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Last active January 31, 2020 00:41
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Branching process model of 2019nCoV spread
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README.md

Branching process model of 2019nCoV spread

This is an attempt to reproduce Figure 1 from Imai et al. 2020, using code from Riou and Althaus (code here). I have included a Jupyter notebook (which includes the output), as well as RMarkdown and plain R files, generated using Jupytext.

Details missing from Imai et al. that I had to guess:

  1. The initial time (I took it to be 2019-12-01).
  2. The distribution of generation times (I took it to be gamma with standard deviation of 3.8).
  3. The summary curve is generated using the median of all cases at a given time (similarly with the 95 percentile range). The language in the figure legend is ambiguous, and could mean generating a median trajectory.

I have also tweaked the Riou and Althaus code, changing the parameterization and wrapping the main loop into a function, and have also used a fixed seed. To reduce computational burden, I have only generated 500 trajectories (cf 5000 in Imai et al.), but this should not affect the results (particularly the median curve) too much. The details of the implementation are missing from Imai et al., and so they could well be using a different language, random number generator, etc..

At present, the figures do not match up; the median number of cases should go through 4000 cases on 2020-01-18. This discrepancy may well be due to my errors in the above assumptions and code refactoring.

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bhbp.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Branching process model of epidemic spread"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This code is adapted from the study of [Riou and Althaus](https://www.biorxiv.org/content/10.1101/2020.01.23.917351v1), using the [code from GitHub](https://github.com/jriou/wcov), stripped down and rewritten for clarity."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"library(ggplot2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Set random number seed."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"set.seed(1234)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Define Bellman-Harris branching process model."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"lines_to_next_cell": 2
},
"outputs": [],
"source": [
"bhbp <- function(R0,k,shape,scale,index_cases,max_cases,max_time){\n",
" t <- rep(0, index_cases)\n",
" times <- t\n",
" tmax <- 0\n",
" cases <- index_cases\n",
" while(cases > 0 & length(times) < max_cases) {\n",
" secondary = rnbinom(cases, size=k, mu=R0)\n",
" t.new = numeric()\n",
" for(j in 1:length(secondary)) {\n",
" t.new = c(t.new, t[j] + rgamma(secondary[j], shape = shape, scale = scale))\n",
" }\n",
" t.new = t.new[t.new < max_time]\n",
" cases = length(t.new)\n",
" t = t.new\n",
" times = c(times, t.new)\n",
" }\n",
" times <- sort(times)\n",
" return(times)\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Set parameter values, using values from [Imai et al.](https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-2019-nCoV-transmissibility.pdf) and assuming a gamma distribution of generation times with mean `mu` 8.4 days and standard deviation `sd` of 3.8 days, taken from [Lipsitch et al. (2003](https://science.sciencemag.org/content/300/5627/1966.full)."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"lines_to_next_cell": 2
},
"outputs": [],
"source": [
"R0 <- 2.6\n",
"k <- 0.16\n",
"mu <- 8.4\n",
"stdev <- 3.8\n",
"shape <- (mu/stdev)^2\n",
"scale <- (stdev^2)/mu"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot the generation time distribution."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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kZAYgsgibgAqV41lsoNqTGu3QdIbAEk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\nOBBAQhAHAkgI4kAACUEcCCAhiAP5P9Tt1sIlEvlYAAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"t <- seq(0,30,by=0.01)\n",
"g <- dgamma(t,shape=shape,scale=scale)\n",
"ggplot(data.frame(GenerationTime=t,Probability=g))+geom_line(aes(x=GenerationTime,y=Probability))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot the offspring distribution."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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up3PC+ZeusvgVQJSGa5hVTuF7ddmDz/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\nRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"i <- seq(0,10)\n",
"d <- dnbinom(i, size=k, mu=R0)\n",
"ggplot(data.frame(Number=i,Probability=d))+geom_bar(aes(x=Number,y=Probability),stat=\"identity\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Initial and stopping conditions."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"lines_to_next_cell": 2
},
"outputs": [],
"source": [
"index_cases <- 40\n",
"max_cases <- 5e4\n",
"max_time <- 90"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Set the number of simulations (note - Imai et al. used 5000)."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"lines_to_next_cell": 2
},
"outputs": [],
"source": [
"nsims <- 500"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Run simulations."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"l <- list()\n",
"for(i in 1:nsims){\n",
" times <- bhbp(R0,k,shape,scale,index_cases,max_cases,max_time)\n",
" # Generates cumulative counts per day\n",
" # Note that this includes the index cases\n",
" l[[i]] <- cumsum(hist(times, breaks = 0:max_time,plot=FALSE)$counts)\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Combine individual runs into a dataframe."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"results <- as.data.frame(do.call(cbind,l))"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"median_cases <- apply(results,1,median)\n",
"lq_cases <- apply(results,1,quantile,0.025)\n",
"uq_cases <- apply(results,1,quantile,0.975)\n",
"summary_results <- data.frame(Day=seq(1,max_time),\n",
" Date=as.Date(\"2019-12-01\")+seq(1,max_time),\n",
" Median=median_cases,\n",
" Lower=lq_cases,Upper=uq_cases)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Add day/dates with day 0 corresponding to 2019-12-01."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"results$Day <- seq(1,max_time)\n",
"results$Date <- as.Date(\"2019-12-01\")+results$Day"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"results$Day <- seq(1,max_time)\n",
"results$Date <- as.Date(\"2019-12-01\")+results$Day"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Reshape results into 'long' format."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"df <- reshape(results,varying=paste(\"V\",1:nsims,sep=\"\"),direction=\"long\",sep=\"\",idvar=\"Day\",timevar=\"Run\",v.names=c(\"Cases\"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot trajectories over time, highlighting 4000 cases on 2020-01-18."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"lines_to_next_cell": 0
},
"outputs": [
{
"data": {
"image/png": 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HMCcFpnFKQ3dP5sJQIQHzqMm+nE/U5xMetkmWfNDbzVLbGoo2JnjMp3h6QpLRMr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\nPvaxbdu2df3NUNVphvEwDMMw65EXXqjdcIM0jOwJdj30zeCaF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RBEEQ8N3vYuCEnCVwwnW1Ub80xiLb7hUK6Z3c5D5ss3lo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"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
},
"text/plain": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"ntraj <- 20\n",
"ggplot(summary_results)+\n",
" geom_line(aes(x=Date,y=Median),color=\"red\")+\n",
" geom_line(aes(x=Date,y=Upper),color=\"blue\")+\n",
" geom_line(aes(x=Date,y=Lower),color=\"blue\")+\n",
" geom_ribbon(aes(x=Date,ymin=Lower,ymax=Upper, linetype = NA), fill=\"blue\", alpha = 0.1)+\n",
" geom_line(aes(x=Date,y=Cases,group=factor(Run)),data=df[df$Run<=ntraj,],color=\"gray\")+\n",
" coord_cartesian(xlim=c(as.Date(\"2019-12-01\"),as.Date(\"2020-01-30\")),ylim=c(1,20000))+\n",
" geom_vline(xintercept=as.Date(\"2020-01-18\"))+\n",
" geom_hline(yintercept=4000)+\n",
" theme_classic()"
]
}
],
"metadata": {
"jupytext": {
"cell_metadata_filter": "-all",
"main_language": "R",
"notebook_metadata_filter": "-all"
},
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.6.2"
}
},
"nbformat": 4,
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}
Raw
bhbp.R
## Branching process model of epidemic spread
# This code is adapted from the study of [Riou and Althaus](https://www.biorxiv.org/content/10.1101/2020.01.23.917351v1), using the [code from GitHub](https://github.com/jriou/wcov), stripped down and rewritten for clarity.
library(ggplot2)
# Set random number seed.
set.seed(1234)
# Define Bellman-Harris branching process model.
bhbp <- function(R0,k,shape,scale,index_cases,max_cases,max_time){
t <- rep(0, index_cases)
times <- t
tmax <- 0
cases <- index_cases
while(cases > 0 & length(times) < max_cases) {
secondary = rnbinom(cases, size=k, mu=R0)
t.new = numeric()
for(j in 1:length(secondary)) {
t.new = c(t.new, t[j] + rgamma(secondary[j], shape = shape, scale = scale))
}
t.new = t.new[t.new < max_time]
cases = length(t.new)
t = t.new
times = c(times, t.new)
}
times <- sort(times)
return(times)
}
# Set parameter values, using values from [Imai et al.](https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-2019-nCoV-transmissibility.pdf) and assuming a gamma distribution of generation times with mean `mu` 8.4 days and standard deviation `sd` of 3.8 days, taken from [Lipsitch et al. (2003](https://science.sciencemag.org/content/300/5627/1966.full).
R0 <- 2.6
k <- 0.16
mu <- 8.4
stdev <- 3.8
shape <- (mu/stdev)^2
scale <- (stdev^2)/mu
# Plot the generation time distribution.
t <- seq(0,30,by=0.01)
g <- dgamma(t,shape=shape,scale=scale)
ggplot(data.frame(GenerationTime=t,Probability=g))+geom_line(aes(x=GenerationTime,y=Probability))
# Plot the offspring distribution.
i <- seq(0,10)
d <- dnbinom(i, size=k, mu=R0)
ggplot(data.frame(Number=i,Probability=d))+geom_bar(aes(x=Number,y=Probability),stat="identity")
# Initial and stopping conditions.
index_cases <- 40
max_cases <- 5e4
max_time <- 90
# Set the number of simulations (note - Imai et al. used 5000).
nsims <- 500
# Run simulations.
l <- list()
for(i in 1:nsims){
times <- bhbp(R0,k,shape,scale,index_cases,max_cases,max_time)
# Generates cumulative counts per day
# Note that this includes the index cases
l[[i]] <- cumsum(hist(times, breaks = 0:max_time,plot=FALSE)$counts)
}
# Combine individual runs into a dataframe.
results <- as.data.frame(do.call(cbind,l))
median_cases <- apply(results,1,median)
lq_cases <- apply(results,1,quantile,0.025)
uq_cases <- apply(results,1,quantile,0.975)
summary_results <- data.frame(Day=seq(1,max_time),
Date=as.Date("2019-12-01")+seq(1,max_time),
Median=median_cases,
Lower=lq_cases,Upper=uq_cases)
# Add day/dates with day 0 corresponding to 2019-12-01.
results$Day <- seq(1,max_time)
results$Date <- as.Date("2019-12-01")+results$Day
results$Day <- seq(1,max_time)
results$Date <- as.Date("2019-12-01")+results$Day
# Reshape results into 'long' format.
df <- reshape(results,varying=paste("V",1:nsims,sep=""),direction="long",sep="",idvar="Day",timevar="Run",v.names=c("Cases"))
# Plot trajectories over time, highlighting 4000 cases on 2020-01-18.
ntraj <- 20
ggplot(summary_results)+
geom_line(aes(x=Date,y=Median),color="red")+
geom_line(aes(x=Date,y=Upper),color="blue")+
geom_line(aes(x=Date,y=Lower),color="blue")+
geom_ribbon(aes(x=Date,ymin=Lower,ymax=Upper, linetype = NA), fill="blue", alpha = 0.1)+
geom_line(aes(x=Date,y=Cases,group=factor(Run)),data=df[df$Run<=ntraj,],color="gray")+
coord_cartesian(xlim=c(as.Date("2019-12-01"),as.Date("2020-01-30")),ylim=c(1,20000))+
geom_vline(xintercept=as.Date("2020-01-18"))+
geom_hline(yintercept=4000)+
theme_classic()
Raw
bhbp.Rmd
## Branching process model of epidemic spread
This code is adapted from the study of [Riou and Althaus](https://www.biorxiv.org/content/10.1101/2020.01.23.917351v1), using the [code from GitHub](https://github.com/jriou/wcov), stripped down and rewritten for clarity.
```{r}
library(ggplot2)
```
Set random number seed.
```{r}
set.seed(1234)
```
Define Bellman-Harris branching process model.
```{r}
bhbp <- function(R0,k,shape,scale,index_cases,max_cases,max_time){
t <- rep(0, index_cases)
times <- t
tmax <- 0
cases <- index_cases
while(cases > 0 & length(times) < max_cases) {
secondary = rnbinom(cases, size=k, mu=R0)
t.new = numeric()
for(j in 1:length(secondary)) {
t.new = c(t.new, t[j] + rgamma(secondary[j], shape = shape, scale = scale))
}
t.new = t.new[t.new < max_time]
cases = length(t.new)
t = t.new
times = c(times, t.new)
}
times <- sort(times)
return(times)
}
```
Set parameter values, using values from [Imai et al.](https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-2019-nCoV-transmissibility.pdf) and assuming a gamma distribution of generation times with mean `mu` 8.4 days and standard deviation `sd` of 3.8 days, taken from [Lipsitch et al. (2003](https://science.sciencemag.org/content/300/5627/1966.full).
```{r}
R0 <- 2.6
k <- 0.16
mu <- 8.4
stdev <- 3.8
shape <- (mu/stdev)^2
scale <- (stdev^2)/mu
```
Plot the generation time distribution.
```{r}
t <- seq(0,30,by=0.01)
g <- dgamma(t,shape=shape,scale=scale)
ggplot(data.frame(GenerationTime=t,Probability=g))+geom_line(aes(x=GenerationTime,y=Probability))
```
Plot the offspring distribution.
```{r}
i <- seq(0,10)
d <- dnbinom(i, size=k, mu=R0)
ggplot(data.frame(Number=i,Probability=d))+geom_bar(aes(x=Number,y=Probability),stat="identity")
```
Initial and stopping conditions.
```{r}
index_cases <- 40
max_cases <- 5e4
max_time <- 90
```
Set the number of simulations (note - Imai et al. used 5000).
```{r}
nsims <- 500
```
Run simulations.
```{r}
l <- list()
for(i in 1:nsims){
times <- bhbp(R0,k,shape,scale,index_cases,max_cases,max_time)
# Generates cumulative counts per day
# Note that this includes the index cases
l[[i]] <- cumsum(hist(times, breaks = 0:max_time,plot=FALSE)$counts)
}
```
Combine individual runs into a dataframe.
```{r}
results <- as.data.frame(do.call(cbind,l))
```
```{r}
median_cases <- apply(results,1,median)
lq_cases <- apply(results,1,quantile,0.025)
uq_cases <- apply(results,1,quantile,0.975)
summary_results <- data.frame(Day=seq(1,max_time),
Date=as.Date("2019-12-01")+seq(1,max_time),
Median=median_cases,
Lower=lq_cases,Upper=uq_cases)
```
Add day/dates with day 0 corresponding to 2019-12-01.
```{r}
results$Day <- seq(1,max_time)
results$Date <- as.Date("2019-12-01")+results$Day
```
```{r}
results$Day <- seq(1,max_time)
results$Date <- as.Date("2019-12-01")+results$Day
```
Reshape results into 'long' format.
```{r}
df <- reshape(results,varying=paste("V",1:nsims,sep=""),direction="long",sep="",idvar="Day",timevar="Run",v.names=c("Cases"))
```
Plot trajectories over time, highlighting 4000 cases on 2020-01-18.
```{r}
ntraj <- 20
ggplot(summary_results)+
geom_line(aes(x=Date,y=Median),color="red")+
geom_line(aes(x=Date,y=Upper),color="blue")+
geom_line(aes(x=Date,y=Lower),color="blue")+
geom_ribbon(aes(x=Date,ymin=Lower,ymax=Upper, linetype = NA), fill="blue", alpha = 0.1)+
geom_line(aes(x=Date,y=Cases,group=factor(Run)),data=df[df$Run<=ntraj,],color="gray")+
coord_cartesian(xlim=c(as.Date("2019-12-01"),as.Date("2020-01-30")),ylim=c(1,20000))+
geom_vline(xintercept=as.Date("2020-01-18"))+
geom_hline(yintercept=4000)+
theme_classic()
```
@pearsonca
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pearsonca commented Jan 30, 2020 •
edited
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So this is a bit faster; the use of data.table is not the main contributor to that. Also set it back to 5k samples.

## Branching process model of epidemic spread

# This code is adapted from the study of [Riou and Althaus](https://www.biorxiv.org/content/10.1101/2020.01.23.917351v1), using the [code from GitHub](https://github.com/jriou/wcov), stripped down and rewritten for clarity.

library(data.table)
library(ggplot2)

# Set random number seed.

set.seed(1234)

# Set parameter values, using values from [Imai et al.](https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-2019-nCoV-transmissibility.pdf) and assuming a gamma distribution of generation times with mean `mu` 8.4 days and standard deviation `sd` of 3.8 days, taken from [Lipsitch et al. (2003](https://science.sciencemag.org/content/300/5627/1966.full).

R0 <- 2.6
k <- 0.16
mu <- 8.4
stdev <- 3.8
shape <- (mu/stdev)^2
scale <- (stdev^2)/mu

rcases <- function(n) rnbinom(n, size=k, mu=R0)
rtimes <- function(n) rgamma(n, shape = shape, scale = scale)

# Define Bellman-Harris branching process model.

bhbp <- function(
  index_cases, max_cases, max_time,
  casedistro = rcases, timedistro = rtimes
){
  cases <- index_cases
  times <- rep(0, cases)
  remaining_cases <- max_cases - cases
  while(cases & (0 < remaining_cases)) {
    secondary = casedistro(cases)
    tms <- timedistro(sum(secondary))
    t.new <- times[rep(1:cases, times = secondary)] + tms
    t.new <- t.new[t.new < max_time]
    cases <- length(t.new)
    remaining_cases <- remaining_cases - cases
    times <- c(t.new, times)
  }
  times <- sort(times)
  return(times)
}

# Plot the generation time distribution.

t <- seq(0,30,by=0.01)
g <- dgamma(t,shape=shape,scale=scale)
ggplot(
  data.table(`Generation Time`=t,Probability=g)
) + 
  aes(`Generation Time`, Probability) +
  geom_line()

# Plot the offspring distribution.

i <- seq(0,10)
d <- dnbinom(i, size=k, mu=R0)
ggplot(
  data.table(Number=i,Probability=d)
) +
  aes(x=Number,y=Probability) +
  geom_bar(stat="identity") +
  scale_x_continuous(breaks=i)

# Initial and stopping conditions.

index_cases <- 40
max_cases <- 5e4
max_time <- 90


# Set the number of simulations (note - Imai et al. used 5000).

nsims <- 5000

# Run simulations.

grid <- data.table(sim=1:nsims)
compute <- grid[, {
  times <- bhbp(index_cases, max_cases, max_time)
  .(
    cases = cumsum(hist(times, breaks = 0:max_time, plot=FALSE)$counts),
    times = 1:max_time
  )
}, by=sim ]

day0 <- as.Date("2019-12-01")

summary_results <- compute[, {
  qs <- quantile(cases, probs = c(0.025, 0.5, 0.975))
  .(Lower=qs[1], Median=qs[2], Upper=qs[3])
}, by=.(Day=times)]
summary_results[, Date := day0+Day ]

# Plot trajectories over time, highlighting 4000 cases on 2020-01-18.

ntraj <- 20
ggplot(summary_results)+
  geom_line(aes(x=Date,y=Median),color="red")+
  geom_line(aes(x=Date,y=Upper),color="blue")+
  geom_line(aes(x=Date,y=Lower),color="blue")+
  geom_ribbon(aes(x=Date,ymin=Lower,ymax=Upper, linetype = NA), fill="blue", alpha = 0.1)+
  geom_line(aes(x=times+day0,y=cases,group=factor(sim)),data=compute[sim<=ntraj,],color="gray")+
  coord_cartesian(xlim=c(as.Date("2019-12-01"),as.Date("2020-01-30")),ylim=c(1,20000))+
  geom_vline(xintercept=as.Date("2020-01-18"))+
  geom_hline(yintercept=4000)+
  theme_classic()

@slwu89
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slwu89 commented Jan 31, 2020

In case anyone wants to play around with a much faster version (posting here so its not only on twitter), I translated the bhbp simulation code into C and wrapped in an R package here: https://github.com/slwu89/nCoV

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