---
title: "Modelling outcomes under uncertainty in infection parameters"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Modelling outcomes under uncertainty in infection parameters}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

This vignette shows how to use _daedalus_ to model outcomes under uncertainty in infection parameters.
We focus on uncertainty in $R_0$, which has a major effect on epidemic trajectories.

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

Load required packages including _daedalus_.

```{r setup}
library(daedalus)
library(ggplot2)
library(dplyr)
```

Consider an infection similar to 2009 influenza, with uncertainty in the $R_0$.
We draw a set of 100 $R_0$ values from a normal distribution to parameterise 100 `<daedalus_infection>` objects, which can be passed as a list to the function [daedalus_multi_infection()].

```{r draw_r0_samples}
flu_2009 <- daedalus_infection("influenza_2009")
flu_2009_r0 <- get_data(flu_2009, "r0")

# draw samples
r0_samples <- flu_2009_r0 * stats::rnorm(100, 1, 0.1)

# view a histogram of samples
ggplot() +
  geom_histogram(aes(r0_samples)) +
  labs(
    x = "R0 value",
    y = "Count"
  )

# parameterise daedalus_infection objects
infection_list <- lapply(
  r0_samples, \(x) daedalus_infection("influenza_2009", r0 = x)
)
```

Run the model for the U.K. with the infection list passed as `infection`.
No mitigation strategies are applied.

```{r model_multi_infect}
# run model with 100 infection objects
output_list <- daedalus_multi_infection(
  "GBR", infection_list,
  time_end = 200
)

# get incidence data and plot epi curves
data_list <- lapply(output_list, get_incidence, "infections")
data_list <- Map(
  data_list, seq_along(data_list),
  f = function(df, i) {
    df$param_set <- i
    df
  }
)
data <- bind_rows(data_list)

# plot curves
ggplot(data) +
  geom_line(
    aes(time, value, group = param_set),
    alpha = 0.4
  ) +
  labs(x = "Time", y = "New infections")
```