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modeling.Rmd
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modeling.Rmd
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---
title: "Cholera outbreak model"
output: github_document
date: "2023-02-27"
editor_options:
chunk_output_type: console
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo=T, eval=FALSE, warning=F)
```
## Load the package
```{r cars}
devtools::load_all()
```
## Run the model
```{r}
devtools::load_all()
params <- initialize_params()
out = seiarw_2ag_erlang(params)
# outbk = simulate_outbreak(params=params)
outbk = simulate_outbreak()
plot(outbk$timeseries$ci)
outbk$outbreak_char
# seiarw requires three following parameters to be a vector of length=1
# parm <- c(vacc_cov=0.4, vacc_eff_v1=0.9, vacc_eff_v2=0.9)
# # update params
# for (nm in names(parm)) params[[nm]] = parm[[nm]]
# out <- seiarw(params)
# out2 <- params$model(params)
# all.equal(out, out2)
```
### Generate outbreaks
```{r}
# read the source data for the Zheng et al. (2022) paper
d = data.table::fread("https://raw.githubusercontent.com/kimfinale/cholera_outbreaks_ssa/main/reference_data/outbreak_data.csv")
names(d)
# d[1,c("duration","threshold","total_suspected_cases","attack_rate","population","time_to_peak..weeks.")]
# outbk = simulate_outbreak(params=params)
# cost
char_obs = d[1,c("duration","threshold","total_suspected_cases","attack_rate",
"population","time_to_peak..weeks.","mean_R0")]
popsize = char_obs[["population"]]
threshold = char_obs[["threshold"]]
outbk_dur = char_obs[["duration"]]
outbk_size = char_obs[["total_suspected_cases"]]
outbk_time_to_peak = char_obs[["time_to_peak..weeks."]]
outbk_R0 = char_obs[["mean_R0"]]
cost_func = function(x) {
# simulate outbreak
params$R0 = outbk_R0
outbk = simulate_outbreak(params=params,
popsize = popsize,
outbreak_threshold = threshold,
prop_eff_pop=x)
sqrt((outbk_size - outbk$outbreak_char[["outbreak_size"]])^2 +
(outbk_dur - outbk$outbreak_char[["outbreak_dur"]])^2 +
(outbk_time_to_peak - outbk$outbreak_char[["time_to_peak"]])^2)
}
sapply(c(0.001, 0.00003, 0.01, 0.1, 0.5), cost_func)
# fit = optim(par=0.1, fn=cost_func)
fit = optimise(cost_func, interval=c(0,1))
```
###
```{r}
devtools::load_all()
params <- initialize_params()
d = data.table::fread("https://raw.githubusercontent.com/kimfinale/cholera_outbreaks_ssa/main/reference_data/outbreak_data.csv")
# cost_func_pars = function(x, pars) {
# # simulate outbreak
# params$R0 = pars[["outbk_R0"]]
# outbk = simulate_outbreak(params = params,
# saveat = 7,
# stat_window = 7,# weekly statistics!
# popsize = pars[["popsize"]],
# outbreak_threshold = pars[["threshold"]],
# prop_eff_pop=x)
#
# os = outbk$outbreak_char[["outbreak_size"]]
# od = outbk$outbreak_char[["outbreak_dur"]]
# ot = outbk$outbreak_char[["time_to_peak"]]
# sqrt(((pars[["outbk_size"]]-os)/os)^2 +
# ((pars[["outbk_dur"]] - od)/od)^2 +
# ((pars[["outbk_time_to_peak"]] - ot)/ot)^2)
# }
fits = data.frame(matrix(NA, nrow=nrow(d), ncol=2))
names(fits) <- c("minimum", "objective")
for (i in 1:nrow(d)) {
cat("i =", i, "\n")
char_obs = d[i, c("duration", "threshold", "total_suspected_cases",
"attack_rate", "population", "time_to_peak..weeks.",
"mean_R0")]
if (all(!is.na(char_obs[1,]))) {
pars = c(
popsize = char_obs[["population"]],
threshold = char_obs[["threshold"]],
outbk_dur = char_obs[["duration"]],
outbk_size = char_obs[["total_suspected_cases"]],
outbk_time_to_peak = char_obs[["time_to_peak..weeks."]],
outbk_R0 = char_obs[["mean_R0"]])
ft = optimise(cost_func_pars, pars=pars, interval=c(0,1))
fits[i,"minimum"] = ft$minimum
fits[i,"objective"] = ft$objective
print(ft)
}
}
saveRDS(fits, paste0("outputs/fits_", tstamp(), ".rds"))
```
### Generate outbreaks
```{r}
devtools::load_all()
params <- initialize_params()
d = data.table::fread("https://raw.githubusercontent.com/kimfinale/cholera_outbreaks_ssa/main/reference_data/outbreak_data.csv")
# fits = readRDS("outputs/fits_20230329.rds")
fits = readRDS("outputs/fits_20230330.rds")
i = 1
outbks = vector('list', length=nrow(d))
for (i in 1:nrow(d)) {
cat("i =", i, "\n")
char_obs = d[i, c("population","threshold","mean_R0")]
if (all(!is.na(char_obs[1,]))) {
pars = c(popsize = char_obs[["population"]],
threshold = char_obs[["threshold"]],
outbk_R0 = char_obs[["mean_R0"]])
params$R0 = pars[["outbk_R0"]]
outbks[[i]] = simulate_outbreak(params=params,
saveat=1,
stat_window=7,
popsize = pars[["popsize"]],
outbreak_threshold = pars[["threshold"]],
prop_eff_pop = fits$minimum[i])
}
}
# saveRDS(outbks, paste0("outputs/fitted_outbreaks_", tstamp(), ".rds"))
```
## Analysis of fitted outbreaks
Outbreaks are analyzed to see first what the issues are with the outbreaks that the current strategy did not allow fitting (eg, outbreak size too big given a population size and R0)
Check when you get NA
If we allow 20% difference for the three metrics, the sum would be 1.2.
Does the outbreaks with good fits cover the outbreaks observed?
```{r}
fits = readRDS("outputs/fits_20230331.rds")
id_goodfits = !is.na(fits$objective) & fits$objective <1.2
dgf = d[id_goodfits,]
# compare good fits
library(ggplot2)
library(magrittr)
ruu = function(str){ ## remove underscore and upper case for the first letter
str = gsub("_", " ", str)
paste(toupper(substr(str, 1, 1)), substr(str, 2, nchar(str)), sep="")
}
strs = c("duration", "threshold", "total_suspected_cases","attack_rate",
"population", "time_to_peak..weeks.", "mean_R0")
d2 = d
d2 = rbind(d2, dgf)
d2$dataset = as.factor(c(rep("All",nrow(d)), rep("Fit", nrow(dgf))))
library(dplyr)
for(str in strs){
p = ggplot(d2)+
geom_histogram(aes(x=eval(parse(text=str)), y=..density.., fill=dataset),
position='identity', alpha=0.4)+
scale_fill_manual(values=c("All"="brown", "Fit"="steelblue"), name="")+
labs(x=ruu(str), y="Density")+
theme_bw()+
facet_wrap(~dataset,nrow=2)
ggsave(paste0("plots/", str, ".png"), p, width=3.4*2, height=2.7*2, unit="in")
}
```
```{r}
d_id_goodfits = d[id_goodfits,]
plot(1:nrow(d), d[[c("duration")]])
points(1:nrow(d_id_goodfits), d_id_goodfits[[c("duration")]], col=2)
outbks = readRDS("outputs/fitted_outbreaks_20230330.rds")
d[id, c("duration", "threshold", "total_suspected_cases","attack_rate",
"population", "time_to_peak..weeks.", "mean_R0")]
apply(fits, 2, summary)
id = match(NA, fits$objective)
d[id,c("duration", "threshold", "total_suspected_cases","attack_rate",
"population", "time_to_peak..weeks.", "mean_R0")]
outbks[[id]]$outbreak_char
fits[id,]
final_epidemic_size(R0=d[id,]$mean_R0)
extract_pars = function(dat, id) {
char_obs = dat[id, c("duration", "threshold", "total_suspected_cases",
"attack_rate", "population", "time_to_peak..weeks.",
"mean_R0")]
if (all(!is.na(char_obs[1,]))) {
pars = c(
popsize = char_obs[["population"]],
threshold = char_obs[["threshold"]],
outbk_dur = char_obs[["duration"]],
outbk_size = char_obs[["total_suspected_cases"]],
outbk_time_to_peak = char_obs[["time_to_peak..weeks."]],
outbk_R0 = char_obs[["mean_R0"]])
}
return(pars)
}
pars = extract_pars(d, id)
# see if increasing R0 would find a reasonable proportion
pars[["outbk_R0"]] = 2
ft = optimise(cost_func_pars, pars=pars, interval=c(0,1))
ft$minimum
ft$objective
```
Let's exclude those that did not generate good fits (eg, is.na(objective) or objective > cutoff for the cutoff is
```{r}
ids_NA = is.na(fits$objective)
summary(fits$minimum[!ids_NA])
fits$objective[fits$objective > 1]
summary(fits)
fits$minimum[fits$minimum > 0.8]
d[which(fits$minimum>0.8),]
fits[which(fits$minimum>0.8),"objective"]
summary(fits[which(fits$minimum<=0.8),"objective"])
```
### Test vaccine impact
```{r}
devtools::load_all()
params <- initialize_params()
d = data.table::fread("https://raw.githubusercontent.com/kimfinale/cholera_outbreaks_ssa/main/reference_data/outbreak_data.csv")
fits = readRDS("outputs/fits_20230329.rds")
i = 1
char_obs = d[i, c("population","threshold","mean_R0")]
if (all(!is.na(char_obs[1,]))) {
pars = c(popsize = char_obs[["population"]],
threshold = char_obs[["threshold"]],
outbk_R0 = char_obs[["mean_R0"]])
params$R0 = pars[["outbk_R0"]]
outbk = simulate_outbreak(params=params,
saveat=1,
stat_window=7,
popsize = pars[["popsize"]],
outbreak_threshold = pars[["threshold"]],
prop_eff_pop = fits$minimum[i])
}
```
## Generate outbreaks in terms of outbreak characteristics
outbreak size, duration of an outbreak, peak incidence, attack rate.
```{r}
# read the source data for the Zheng et al. (2022) paper
d = data.table::fread("https://raw.githubusercontent.com/kimfinale/cholera_outbreaks_ssa/main/reference_data/outbreak_data.csv")
names(d)
d[1,c("duration","threshold","total_suspected_cases","attack_rate","population","time_to_peak..weeks.")]
outbk = simulate_outbreak(params=params)
cost
d[1,c("duration","threshold","total_suspected_cases","attack_rate","population","time_to_peak..weeks.")]
pr=c(0.025,0.25,0.5,0.75,0.975)
summary(d$duration)
boxplot(d$duration)
dshort = d[duration < 50]
summary(dshort$duration)
boxplot(dshort$duration)
dvar = d[,c("population","duration","attack_rate",
"time_to_peak..weeks.")]
dvar$logpop = log10(dvar$population)
pairs(dvar[,-c("population")])
library(Hmisc)
rcorr(as.matrix(dvar[,-c("population")]))
#if I select outbreaks
```
```{r}
PARAMETERS$model <- seiarw
pop <- 1e5
pop_scale <- 0.07
prop_init_R <- 0.6
prop_init_I <- 0.001
PARAMETERS$init$R <- prop_init_R * pop * pop_scale
PARAMETERS$init$I <- prop_init_I * pop * pop_scale
PARAMETERS$init$S <- pop * pop_scale - PARAMETERS$init$I - PARAMETERS$init$I
parm = PARAMETERS
out = seiarw(parm)
# plot(1:nrow(d), d$CI, type="l")
# ?data.table::frollsum
df <- data.frame(matrix(NA, nrow=52, ncol=10))
df$week=1:52
for(i in 1:10){
parm <- c(R0=2, R0W=1, case_threshold=10, alpha=(i-1)/10)
d <- daily_incidence(pars=parm)
weekroll <- data.table::frollsum(d$CI, n=7)
sq <- seq(7, length(weekroll), by=7)
df[, i] <- weekroll[sq]
}
head(df, n=20)
names(df) <- c(paste0(seq(0,90,10)," %"), "Week")
df <- df[,c(seq(1,9,2),11)]
library(tidyr)
# dflong <- pivot_longer(df, cols=1:ncol(df), names_to = "Reduction")
dflong <- pivot_longer(df, cols=(!Week), names_to = "Reduction")
library(ggplot2)
p <- ggplot(dflong) +
geom_line(aes(Week, value, color=Reduction), linewidth=1)+
labs(x="Week", y="Case")+
scale_color_manual("Intervention", values=mycolors[1:10])+
theme_classic()+
theme(panel.grid.major = element_line(colour="grey95", linewidth=0.3),
text = element_text(size=14), axis.text = element_text(size=14))
p
ggsave("plots/outbreak_intervention.png", p, width=3.4*2, height=2.7*2, unit="in")
# sum(d$CI)
cat("outbreak size:", round(sum(weekly)), "\n")
# df <- data.frame(week = 1:length(weekly), case = weekly)
# library(ggplot2)
# p <- ggplot(df) +
# geom_col(aes(week, case), fill = "brown") +
# labs(x="Week", y="Case")+
# theme_classic()+
# theme(panel.grid.major = element_line(colour="grey95", linewidth=0.3),
# text = element_text(size=14),
# axis.text = element_text(size=14))
# p
# ggsave("plots/typical_outbreak.png", p, width=3.4*2, height=2.7*2, unit="in")
out <- PARAMETERS$model(PARAMETERS)
day_filter <- seq(1, by=round(1/PARAMETERS$tau), length.out=(PARAMETERS$ndays+1))
out <- out[day_filter, ]
```
## Vaccination campaign
```{r}
PARAMETERS <- initialize_params()
# PARAMETERS$model <- seiarw
pop <- 1e5
pop_scale <- 0.07
prop_init_R <- 0.6
prop_init_I <- 0.001
PARAMETERS$init$R <- prop_init_R * pop * pop_scale
PARAMETERS$init$I <- prop_init_I * pop * pop_scale
PARAMETERS$init$S <- pop * pop_scale - PARAMETERS$init$I - PARAMETERS$init$I
parm <- c(R0=2, R0W=1, case_threshold=10, alpha=0, vacc_cov=0.4,
vacc_eff_v1 = 0.9, vacc_eff_v2 = 0.9)
params <- PARAMETERS
for (n in names(parm)) {
params[[n]] <- parm[[n]]
}
out <- seiarw2(params)
# out <- params$model(params)
d <- daily_incidence(pars=parm, variable = names(out))
plot(1:nrow(d), d$CI, type="l")
```
### Plot
```{r}
# ?data.table::frollsum
df <- data.frame(matrix(NA, nrow=52, ncol=10))
df$week=1:52
for(i in 1:10){
parm <- c(R0=2, R0W=1, case_threshold=10, alpha=(i-1)/10)
d <- daily_incidence(pars=parm)
weekroll <- data.table::frollsum(d$CI, n=7)
sq <- seq(7, length(weekroll), by=7)
df[, i] <- weekroll[sq]
}
head(df, n=20)
names(df) <- c(paste0(seq(0,90,10)," %"), "Week")
df <- df[,c(seq(1,9,2),11)]
library(tidyr)
# dflong <- pivot_longer(df, cols=1:ncol(df), names_to = "Reduction")
dflong <- pivot_longer(df, cols=(!Week), names_to = "Reduction")
library(ggplot2)
mycolors <- my_discrete_colors
p <- ggplot(dflong) +
geom_line(aes(Week, value, color=Reduction), linewidth=1)+
labs(x="Week", y="Case")+
scale_color_manual("Intervention", values=mycolors[1:10])+
theme_classic()+
theme(panel.grid.major = element_line(colour="grey95", linewidth=0.3),
text = element_text(size=14), axis.text = element_text(size=14))
p
ggsave("plots/outbreak_intervention.png", p, width=3.4*2, height=2.7*2, unit="in")
# sum(d$CI)
cat("outbreak size:", round(sum(weekly)), "\n")
# df <- data.frame(week = 1:length(weekly), case = weekly)
# library(ggplot2)
# p <- ggplot(df) +
# geom_col(aes(week, case), fill = "brown") +
# labs(x="Week", y="Case")+
# theme_classic()+
# theme(panel.grid.major = element_line(colour="grey95", linewidth=0.3),
# text = element_text(size=14),
# axis.text = element_text(size=14))
# p
# ggsave("plots/typical_outbreak.png", p, width=3.4*2, height=2.7*2, unit="in")
out <- PARAMETERS$model(PARAMETERS)
day_filter <- seq(1, by=round(1/PARAMETERS$tau), length.out=(PARAMETERS$ndays+1))
out <- out[day_filter, ]
```
### SEIARW Erlang distributed model
```{r, echo=FALSE}
# PARAMETERS <- initialize_params()
# # PARAMETERS$model <- seiarw
# pop <- 1e5
# pop_scale <- 0.07
# prop_init_R <- 0.6
# prop_init_I <- 0.001
# PARAMETERS$init$R <- prop_init_R * pop * pop_scale
# PARAMETERS$init$I <- prop_init_I * pop * pop_scale
# PARAMETERS$init$S <- pop * pop_scale - PARAMETERS$init$I - PARAMETERS$init$I
#
# parm <- c(R0=2, R0W=1, prop_children=0.1)
# params <- PARAMETERS
# for (n in names(parm)) {
# params[[n]] <- parm[[n]]
# }
# library(Rcpp)
# sourceCpp("src/seiarw.cpp")
# out <- seiarw(params)
params <- initialize_params()
pop <- 1e5
pop_scale <- 1
prop_init_R <- 0.0
prop_init_I <- 0.001
params$init$R <- prop_init_R * pop * pop_scale
params$init$I <- prop_init_I * pop * pop_scale
params$init$S <- pop * pop_scale - params$init$I - params$init$I
params$vacc_cov <- c(0.0, 0.0)
params$delay_until_2nd_campaign <- 30
params$R0 <- 2
params$R0W <- 0
params$alpha <- 0
params$fA <- 0.0
params$tau <- 0.1
# out <- seiarw_2ag_erlang(params)
params$sigma <- 0
out <- run_model(seiarw_2ag_erlang, params, output_time = 7, output_var = c("CI.1","CI.2"))
df = data.frame(ci=out$CI.1 + out$CI.2)
df$time = seq(0, length.out=nrow(df), by=7)
plot(diff(out$CI.1)+diff(out$CI.2), type="l")
sum(tail(out, 1))/pop/(1-params$fA)
final_epidemic_size(R0=params$R0)
## seiarw model, age-group specific parameters need to be adjusted
params2 <- params
params2$vacc_cov <- 0
params2$vacc_eff_v1 <- 0
params2$vacc_eff_v2 <- 0
out2 <- run_model(seiarw, params2, output_time = 7, output_var = c("CI"))
sum(tail(out2, 1))/pop
# plot(diff(out$CI.1)+diff(out$CI.2), type="l")
# plot(diff(out2$CI), type="l")
# head(out)
# tail(out)
# plot(out$S.1, type="l")
# # plot(out$S.2, type="l")
# # plot(out$I1.1, type="l")
# plot(out$O1.1, type="l")
# plot((out$O1.1 + out$O2.1), type="l")
# plot(out$T2.1, type="l")
# plot(out$T2.1, type="l")
# head(out)
# tail(out)
```
##
surveillance activity?
```{r}
# extract outbreak characteristics (outbreak duration, peak incidence)
out1=out
out2=out+rnorm(nrow(out))
nsamp = 1
nfeat = 3
threshold = 7
popsize = 1e5
df = data.frame(matrix(NA, nrow=nsamp, ncol=nfeat))
names(df) = c("peak_inc","outbreak_dur","attack_rate")
for(i in 1:nsamp){
weekly = diff(out$CI.1)
df[i, "peak_inc"] = max(out$CI.1)
over = which(weekly > threshold)
df[i, "outbreak_dur"] = out$time[max(over)] - out$time[min(over)]
df[i, "attack_rate"] = tail(out$CI.1, 1) / popsize
}
df
```
# Grid search
See if how the proportion of already-immune people for a given threshold
```{r}
params <- initialize_params()
params$vacc_cov <- c(0.0, 0.0)
params$delay_until_2nd_campaign <- 30
params$alpha <- 0
params$tau <- 0.1
params$R0 = 2
params$R0W = 2
outbk = simulate_outbreak(params=params)
run_outbreak = function(params,
model=seiarw_2ag_erlang,
popsize=1e5,
inc_ref_pop=1e3,
prop_s=1,
prop_eff_pop=1,
output_var=c("CI.1","CI.2"),
output_time=7,
threshold=1){
params$init$R <- (1-prop_s) * popsize * prop_eff_pop
params$init$I <- 0.001 * popsize * prop_eff_pop
params$init$S <- popsize * prop_eff_pop - params$init$I
out <- run_model(model, params,
output_time=output_time,
output_var=output_var)
df = data.frame(ci = out$CI.1 + out$CI.2)
df$time = out$time / output_time # make it a week
weekly = diff(df$ci)
over = which(weekly > threshold) # index for the week of which the incid is over the threshold
start = df$time[min(over)]
end = df$time[max(over)]
peak = df$time[which.max(weekly)]
peak_inc_per_1e3 = weekly[peak] / popsize * inc_ref_pop
time_to_peak = (peak - start)
outbreak_dur = (end - start)
outbreak_size = tail(df$ci, 1)
attack_rate_per_1e3 = outbreak_size / popsize * inc_ref_pop
return(c(outbreak_dur=outbreak_dur,
time_to_peak=time_to_peak,
peak_inc_per_1e3=peak_inc_per_1e3,
outbreak_size=outbreak_size,
attack_rate_per_1e3=attack_rate_per_1e3))
}
res = run_outbreak(params=params)
get_outbreak_char = function(df, threshold=1, popsize=1e5,
inc_ref_pop=1e3){
weekly = diff(df$ci)
over = which(weekly > threshold)
start = df$time[min(over)]
end = df$time[max(over)]
peak = df$time[which.max(weekly)]
peak_inc_per_1e3 = weekly[peak] / popsize * inc_ref_pop
time_to_peak = (peak - start)
outbreak_dur = (end - start)
outbreak_size = tail(df$ci, 1)
attack_rate_per_1e3 = outbreak_size / popsize * inc_ref_pop
return(c(outbreak_dur=outbreak_dur, time_to_peak=time_to_peak,
peak_inc_per_1e3=peak_inc_per_1e3,
outbreak_size = outbreak_size,
attack_rate_per_1e3=attack_rate_per_1e3))
}
out <- run_model_with_varying_S(prop_s=0.3)
plot(out$time, c(0,diff(out$ci)), type="b")
get_outbreak_char(df=out)
plot(out$time, c(0,diff(out$ci)), type="b")
cnt <- 1
my_discrete_colors[1:9]
for(i in seq(0.1,0.9,0.1)){
out <- run_model_with_varying_S(params=params,prop_s=1-i)
lines(out$time, c(0,diff(out$ci)), col=my_discrete_colors[cnt], lwd=2)
res = get_outbreak_char(df=out, threshold=7, popsize=1e5)
cat("dur=", res$outbreak_dur, ", size=", res$outbreak_size, ", time_to_peak=", res$time_to_peak, ", peak_inc=",
res$peak_inc_per_1e3, ", ar=", res$attack_rate_per_1e3, "\n")
cnt = cnt + 1
}
```
### EpiEstim
```{r}
params <- initialize_params()
params$vacc_cov <- c(0.0, 0.0)
params$delay_until_2nd_campaign <- 30
params$alpha <- 0
params$tau <- 0.01
params$R0W = 0
params$prop_children <- 0
params$fA = 0
params$sigma = 0 # or immunity waning
params$R0=2
out=simulate_outbreak(params=params,
prop_s=1,
output_time=1)
library(EpiEstim)
day_incid = diff(out$timeseries$ci)
t_start <- seq(2, length(day_incid)-1)
t_end <- t_start + 1
res <- estimate_R(incid = day_incid,
method = "parametric_si",
config = make_config(list(
mean_si = 4.5,
std_si = 3,
t_start = t_start,
t_end = t_end)))
res$R$`Mean(R)`[1:20]
plot(res$R$`Mean(R)`[1:50])
```
## Grid search
```{r}
params <- initialize_params()
params$vacc_cov <- c(0.0, 0.0)
params$delay_until_2nd_campaign <- 30
params$alpha <- 0
params$tau <- 0.1
params$R0 <- 2
params$R0W <- 0
# first few columns are parameters varied
res = expand.grid(prop_s=seq(0.1,1.0,0.1),
threshold=1,
eff_pop_prop=seq(0.1,0.9,0.1))
res$outbreak_dur = NA
res$outbreak_size = NA
res$time_to_peak = NA
res$peak_inc_per_1e3 = NA
res$attack_rate_per_1e3 = NA
res$prop_peak_inc = NA
output = vector("list", nrow(res))
for(i in 1:nrow(res)){
cat("i =", i, "\n")
out <- simulate_outbreak(params=params,
prop_s=res$prop_s[i],
prop_eff_pop=res$eff_pop_prop[i])
output[[i]] = out
res[i, "outbreak_dur"] = out$outbreak_char[["outbreak_dur"]]
res[i, "outbreak_size"] = out$outbreak_char[["outbreak_size"]]
res[i, "time_to_peak"] = out$outbreak_char[["time_to_peak"]]
res[i, "peak_inc_per_1e3"] = out$outbreak_char[["peak_inc_per_1e3"]]
res[i, "attack_rate_per_1e3"] = out$outbreak_char[["attack_rate_per_1e3"]]
res[i, "prop_peak_inc"] = out$outbreak_char[["prop_peak_inc"]]
}
```
### $R_t = R_0 S$ during the initial period
$R_t$ measured over the initial period of an outbreak through the use of EpiEstim package gives $R_0 S$ where $S$ is the fraction of susceptibles rather than $R_0$. For an endemic disease like cholera, $S$ can be lower than 1 and therefore, $R_t$ during the initial phase of a cholera outbreak can lead to an underestimate of $R_0$. See the code block below to check if the incidence is the same regardless of $R_0$ as long as the $R_0 S$ remains constant. This implies that given the value of initial Rt we can choose different combinations of $R_0$ and $S$. Instead, we assumed that $R_t=R_0$ and assumed $S=1$. Then, we explored the varying size of the population (i.e., S) that produced the observed characteristics of the outbreak.
```{r}
R0S = 4
parm <- initialize_params()
parm$vacc_cov <- c(0.0, 0.0)
parm$delay_until_2nd_campaign <- 30
parm$alpha <- 0
parm$tau <- 0.1
parm$R0 <- 2
parm$R0W <- 0
prop_s <- R0S/parm$R0
out = simulate_outbreak(params=parm, prop_s=prop_s, output_time=1)
head(out$timeseries, n=10)
# parm2 <- initialize_params()
# parm2$vacc_cov <- c(0.0, 0.0)
# parm2$delay_until_2nd_campaign <- 30
# parm2$alpha <- 0
# parm2$tau <- 0.1
parm2 <- parm
parm2$R0 <- 4
# parm2$R0W <- 0
prop_s = R0S/parm2$R0
out2 = simulate_outbreak(params=parm2, prop_s=prop_s, output_time=1)
head(out2$timeseries, n=20)
df=data.frame(ci1=out$timeseries$ci, ci2=out$timeseries$ci)
df$diff <- df$ci1 - df$ci2
summary(df$diff)
```
### Time series data
```{r}
devtools::load_all()
dat_ts = readRDS("inst/extdata/outbreak_data_ts.rds")
dat_long = data.table::fread("inst/extdata/ocv_long_dataset.csv")
# outbreaks without OCV campaign
outbks_no_ocv = dat_long[OCV_before_1 == FALSE & OCV_before_2 == FALSE &
OCV_before_3 == FALSE & OCV_during == FALSE]
table(outbks_no_ocv$OCV_after_1)
ids_outbks_no_ocv = unique(outbks_no_ocv$ID_outbreak)
# to record impressions of the oubreak ts after visualizing
data.table::fwrite(data.frame(outbreak_id = ids_outbks_no_ocv), "outputs/outbreak_no_ocv.csv")
library(ggplot2)
for (i in 1:length(ids_outbks_no_ocv)) {
x = dat_ts[dat_ts$ID_outbreak == ids_outbks_no_ocv[i],]
p <- ggplot(data=x)+
geom_point(aes(x=TL, y=sCh))+
labs(x="", y="Suspected cases", title=ids_outbks_no_ocv[i])+
scale_x_date(date_breaks="1 week", date_labels="%d %b",
limits=c(min(x$TL), max(x$TL)))+
theme(axis.text.x=element_text(angle=60, hjust=1))
ggsave(paste0("plots/ts_", i, ".png"), plot=p)
# png(filename = paste0("plots/ts_", i, ".png"))
# plot(x$TL, x$sCh, main = ids_outbks_no_ocv[i])
# axis(1, x$TL, format(x$TL, "%b %d"), cex.axis = .7)
# dev.off()
}
```
### Fit
Parameter fitting
Population size is assumed to be the same as the
Parameters to vary
1. time of the outbreak start
2. reproduction number
2. proportion of the population that is susceptible to infection
4. reporting rate, which determines the proportion of the symptomatic cases
(I in the SEIRW model) observed during the outbreak
5. dispersion parameter of the negative binomial distribution (optional)
"time of outbreak start" is an integer. Optimization algorithm is usually
designed to work with continuous variable and doesn't work well for the mixed (discrete and continuous) programming case. I therefore chose a priori the
range of plausible range of values for the introduction (1-35 days) and took the brute force parameter estimation.
```{r}
devtools::load_all()
dat = data.table::fread("https://raw.githubusercontent.com/kimfinale/cholera_outbreaks_ssa/main/reference_data/outbreak_data.csv")
dat_ts = readRDS("inst/extdata/outbreak_data_ts.rds")
dat_long = data.table::fread("inst/extdata/ocv_long_dataset.csv")
outbks_no_ocv = dat_long[OCV_before_1 == FALSE & OCV_before_2 == FALSE &
OCV_before_3 == FALSE & OCV_during == FALSE]
ids_outbks_no_ocv = unique(outbks_no_ocv$ID_outbreak)
i = 1
id <- ids_outbks_no_ocv[i]
pop = dat[location == gsub("[0-9+]|-", "", id), population]
x = dat_ts[dat_ts$ID_outbreak == id,]
plot(x$TL, x$sCh, main = id, xlab="", ylab="Suspected cases")
(obs_len = sum(as.double(gsub(".*?([0-9]+).*", "\\1", x$date_range))))
params = initialize_params(Population=pop, obs_length = obs_len)
parm = c(day1 = 14, prop_immune=0.2, R0=3, reporting_rate=0.1)
inc = incidence(pars = parm, pars_baseline = params)
negloglik(pars=parm, pars_baseline=params, obs=x$sCh)
```
### Optim
```{r}
NLL <- function(pi=0.1,r0=3,pr=0.2,pep=0.1) {
parm = c(day1=day1,
prop_immune=expit(pi),
R0=(exp(r0)+1),
prop_report=expit(pr),
prop_eff_pop=expit(pep))
nll = negloglik(pars=parm, pars_baseline=PARAMS, obs=x$sCh)
return(nll)
}
library(bbmle)
fit1 <- mle2(minuslogl=NLL, method="L-BFGS-B", start=c(pi=logit(0.2),r0=log(5),pr=logit(0.4),pep=logit(0.1)))
summary(fit1)
expit(coef(fit1)[c(1,3,4)])
exp(coef(fit1)[c(2)])+1
# fit2 <- mle2(NLL, optimizer="nlminb", lower=c(pi=1e-6,r0=1.01,pr=1e-6), upper=c(pi=0.99,r0=20,rr=0.99)))
fit2 <- mle2(NLL, optimizer="nlminb", start=c(pi=logit(0.2),r0=log(5),pr=logit(0.4),pep=logit(0.1)))
#
summary(fit2)
#differential evolution
parm = c(Day1=14, prop_immune=0.2, R0=5, prop_report=0.2)
```
### Differential evolution
```{r}
devtools::load_all()
dat = data.table::fread("https://raw.githubusercontent.com/kimfinale/cholera_outbreaks_ssa/main/reference_data/outbreak_data.csv")
dat_ts = readRDS("inst/extdata/outbreak_data_ts.rds")
dat_long = data.table::fread("inst/extdata/ocv_long_dataset.csv")
outbks_no_ocv = dat_long[OCV_before_1 == FALSE & OCV_before_2 == FALSE &
OCV_before_3 == FALSE & OCV_during == FALSE]
ids_outbks_no_ocv = unique(outbks_no_ocv$ID_outbreak)
i = 1
id <- ids_outbks_no_ocv[i]
pop = dat[location == gsub("[0-9+]|-", "", id), population]
x = dat_ts[dat_ts$ID_outbreak == id,]
obs_len = nrow(x)
# get_output_days <- function(x) {
# unitdays = gsub("^([0-9]+).*", "\\1", x$date_range)
# l = length(unique(unitdays))
# if (l != 1){
# stop("Output days have more than one kind")
# }
# return(as.double(unique(unitdays)))
# }
output_day = get_output_days(x)
# (obs_len = sum(as.double(gsub("^([0-9]+).*", "\\1", x$date_range))))
OBS <- x$sCh
PARAMS <- initialize_params(population=pop,
obs_length=obs_len,
output_days=output_day,
output_state="CI")
# day1 = 14
#
# parm = c(day1=4, prop_immune=0.2, R0=3, prop_report=0.1, prop_eff_pop=0.2)
NLL <- function(parm, fixed) {
# just in case parm already has names, which appears to mess up
parm = c(day1=fixed[[1]],
prop_immune=parm[[1]],
R0=parm[[2]],
prop_report=parm[[3]],
prop_eff_pop=parm[[4]])
nll = negloglik(pars=parm, pars_baseline=PARAMS, obs=OBS)
return(nll)
}
library(RcppDE)
fitlist <- vector('list', length=20)
id <- 1
for (i in 21:40) {
day1 = i
cat("day 1 =", day1, "\n")
fit <- DEoptim(fn=NLL,
lower=c(1e-6, 1.01, 1e-6, 1e-6),
upper=c(0.99, 30, 0.99, 0.99),
control=DEoptim.control(NP=200, itermax=200, trace=FALSE),
fixed=i)
fitlist[[id]] <- fit
id <- id + 1
(p = fit$optim$bestmem)
# par1 par2 par3 par4
# 0.7283755 3.5943194 0.0318457 0.2340129
parm = c(day1=day1,
prop_immune=p[[1]],
R0=p[[2]],
prop_report=p[[3]],
prop_eff_pop=p[[4]])
inc = incidence(pars=parm, pars_baseline=PARAMS)
inc$param
m = rowSums(inc$inc)
tot = length(m)
plot(1:tot, m, type="l")
points((tot-length(OBS)+1):tot, OBS, col=2)
}
lapply(fitlist, function(x) x$optim$bestmem)
```
### DEoptim::DEoptim
1. fnMap option for integer programming
2. parallel
```{r}
library(CholeraOutbreakModel)
dat = data.table::fread("https://raw.githubusercontent.com/kimfinale/cholera_outbreaks_ssa/main/reference_data/outbreak_data.csv")
dat_ts = readRDS("inst/extdata/outbreak_data_ts.rds")
dat_long = data.table::fread("inst/extdata/ocv_long_dataset.csv")
outbks_no_ocv = dat_long[OCV_before_1 == FALSE & OCV_before_2 == FALSE &
OCV_before_3 == FALSE & OCV_during == FALSE]
ids_outbks_no_ocv = unique(outbks_no_ocv$ID_outbreak)
i = 1
id <- ids_outbks_no_ocv[i]
pop = dat[location == gsub("[0-9+]|-", "", id), population]
x = dat_ts[dat_ts$ID_outbreak == id,]
obs_len = nrow(x)
output_day = get_output_days(x)
# Variables to be passed to nodes
OBS <- x$sCh
PARAMS <- initialize_params(population=pop,
obs_length=obs_len,
output_days=output_day,
output_state="CI")
mapfun <- function(x){
x[5] <- round(x[5])
return(x)
}
NLL <- function(parm) {
# just in case parm already has names, which appears to mess up
parm = c(day1=parm[[5]],
prop_immune=parm[[1]],
R0=parm[[2]],
prop_report=parm[[3]],
prop_eff_pop=parm[[4]])