10.deaths <- df2$dateRep - df2$date.first.10.deaths


n <- df2 %>% filter(dateRep == format(Sys.time(),"%Y-%m-%d")) %>%
 top_n(20, cumsum.cases) %>%
 arrange(desc(cumsum.cases))

g<-
df2 %>%
  filter(countriesAndTerritories %in% n$countriesAndTerritories, as.numeric(df2$days.since.100.cases)>0) %>%
  ggplot(aes(as.numeric(days.since.100.cases), cumsum.cases, group=countriesAndTerritories, color=countriesAndTerritories)) +
 geom_line() +
 theme_minimal(base_size=14) +
  ylab("Cumulative confirmed number of cases") +
  ggtitle("Top 20 countries - cumulative") +
 geom_text_repel(aes(label=countriesAndTerritories),
 function(d) d[d$dateRep == format(Sys.time(),"%Y-%m-%d"),]) +
 theme_minimal(base_size=14) +
 theme(legend.position = "none")


#g
# and in log space
g + scale_y_log10() 

```

And do the same for the number of cumulative cases per one million people.

```{r, fig.height=6, fig.width=8, echo=FALSE}
g<-
df2 %>%
  filter(countriesAndTerritories %in% n$countriesAndTerritories, as.numeric(df2$days.since.100.cases)>0) %>%
  ggplot(aes(as.numeric(days.since.100.cases), cases.per.e06, group=countriesAndTerritories, color=countriesAndTerritories)) +
 geom_line() +
 theme_minimal(base_size=14) +
  ylab("Cumulative cases per million people") +
  ggtitle("Top 20 countries - cumulative") +
 geom_text_repel(aes(label=countriesAndTerritories),
 function(d) d[d$dateRep == format(Sys.time(),"%Y-%m-%d"),]) +
 theme_minimal(base_size=14) +
 theme(legend.position = "none")


#g
# and in log space
g + scale_y_log10() 

```

## Country-level summaries
How are different countries doing? I am testing a function that takes a country as an argument and fits both an exponential growth and a logistic growth model to the number of cumulative cases.

```{r, fig.height=6, fig.width=8, echo=FALSE}
my.logistic.fct <- function(a=100, b=0.1, c=1E03, ti){
  out <- c / (1 + (((c-a)/a)*exp(-b*ti)))
  return(out)
}


country.deaths.fct <- function(g.id){
  this.df <- filter(df2, geoId==g.id, cumsum.deaths>=10)

  ## 15 deaths per one million as a starting value for the asymptote c
  c.init <- 15 * (unique(this.df$popData2018)/1E06)
  #a.init <- c.init/100
    
  my.lm <- lm(log(cumsum.deaths)~days.since.10.deaths, data=this.df)
  pred.lm <- data.frame(dateRep=this.df$dateRep, cumsum.deaths=exp(fitted(my.lm)))

  initial.num.deaths <- this.df[as.numeric(this.df$days.since.10.deaths)==0,"cumsum.deaths"]
  
  my.logistic <- nls(cumsum.deaths ~ my.logistic.fct(a=initial.num.deaths, b, c, as.numeric(days.since.10.deaths)), data=this.df, start=list(b=0.34,c=c.init))
  logistic.pred <- data.frame(dateRep=this.df$dateRep, days.since.10.deaths=as.numeric(this.df$days.since.10.deaths), cumsum.deaths=fitted(my.logistic))
  ## inflection point
  t50 <- (log((coef(my.logistic)[2]-initial.num.deaths)/initial.num.deaths) - log(1))/coef(my.logistic)[1]
  n50 <- my.logistic.fct(a=initial.num.deaths, coef(my.logistic)[1], coef(my.logistic)[2], ti=t50)
  logistic.text <- paste0("Inflection point: ", round(t50,0), " days and ", round(n50,0), " deaths")
  
  country.name <- paste0(as.character(unique(this.df$countriesAndTerritories)), " - ", format(max(this.df$cumsum.deaths),big.mark=","), " cumulative deaths")
    
  
  g<-ggplot(this.df, aes(dateRep, cumsum.deaths)) +
    geom_line(aes(color="data")) +
    geom_point(aes(color="data")) +
    geom_line(data=pred.lm, aes(dateRep, cumsum.deaths, color="exponential model"), linetype=2) +
    geom_line(data=logistic.pred, aes(dateRep, cumsum.deaths, color="logistic model"), linetype=1) +
    guides(color=guide_legend("Model type")) +
    ggtitle(country.name) +
    geom_point(aes(x=min(dateRep)+t50, y=n50)) +
    annotate("text",x=min(this.df$dateRep)+(as.numeric(diff(range(this.df$dateRep)))*0.4), y=n50, label=logistic.text) +
    ylim(0,max(this.df$cumsum.deaths)*1.2)

  g
    
}

country.deaths.fct("IT")
country.deaths.fct("ES")
country.deaths.fct("US")
country.deaths.fct("FR")
country.deaths.fct("IR")
country.deaths.fct("UK")
country.deaths.fct("BE")
country.deaths.fct("CH")
country.deaths.fct("CA")
country.deaths.fct("CL")
```

```{r, fig.height=6, fig.width=8, echo=FALSE}

country.cases.fct <- function(g.id){
  this.df <- filter(df2, geoId==g.id, cumsum.cases>=100)

  ## 1500 cases per one million as a starting value for the asymptote c
  c.init <- 1500 * (unique(this.df$popData2018)/1E06)
  #a.init <- c.init/100
    
  my.lm <- lm(log(cumsum.cases)~days.since.100.cases, data=this.df)
  pred.lm <- data.frame(dateRep=this.df$dateRep, cumsum.cases=exp(fitted(my.lm)))
  
  initial.num.cases <- this.df[as.numeric(this.df$days.since.100.cases)==0,"cumsum.cases"]
  my.logistic <- nls(cumsum.cases ~ my.logistic.fct(a=initial.num.cases, b,c,as.numeric(days.since.100.cases)), data=this.df, start=list(b=0.4,c=c.init))
  logistic.pred <- data.frame(dateRep=this.df$dateRep, days.since.100.cases=as.numeric(this.df$days.since.100.cases), cumsum.cases=fitted(my.logistic))
  ## inflection point
  t50 <- (log((coef(my.logistic)[2]-initial.num.cases)/initial.num.cases) - log(1))/coef(my.logistic)[1]
  n50 <- my.logistic.fct(a=initial.num.cases, coef(my.logistic)[1], coef(my.logistic)[2], ti=t50)
  logistic.text <- paste0("Inflection point: ", round(t50,0), " days and ", round(n50,0), " cases")
  
  country.name <- paste0(as.character(unique(this.df$countriesAndTerritories)), " - ", format(max(this.df$cumsum.cases),big.mark=","), " cumulative cases")
    
  
  g<-ggplot(this.df, aes(dateRep, cumsum.cases)) +
    geom_line(aes(color="data")) +
    geom_point(aes(color="data")) +
    geom_line(data=pred.lm, aes(dateRep, cumsum.cases, color="exponential model"), linetype=2) +
    geom_line(data=logistic.pred, aes(dateRep, cumsum.cases, color="logistic model"), linetype=1) +
    guides(color=guide_legend("Model type")) +
    ggtitle(country.name) +
    geom_point(aes(x=min(dateRep)+t50, y=n50)) +
    annotate("text",x=min(this.df$dateRep)+(as.numeric(diff(range(this.df$dateRep)))*0.4), y=n50, label=logistic.text) +
    ylim(0,max(this.df$cumsum.cases)*1.2)

  g
    
}


country.cases.fct("US")
country.cases.fct("IT")
country.cases.fct("ES")
country.cases.fct("CN")
country.cases.fct("DE")
country.cases.fct("FR")
country.cases.fct("IR")
country.cases.fct("UK")
country.cases.fct("CH")
country.cases.fct("TR")
country.cases.fct("BE")
country.cases.fct("NL")
country.cases.fct("AT")
country.cases.fct("KR")
country.cases.fct("CA")
country.cases.fct("PT")
country.cases.fct("BR")
country.cases.fct("IL")
country.cases.fct("AU")
country.cases.fct("NO")
country.cases.fct("CL")

#country.cases.fct("CZ")



#test.df <- data.frame(
#  ti=0:50)
#test.df$y <- my.logistic.fct(a=10, b=0.2, c=1E03, ti=test.df$ti)

#(log(100) - log(1))/0.2
#test.df[test.df$ti==23,]
```



