Corona_Prediction.Rmd

---
title: "Corona_Analysis"
author: "Steven Smith, PhD"
date: "3/18/2020"
output:
  html_document:
    toc: yes
  pdf_document:
    toc: yes
---

# The 2019-2020 Coronavirus Pandemic Analysis
Contact: [Smith Research](https://stevenbsmith.net) 

## BACKGROUND & APPROACH
I wanted to track and trend the coronavirus outbreak on my own curiosity. There are some interesting questions that may fall out of this, as it is a very historic moment, including scientifically and analytically (we have a large amount of data being shared across the globe, analyzed in real-time). The world has come to a halt because of it.  
This analysis attempts to answer the following questions (more to come):


1. What does the trend of the pandemic look like to date?  
2. What are future case predictions based on historical model?
3. What interesting quirks or patterns emerge?  



ASSUMPTIONS & LIMITATIONS: 
* This data is limited by the source. I realized early on that depending on source there were conflicting # of cases. Originally I was using JHU data... but this was always 'ahead' of the Our World In Data. I noticed that JHU's website was buggy- you clicked on the U.S. stats but it didn't reflect the U.S.. So I changed data sources to be more consistent with what is presented in the media (and Our World In Data has more extensive plots I can compare my own to). An interesting aside might be why the discrepancy? Was I missing something?  
* Defintiions are important as is the idea that multiple varibales accumulate in things like total cases (more testing for example). 

SOURCE RAW DATA: 
* https://ourworldindata.org/coronavirus  
* https://github.com/CSSEGISandData/COVID-19/   
* <mobility>  

INPUT DATA LOCATION: github (https://github.com/sbs87/coronavirus/tree/master/data)  

OUTPUT DATA LOCATIOn: github (https://github.com/sbs87/coronavirus/tree/master/results)  


## TIMESTAMP
Start: `r paste(timestamp())`

## PRE-ANALYSIS
The following sections are outside the scope of the 'analysis' but are still needed to prepare everything

### UPSTREAM PROCESSING/ANALYSIS
1. Google Mobility Scraping, script available at [get_google_mobility.py](https://github.com/sbs87/coronavirus/blob/master/get_google_mobility.py) 
```{bash process_remote_server, eval=F,tidy=T}
# Mobility data has to be extracted from Google PDF reports using a web scraping script (python , written by Peter Simone, https://github.com/petersim1/MIT_COVID19)

# See get_google_mobility.py for local script 

python3 get_google_mobility.py
# writes csv file of mobility data as "mobility.csv"

# TODO: customize get_google_mobility.py script, add arguments

```

### SET UP ENVIORNMENT
Load libraries and set global variables
```{r setup, eval=T,collapse=T,tidy=T}
#timestamp start
timestamp()

# clear previous enviornment
rm(list = ls())

##------------------------------------------
## LIBRARIES
##------------------------------------------
library(plyr)
library(tidyverse)
library(ggplot2)
library(reshape2)
library(plot.utils)
library(utils)
library(knitr)

##------------------------------------------

##------------------------------------------
# GLOBAL VARIABLES
##------------------------------------------
user_name<-Sys.info()["user"]
working_dir<-paste0("/Users/",user_name,"/Projects/coronavirus/") # don't forget trailing /
results_dir<-paste0(working_dir,"results/") # assumes diretory exists
results_dir_custom<-paste0(results_dir,"custom/") # assumes diretory exists


Corona_Cases.source_url<-"https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv"
Corona_Cases.US.source_url<-"https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_US.csv"
Corona_Deaths.US.source_url<-"https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_US.csv"
Corona_Deaths.source_url<-"https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_global.csv"

Corona_Cases.fn<-paste0(working_dir,"data/",basename(Corona_Cases.source_url))
Corona_Cases.US.fn<-paste0(working_dir,"data/",basename(Corona_Cases.US.source_url))
Corona_Deaths.fn<-paste0(working_dir,"data/",basename(Corona_Deaths.source_url))
Corona_Deaths.US.fn<-paste0(working_dir,"data/",basename(Corona_Deaths.US.source_url))
default_theme<-theme_bw()+theme(text = element_text(size = 14)) # fix this
##------------------------------------------

```
### FUNCTIONS
List of functions

function_name | description
------------- | -----------
prediction_model |  outputs case estumate for given log-linear moder parameters slope and intercept 
make_long        |  converts input data to long format (specialized cases)
name_overlaps    |  outputs the column names intersection and set diffs of two data frame


```{r functions, eval=T}
##------------------------------------------
## FUNCTION: prediction_model
##------------------------------------------
## --- //// ----
# Takes days vs log10 (case) linear model parameters and a set of days since 100 cases and outputs a dataframe with total number of predicted cases for those days
## --- //// ----
prediction_model<-function(m=1,b=0,days=1){
  total_cases.log<-m*days+b
  total_cases<-10^total_cases.log
  prediction<-data.frame(Days_since_100=days,Total_confirmed_cases=total_cases,Total_confirmed_cases.log=total_cases.log)
  return(prediction)
}
##------------------------------------------

##------------------------------------------
## FUNCTION: make_long
##------------------------------------------
## --- //// ----
# Takes wide-format case data and converts into long format, using date and total cases as variable/values. Also enforces standardization/assumes data struture naming by using fixed variable name, value name, id.vars, 
## --- //// ----
make_long<-function(data_in,variable.name = "Date",
                   value.name = "Total_confirmed_cases",
                   id.vars=c("case_type","Province.State","Country.Region","Lat","Long","City","Population")){

long_data<-melt(data_in,
                id.vars = id.vars,
                variable.name=variable.name,
                value.name=value.name)
return(long_data)

}
##------------------------------------------

## THIS WILL BE IN UTILS AT SOME POINT
name_overlaps<-function(df1,df2){
i<-intersect(names(df1),
names(df2))
sd1<-setdiff(names(df1),
names(df2))
sd2<-setdiff(names(df2),names(df1))
cat("intersection:\n",paste(i,"\n"))
cat("in df1 but not df2:\n",paste(sd1,"\n"))
cat("in df2 but not df1:\n",paste(sd2,"\n"))
return(list("int"=i,"sd_1_2"=sd1,"sd_2_1"=sd2))
}

```



### READ IN DATA
* total number of cases. current source: https://github.com/CSSEGISandData (precvious source https://ourworldindata.org/coronavirus)

```{r read_in_data, eval=T,tidy=T}
# Q: do we want to archive previous versions? Maybe an auto git mv? 

##------------------------------------------
## Download and read in latest data from github
##------------------------------------------
download.file(Corona_Cases.source_url,destfile = Corona_Cases.fn)
Corona_Totals.raw<-read.csv(Corona_Cases.fn,header = T,stringsAsFactors = F)

download.file(Corona_Cases.US.source_url,destfile = Corona_Cases.US.fn)
Corona_Totals.US.raw<-read.csv(Corona_Cases.US.fn,header = T,stringsAsFactors = F)

download.file(Corona_Deaths.source_url,destfile = Corona_Deaths.fn)
Corona_Deaths.raw<-read.csv(Corona_Deaths.fn,header = T,stringsAsFactors = F)

download.file(Corona_Deaths.US.source_url,destfile = Corona_Deaths.US.fn)
Corona_Deaths.US.raw<-read.csv(Corona_Deaths.US.fn,header = T,stringsAsFactors = F)

#latest date on all data:
paste("US deaths:",names(Corona_Deaths.US.raw)[ncol(Corona_Deaths.US.raw)])
paste("US total:",names(Corona_Totals.US.raw)[ncol(Corona_Totals.US.raw)])
paste("World deaths:",names(Corona_Deaths.raw)[ncol(Corona_Deaths.raw)])
paste("World total:",names(Corona_Totals.raw)[ncol(Corona_Totals.raw)])
```


### PROCESS DATA
* Convert to long format  
* Fix date formatting/convert to numeric date  
* Log10 transform total # cases  

```{r process, eval=T}

##------------------------------------------
## Combine death and total data frames
##------------------------------------------
Corona_Totals.raw$case_type<-"total"
Corona_Totals.US.raw$case_type<-"total"
Corona_Deaths.raw$case_type<-"death"
Corona_Deaths.US.raw$case_type<-"death"

# for some reason, Population listed in US death file but not for other data... Weird. When combining, all datasets will have this column, but US deaths is the only useful one.  
Corona_Totals.US.raw$Population<-"NA" 
Corona_Totals.raw$Population<-"NA"
Corona_Deaths.raw$Population<-"NA"

Corona_Cases.raw<-rbind(Corona_Totals.raw,Corona_Deaths.raw)
Corona_Cases.US.raw<-rbind(Corona_Totals.US.raw,Corona_Deaths.US.raw)
#TODO: custom utils- setdiff, intersect names... option to output in merging too
##------------------------------------------
# prepare raw datasets for eventual combining
##------------------------------------------
Corona_Cases.raw$City<-"NA" # US-level data has Cities
Corona_Cases.US.raw$Country_Region<-"US_state" # To differentiate from World-level stats

Corona_Cases.US.raw<-plyr::rename(Corona_Cases.US.raw,c("Province_State"="Province.State",
                                                  "Country_Region"="Country.Region",
                                                  "Long_"="Long",
                                                  "Admin2"="City"))


##------------------------------------------
## Convert to long format
##------------------------------------------
#JHU has a gross file format. It's in wide format with each column is the date in MM/DD/YY. So read this in as raw data but trasnform it to be better suited for analysis
# Furthermore, the World and US level data is formatted differently, containing different columns, etc. Recitfy this and combine the world-level stats with U.S. level stats.

Corona_Cases.long<-rbind(make_long(select(Corona_Cases.US.raw,-c(UID,iso2,iso3,code3,FIPS,Combined_Key))),
make_long(Corona_Cases.raw))


##------------------------------------------
## Fix date formatting, convert to numeric date
##------------------------------------------
Corona_Cases.long$Date<-gsub(Corona_Cases.long$Date,pattern = "^X",replacement = "0") # leading 0 read in as X
Corona_Cases.long$Date<-gsub(Corona_Cases.long$Date,pattern = "20$",replacement = "2020") # ends in .20 and not 2020
Corona_Cases.long$Date<-as.Date(Corona_Cases.long$Date,format = "%m.%d.%y")
Corona_Cases.long$Date.numeric<-as.numeric(Corona_Cases.long$Date)

kable(table(select(Corona_Cases.long,c("Country.Region","case_type"))),caption = "Number of death and total case longitudinal datapoints per geographical region")


# Decouple population and lat/long data, refactor to make it more tidy
metadata_columns<-c("Lat","Long","Population")
metadata<-unique(select(filter(Corona_Cases.long,case_type=="death"),c("Country.Region","Province.State","City",all_of(metadata_columns))))
Corona_Cases.long<-select(Corona_Cases.long,-all_of(metadata_columns))

# Some counties are not summarized on the country level. collapse all but US
Corona_Cases.long<-rbind.fill(ddply(filter(Corona_Cases.long,!Country.Region=="US_state"),c("case_type","Country.Region","Date","Date.numeric"),summarise,Total_confirmed_cases=sum(Total_confirmed_cases)),filter(Corona_Cases.long,Country.Region=="US_state"))

# Put total case and deaths side-by-side (wide)
Corona_Cases<-spread(Corona_Cases.long,key = case_type,value = Total_confirmed_cases)

#Compute moratlity rate
Corona_Cases$mortality_rate<-Corona_Cases$death/Corona_Cases$total

#TMP
Corona_Cases<-plyr::rename(Corona_Cases,c("total"="Total_confirmed_cases","death"="Total_confirmed_deaths"))

##------------------------------------------
## log10 transform total # cases
##------------------------------------------
Corona_Cases$Total_confirmed_cases.log<-log(Corona_Cases$Total_confirmed_cases,10)
Corona_Cases$Total_confirmed_deaths.log<-log(Corona_Cases$Total_confirmed_deaths,10)
##------------------------------------------
       
##------------------------------------------
## Compute # of days since 100th for US data
##------------------------------------------

# Find day that 100th case was found for Country/Province. NOTE: Non US countries may have weird provinces. For example, Frane is summairzed at the country level but also had 3 providences. I've only ensured the U.S. case100 works... so the case100_date for U.S. is summarized both for the entire country (regardless of state) and on a per-state level. 
# TODO: consider city-level summary as well. This data may be sparse

Corona_Cases<-merge(Corona_Cases,ddply(filter(Corona_Cases,Total_confirmed_cases>100),c("Country.Region"),summarise,case100_date=min(Date.numeric)))
Corona_Cases$Days_since_100<-Corona_Cases$Date.numeric-Corona_Cases$case100_date

##------------------------------------------
## Add population and lat/long data (CURRENTLY US ONLY)
##------------------------------------------
# TODO Add population data for non US cities/regions
kable(filter(metadata,(is.na(Country.Region) | is.na(Population) )) %>% select(c("Country.Region","Province.State","City")) %>% unique(),caption = "Regions for which either population or Country is NA")

# Drop missing data 
metadata<-filter(metadata,!(is.na(Country.Region) | is.na(Population) ))
# Convert remaining pop to numeric
metadata$Population<-as.numeric(metadata$Population)

# Add metadata to cases
Corona_Cases<-merge(Corona_Cases,metadata,all.x = T)

##------------------------------------------
## Compute total and death cases relative to population 
##------------------------------------------

Corona_Cases$Total_confirmed_cases.per100<-100*Corona_Cases$Total_confirmed_cases/Corona_Cases$Population
Corona_Cases$Total_confirmed_deaths.per100<-100*Corona_Cases$Total_confirmed_deaths/Corona_Cases$Population


##------------------------------------------
## Filter df for US state-wide stats
##------------------------------------------

Corona_Cases.US_state<-filter(Corona_Cases,Country.Region=="US_state" & Total_confirmed_cases>0 ) 
kable(table(select(Corona_Cases.US_state,c("Province.State"))),caption = "Number of longitudinal datapoints (total/death) per state")
Corona_Cases.US_state<-merge(Corona_Cases.US_state,ddply(filter(Corona_Cases.US_state,Total_confirmed_cases>100),c("Province.State"),summarise,case100_date_state=min(Date.numeric)))
Corona_Cases.US_state$Days_since_100_state<-Corona_Cases.US_state$Date.numeric-Corona_Cases.US_state$case100_date_state


```
## ANALYSIS
 
### Q1: What is the trend in cases, mortality across geopgraphical regions?
Plot # of cases vs time   
* For each geographical set:  
* comparative longitudinal case trend (absolute & log scale)    
* comparative longitudinal mortality trend    
* death vs total correlation    


question | dataset | x | y | color | facet | pch | dimentions  
-------- | ------- | - | - | ----- | ----- | --- | ----------   
comparative_longitudinal_case_trend | long | time | log_cases | geography | none (case type?) | case_type | [15, 50, 4] geography x (2 scale?) case type  
comparative longitudinal case trend|long|time|cases|geography|case_type|?|[15, 50, 4] geography x (2+ scale) case type    
comparative longitudinal mortality trend|wide|time|mortality rate|geography|none|none|[15, 50, 4] geography    
death vs total correlation|wide|cases|deaths|geography|none|none|[15, 50, 4] geography    

```{r, eval=T}
# total cases vs time
# death cases vs time
# mortality rate vs time
# death vs mortality


  # death vs mortality
  # total & death case vs time (same plot)

#<question> <x> <y> <colored> <facet> <dataset>
## trend in case/deaths over time, comapred across regions <time> <log cases> <geography*> <none> <.wide>
## trend in case/deaths over time, comapred across regions <time> <cases> <geography*> <case_type> <.long>
## trend in mortality rate over time, comapred across regions <time> <mortality rate> <geography*> <none>
## how are death/mortality related/correlated? <time> <log cases> <geography*> <none>
## how are death and case load correlated? <cases> <deaths>

# lm for each?? - > apply lm from each region starting from 100th case. m, b associated with each.
    # input: geographical regsion, logcase vs day (100th case)
    # output: m, b for each geographical region ID



#total/death on same plot-  diffeer by 2 logs, so when plotting log, use pch. when plotting absolute, need to use free scales
#when plotting death and case on same, melt. 

#CoronaCases - > filter sets (3)
  #world - choose countries with sufficent data

N<-ddply(filter(Corona_Cases,Total_confirmed_cases>100),c("Country.Region"),summarise,n=length(Country.Region))
ggplot(filter(N,n<100),aes(x=n))+
  geom_histogram()+
  default_theme+
  ggtitle("Distribution of number of days with at least 100 confirmed cases for each region")

kable(arrange(N,-n),caption="Sorted number of days with at least 100 confirmed cases")
# Pick top 15 countries with data
max_colors<-12
# find way to fix this- China has diff provences. Plot doesnt look right...
sufficient_data<-arrange(filter(N,!Country.Region %in% c("US_state", "Diamond Princess")),-n)[1:max_colors,]
kable(sufficient_data,caption = paste0("Top ",max_colors," countries with sufficient data"))
Corona_Cases.world<-filter(Corona_Cases,Country.Region %in% c(sufficient_data$Country.Region))


  #us 
  #    - by state
Corona_Cases.US<-filter(Corona_Cases,Country.Region=="US" & Total_confirmed_cases>0)
# summarize 
#!City %in% c("Unassigned") 
  #    - specific cities
#mortality_rate!=Inf & mortality_rate<=1
Corona_Cases.UScity<-filter(Corona_Cases,Province.State %in% c("Pennsylvania","Maryland","New York","New Jersey") & City %in% c("Bucks","Baltimore City", "New York","Burlington"))

measure_vars_long<-c("Total_confirmed_cases.log","Total_confirmed_cases","Total_confirmed_deaths","Total_confirmed_deaths.log")
melt_arg_list<-list(variable.name = "case_type",value.name = "cases",measure.vars = c("Total_confirmed_cases","Total_confirmed_deaths"))
melt_arg_list$data=NULL


melt_arg_list$data=select(Corona_Cases.world,-ends_with(match = "log"))
Corona_Cases.world.long<-do.call(melt,melt_arg_list)
melt_arg_list$data=select(Corona_Cases.UScity,-ends_with(match = "log"))
Corona_Cases.UScity.long<-do.call(melt,melt_arg_list)
melt_arg_list$data=select(Corona_Cases.US_state,-ends_with(match = "log"))
Corona_Cases.US_state.long<-do.call(melt,melt_arg_list)

Corona_Cases.world.long$cases.log<-log(Corona_Cases.world.long$cases,10)
Corona_Cases.US_state.long$cases.log<-log(Corona_Cases.US_state.long$cases,10)
Corona_Cases.UScity.long$cases.log<-log(Corona_Cases.UScity.long$cases,10)


# what is the current death and total case load for US? For world? For states?
#-absolute
#-log

# what is mortality rate (US, world)
#-absolute

#how is death and case correlated? (US, world)
#-absolute

```

```{r question1, eval=T}


#Corona_Cases.US<-filter(Corona_Cases,Country.Region=="US" & Total_confirmed_cases>0)
#Corona_Cases.US.case100<-filter(Corona_Cases.US, Days_since_100>=0)
# linear model parameters
#(model_fit<-lm(formula = Total_confirmed_cases.log~Days_since_100,data= Corona_Cases.US.case100 ))

#(slope<-model_fit$coefficients[2])
#(intercept<-model_fit$coefficients[1])

# Correlation coefficient
#cor(x = Corona_Cases.US.case100$Days_since_100,y = Corona_Cases.US.case100$Total_confirmed_cases.log)

##------------------------------------------
## Plot World Data
##------------------------------------------
# Timestamp for world
timestamp_plot.world<-paste("Most recent date for which data available:",max(Corona_Cases.world$Date))#timestamp(quiet = T,prefix = "Updated ",suffix = " (EST)")


# Base template for plots
baseplot.world<-ggplot(data=NULL,aes(x=Days_since_100,col=Country.Region))+
  default_theme+
  scale_color_brewer(type = "qualitative",palette = "Paired")+
  ggtitle(paste("Log10 cases over time,",timestamp_plot.world))+
  theme(legend.position = "bottom",plot.title = element_text(size=12))


##/////////////////////////
### Plot Longitudinal cases

(Corona_Cases.world.long.plot<-baseplot.world+
    geom_point(data=Corona_Cases.world.long,aes(y=cases))+
    geom_line(data=Corona_Cases.world.long,aes(y=cases))+
    facet_wrap(~case_type,scales = "free_y",ncol=1)+
    ggtitle(timestamp_plot.world)
    )

(Corona_Cases.world.loglong.plot<-baseplot.world+
    geom_point(data=Corona_Cases.world.long,aes(y=cases.log))+
    geom_line(data=Corona_Cases.world.long,aes(y=cases.log))+
    facet_wrap(~case_type,scales = "free_y",ncol=1)+
    ggtitle(timestamp_plot.world))

##/////////////////////////
### Plot Longitudinal mortality rate

(Corona_Cases.world.mortality.plot<-baseplot.world+
    geom_point(data=Corona_Cases.world,aes(y=mortality_rate))+
    geom_line(data=Corona_Cases.world,aes(y=mortality_rate))+
    ylim(c(0,0.3))+
    ggtitle(timestamp_plot.world))

##/////////////////////////
### Plot death vs total case correlation

(Corona_Cases.world.casecor.plot<-ggplot(Corona_Cases.world,aes(x=Total_confirmed_cases,y=Total_confirmed_deaths,col=Country.Region))+
  geom_point()+
  geom_line()+
  default_theme+
  scale_color_brewer(type = "qualitative",palette = "Paired")+
  ggtitle(paste("Log10 cases over time,",timestamp_plot.world))+
  theme(legend.position = "bottom",plot.title = element_text(size=12))+
    ggtitle(timestamp_plot.world))

### Write polots

write_plot(Corona_Cases.world.long.plot,wd = results_dir)
write_plot(Corona_Cases.world.loglong.plot,wd = results_dir)
write_plot(Corona_Cases.world.mortality.plot,wd = results_dir)
write_plot(Corona_Cases.world.casecor.plot,wd = results_dir)


##------------------------------------------
## Plot US State Data
##-----------------------------------------

baseplot.US<-ggplot(data=NULL,aes(x=Days_since_100_state,col=case_type))+
  default_theme+
  facet_wrap(~Province.State)+
  ggtitle(paste("Log10 cases over time,",timestamp_plot.world))

Corona_Cases.US_state.long.plot<-baseplot.US+geom_point(data=Corona_Cases.US_state.long,aes(y=cases.log))
##------------------------------------------
## Plot US City Data
##-----------------------------------------

Corona_Cases.US.plotdata<-filter(Corona_Cases.US_state,Province.State %in% c("Pennsylvania","Maryland","New York","New Jersey") &
                                   City %in% c("Bucks","Baltimore City", "New York","Burlington") &
                                   Total_confirmed_cases>0) 
timestamp_plot<-paste("Most recent date for which data available:",max(Corona_Cases.US.plotdata$Date))#timestamp(quiet = T,prefix = "Updated ",suffix = " (EST)")

city_colors<-c("Bucks"='#beaed4',"Baltimore City"='#386cb0', "New York"='#7fc97f',"Burlington"='#fdc086')

##/////////////////////////
### Plot death vs total case correlation

(Corona_Cases.city.loglong.plot<-ggplot(melt(Corona_Cases.US.plotdata,measure.vars = c("Total_confirmed_cases.log","Total_confirmed_deaths.log"),variable.name = "case_type",value.name = "cases"),aes(x=Date,y=cases,col=City,pch=case_type))+
  geom_point(size=4)+
    geom_line()+
  default_theme+
  #facet_wrap(~case_type)+
    ggtitle(paste("Log10 total and death cases over time,",timestamp_plot))+
theme(legend.position = "bottom",plot.title = element_text(size=12))+
    scale_color_manual(values = city_colors))


(Corona_Cases.city.long.plot<-ggplot(filter(Corona_Cases.US.plotdata,Province.State !="New York"),aes(x=Date,y=Total_confirmed_cases,col=City))+
  geom_point(size=4)+
  geom_line()+
  default_theme+
  facet_grid(~Province.State,scales = "free_y")+
  ggtitle(paste("MD, PA, NJ total cases over time,",timestamp_plot))+
  theme(legend.position = "bottom",plot.title = element_text(size=12))+
  scale_color_manual(values = city_colors))


(Corona_Cases.city.mortality.plot<-ggplot(Corona_Cases.US.plotdata,aes(x=Date,y=mortality_rate,col=City))+
  geom_point(size=3)+
  geom_line(size=2)+
  default_theme+
  ggtitle(paste("Mortality rate (deaths/total) over time,",timestamp_plot))+
  theme(legend.position = "bottom",plot.title = element_text(size=12))+
  scale_color_manual(values = city_colors))


(Corona_Cases.city.casecor.plot<-ggplot(filter(Corona_Cases.US.plotdata,Province.State !="New York"),aes(x=Total_confirmed_deaths,y=Total_confirmed_cases,col=City))+
  geom_point(size=3)+
  geom_line(size=2)+
  default_theme+
  ggtitle(paste("Correlation of death vs total cases,",timestamp_plot))+
  theme(legend.position = "bottom",plot.title = element_text(size=12))+
  scale_color_manual(values = city_colors))


(Corona_Cases.city.long.normalized.plot<-ggplot(filter(Corona_Cases.US.plotdata,Province.State !="New York"),aes(x=Date,y=Total_confirmed_cases.per100,col=City))+
  geom_point(size=4)+
  geom_line()+
  default_theme+
  facet_grid(~Province.State)+
  ggtitle(paste("MD, PA, NJ total cases over time per 100 people,",timestamp_plot))+
  theme(legend.position = "bottom",plot.title = element_text(size=12))+
  scale_color_manual(values = city_colors))

write_plot(Corona_Cases.city.long.plot,wd = results_dir_custom)
write_plot(Corona_Cases.city.loglong.plot,wd = results_dir_custom)
write_plot(Corona_Cases.city.mortality.plot,wd = results_dir_custom)
write_plot(Corona_Cases.city.casecor.plot,wd = results_dir_custom)
write_plot(Corona_Cases.city.long.normalized.plot,wd = results_dir_custom)

```
### Q2: What is the predicted number of cases?

#### What is the prediction of COVID-19 based on model thus far?
Additional questions:

WHy did it take to day 40 to start a log linear trend?
How long will it be till x number of cases?
When will the plateu happen?
Are any effects noticed with social distancing? Delays
```{r prediction, eval=F}

##------------------------------------------
## Prediction and Prediction Accuracy
##------------------------------------------

# What is the predict # of cases for the next few days?
# How is the model performing historically?

# Formula for # of cases by x days
paste0("log10_total_cases = ",slope,"*days + ",intercept)
paste0("total_cases = 10^(",slope,"*days + ",intercept,")")
#Days untill... cases:
# 2.5k, 5k and 1M:
paste0("2.5k cases is ",(log(2.5E5,10) - intercept)/slope," days")
paste0("5k cases is ",(log(5E5,10)- intercept)/slope," days")
paste0("1M cases is ",(log(1E6,10)- intercept)/slope," days")

head(filter(Corona_Cases.raw,Country.Region=="US"))
today_num<-max(Corona_Cases.US$Days_since_100)
predicted_days<-today_num+c(1,2,3,7)

#mods = dlply(mydf, .(x3), lm, formula = y ~ x1 + x2)
#today:
Corona_Cases.US[Corona_Cases.US$Days_since_100==(today_num-1),]
Corona_Cases.US[Corona_Cases.US$Days_since_100==today_num,]
Corona_Cases.US$type<-"Historical"
names(Corona_Cases)

Corona_Cases_wprediction<-rbind.fill(Corona_Cases.US,data.frame(Code="USA",type="MAR26_prediction",prediction_model(m=slope,b=intercept,days = predicted_days)))

Corona_Cases.US.prediction<-Corona_Cases_wprediction 
prediction_values<-prediction_model(m=slope,b=intercept,days = predicted_days)$Total_confirmed_cases

histoical_model<-data.frame(date=today_num,m=slope,b=intercept)

# model for previous y days
historical_model_predictions<-data.frame(day_x=NULL,Days_since_100=NULL,Total_confirmed_cases=NULL,Total_confirmed_cases.log=NULL)
for(i in c(1,2,3,4,5,6,7,8,9,10)){
  #i<-1
day_x<-today_num-i # 1, 2, 3, 4
day_x_nextweek<-day_x+c(1,2,3)
model_fit_x<-lm(data = filter(Corona_Cases.US.case100,Days_since_100 < day_x),formula = Total_confirmed_cases.log~Days_since_100)
prediction_day_x_nextweek<-prediction_model(m = model_fit_x$coefficients[2],b = model_fit_x$coefficients[1],days = day_x_nextweek)
prediction_day_x_nextweek$type<-"Predicted"
acutal_day_x_nextweek<-filter(Corona_Cases.US,Days_since_100 %in% day_x_nextweek) %>% select(c(Days_since_100,Total_confirmed_cases,Total_confirmed_cases.log))
acutal_day_x_nextweek$type<-"Historical"
historical_model_predictions.i<-data.frame(day_x=day_x,rbind(acutal_day_x_nextweek,prediction_day_x_nextweek))
historical_model_predictions<-rbind(historical_model_predictions.i,historical_model_predictions)
}

historical_model_predictions.withHx<-rbind.fill(historical_model_predictions,data.frame(Corona_Cases.US,type="Historical"))
historical_model_predictions.withHx$Total_confirmed_cases.log2<-log(historical_model_predictions.withHx$Total_confirmed_cases,2)
#TODO: fix case_type.. are we predicting deaths too?
#TODO: better analysis of death rate!
(historical_model_predictions.plot<-ggplot(historical_model_predictions.withHx,aes(x=Days_since_100,y=Total_confirmed_cases.log,col=type))+
    geom_point(size=3)+
    default_theme+
    theme(legend.position = "bottom")+ 
      #geom_abline(slope = slope,intercept =intercept,lty=2)+
    #facet_wrap(~case_type,ncol=1)+
    scale_color_manual(values = c("Historical"="#377eb8","Predicted"="#e41a1c")))
write_plot(historical_model_predictions.plot,wd=results_dir)
```


```{r question2, eval=F}

##------------------------------------------
## filter input_data1
##------------------------------------------
input_data1.filter<-fitler(input_data1,col1=="foo")
##------------------------------------------

##------------------------------------------
## sub question 1
##------------------------------------------
table(input_data1.filter$col<5)
##------------------------------------------

##------------------------------------------
## sub question 2
##------------------------------------------
table(input_data1.filter$col<10)
##------------------------------------------

##------------------------------------------
## plot data
##------------------------------------------
(input_data1.filter.plot<-ggplot(input_data1.filter,aes(x=col1,y=col2.log))+
   geom_point()+
   default_plot_theme)
write_plot(input_data1.filter.plot,wd=results_dir)
##------------------------------------------
results_dir
```

### Q3: What is the effect on social distancing, descreased mobility on case load?
Load data from Google which compoutes % change in user mobility relative to baseline for
* Recreation  
* Workplace  
* Residence  
* Park  
* Grocery  

Data from https://www.google.com/covid19/mobility/
```{r mobility, eval=T}
# See pre-processing section for script on gathering mobility data

# UNDER DEVELOPMENT
# TODO convert % to numeric in mobility data
# TODO standardize headers in mobility data
# TODO standardize counties in mobility data to JHU source
# TODO normalize case load to population for mobility data
# TODO automate get_mobility.py script so most recent data is availble 
mobility<-read.csv("/Users/stevensmith/Projects/MIT_COVID19/mobility.csv",header = T,stringsAsFactors = F)
#mobility$Retail_Recreation<-as.numeric(sub(mobility$Retail_Recreation,pattern = "%",replacement = ""))
#mobility$Workplace<-as.numeric(sub(mobility$Workplace,pattern = "%",replacement = ""))
#mobility$Residential<-as.numeric(sub(mobility$Residential,pattern = "%",replacement = ""))

##------------------------------------------
## Show relationship between mobility and caseload
##------------------------------------------
mobility$County<-gsub(mobility$County,pattern = " County",replacement = "")
Corona_Cases.US_state.mobility<-merge(Corona_Cases.US_state,plyr::rename(mobility,c("State"="Province.State","County"="City")))

#Corona_Cases.US_state.tmp<-merge(metadata,Corona_Cases.US_state.tmp)
# Needs to happen upsteam, see todos
#Corona_Cases.US_state.tmp$Total_confirmed_cases.perperson<-Corona_Cases.US_state.tmp$Total_confirmed_cases/as.numeric(Corona_Cases.US_state.tmp$Population)
mobility_measures<-c("Retail_Recreation","Grocery_Pharmacy","Parks","Transit","Workplace","Residential")

plot_data<-filter(Corona_Cases.US_state.mobility, Date.numeric==max(Corona_Cases.US_state$Date.numeric) ) %>% melt(measure.vars=mobility_measures) 
plot_data$value<-as.numeric(gsub(plot_data$value,pattern = "%",replacement = ""))
plot_data<-filter(plot_data,!is.na(value))

(mobility.plot<-ggplot(filter(plot_data,Province.State %in% c("Pennsylvania","Maryland","New Jersey","California","Delaware","Connecticut")),aes(y=Total_confirmed_cases.per100,x=value))+geom_point()+
  facet_grid(Province.State~variable,scales = "free")+
  xlab("Mobility change from baseline (%)")+
  ylab(paste0("Confirmed cases per 100 people(Today)"))+
  default_theme+
  ggtitle("Mobility change vs cases"))

(mobility.global.plot<-ggplot(plot_data,aes(y=Total_confirmed_cases.per100,x=value))+geom_point()+
  facet_wrap(~variable,scales = "free")+
  xlab("Mobility change from baseline (%)")+
  ylab(paste0("Confirmed cases (Today) per 100 people"))+
  default_theme+
  ggtitle("Mobility change vs cases"))


plot_data.permobility_summary<-ddply(plot_data,c("Province.State","variable"),summarise,cor=cor(y =Total_confirmed_cases.per100,x=value),median_change=median(x=value)) %>% arrange(-abs(cor))

kable(plot_data.permobility_summary,caption = "Ranked per-state mobility correlation with total confirmed cases")

# sanity check
ggplot(filter(plot_data,Province.State %in% c("Pennsylvania","Maryland","New Jersey","California","Delaware","Connecticut")),aes(x=Total_confirmed_cases.per100,fill=variable))+geom_histogram()+
  facet_grid(~Province.State)+
    default_theme+
  theme(legend.position = "bottom")

write_plot(mobility.plot,wd = results_dir)
write_plot(mobility.global.plot,wd = results_dir)

# TODO secondary question: rank greatest to least mobility

(plot_data.permobility_summary.plot<-ggplot(plot_data.permobility_summary,aes(x=variable,y=median_change))+
  geom_jitter(size=2,width=.2)+
  #geom_jitter(data=plot_data.permobility_summary %>% arrange(-abs(median_change)) %>% head(n=15),aes(col=Province.State),size=2,width=.2)+
  default_theme+
  ggtitle("Per-Sate Median Change in Mobility")+
  xlab("Mobility Meaure")+
  ylab("Median Change from Baseline"))
write_plot(plot_data.permobility_summary.plot,wd = results_dir)

```

# DELIVERABLE MANIFEST
The following link to commited documents pushed to github. These are provided as a convienence, but note this is a manual process. The generation of reports, plots and tables is not coupled to the execution of this markdown. 
## Report
This report, html & pdf

## Plots
```{r}
github_root<-"https://github.com/sbs87/coronavirus/blob/master/"
link<-paste0(github_root,"results/Corona_Cases.world.casecor.plot.png")
section_ref<-'Q3'
plot_handle<-c("Corona_Cases.world.casecor.plot","Corona_Cases.world.long.plot")
name<-"World total & death cases, correlation"
deliverable_manifest<-data.frame(
  name=c("World total & death cases, correlation",
         "World total & death cases, longitudinal"),
  plot_handle=plot_handle,
  link=paste0(github_root,"results/",plot_handle,".png")
)
(tmp<-data.frame(row_out=apply(deliverable_manifest,MARGIN = 1,FUN = function(x) paste(x[1],x[2],x[3],sep=" | "))))
row_out<-apply(tmp, 2, paste, collapse="\t\n")

```
name | handle | link
---- | ------ | ----
`r row_out`

## Tables

# CONCLUSION
Overall, the trends of COVID-19 cases is no longer in log-linear phase for world or U.S. (but some regions like MD are still in the log-linear phase). Mortality rate (deaths/confirmed RNA-based cases) is >1%, with a range depending on region. Mobility is not a strong indicator of caseload (U.S. data).

See table below for detailed breakdown.


Question  | Answer
------------- | ------------- 
<a href="#Q3: What is the effect on social distancing, descreased mobility on case load?">What is the effect on social distancing, descreased mobility on case load?</a><br>    | There is not a strong apparent effect on decreased mobility (work, grocery, retail) or increased mobility (at residence, parks) on number of confirmed cases, either as a country (U.S.) or state level. California appears to have one of the best correlations, but this is a mixed bag
<a href="#Q1: What is the trend in cases, mortality across geopgraphical regions?">What is the trend in cases, mortality across geopgraphical regions?</a><br>         | The confirmed total casees and mortality is overall log-linear for most countries, with a trailing off beginning for most (inlcuding U.S.). On the state level, NY, NJ, PA starting to trail off; MD is still in log-linear phase. Mortality and case load are highly correlated for NY, NJ, PA, MD. The mortality rate flucutates for a given region, but is about 3% overall. 

#END
End: `r paste(timestamp())`

Cheatsheet:
http://rmarkdown.rstudio.com>
# TODO
* mkdir the results dir if it doesn't exist 
* make ggplot a dependency for plot.utils?  
* automated way of downloading daily data 
* fix plot_utils, add dataset and documentation 
* Auto git mv the new data? 



# Sandbox

```{r eval=F}
##TODO:
# Geographical heatmap!
install.packages("maps")
library(maps)
library
mi_counties <- map_data("county", "pennsylvania") %>% 
  select(lon = long, lat, group, id = subregion)
head(mi_counties)

ggplot(mi_counties, aes(lon, lat)) + 
  geom_point(size = .25, show.legend = FALSE) +
  coord_quickmap()
mi_counties$cases<-1:2226
name_overlaps(metadata,Corona_Cases.US_state)

tmp<-merge(Corona_Cases.US_state,metadata)
ggplot(filter(tmp,Province.State=="Pennsylvania"), aes(Long, Lat, group = as.factor(City))) +
  geom_polygon(aes(fill = Total_confirmed_cases), colour = "grey50") + 
  coord_quickmap()



```


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