Add vignette on generations required to achieve a set outbreak size

_pkgdown.yml

@@ -9,6 +9,7 @@ articles:
 - title: Package vignettes
  navbar: Package vignettes
  contents:
+ - gens_to_n_cases
 - title: Modelling guides and background
  navbar: Modelling guides and background
  contents:

vignettes/gens_to_n_cases.Rmd

@@ -0,0 +1,46 @@
+---
+title: "Number of generations to achieve a set outbreak size"
+author: "James Azam"
+output:
+ bookdown::html_vignette2:
+ fig_caption: yes
+ code_folding: show
+pkgdown:
+ as_is: true
+bibliography: references.json
+link-citations: true
+vignette: >
+ %\VignetteEncoding{UTF-8}
+ %\VignetteIndexEntry{Number of generations to achieve a set outbreak size}
+ %\VignetteEngine{knitr::rmarkdown}
+editor_options: 
+ chunk_output_type: console
+---
+
+```{r setup, include=FALSE}
+knitr::opts_chunk$set(
+ echo = TRUE,
+ message = FALSE,
+ warning = FALSE,
+ collapse = TRUE,
+ comment = "#>"
+)
+```
+
+# Outline
+
+* Question: At what generation does an outbreak reach a size of 100, given that
+ it was started by a single individual with R0 = 1.5, and individual
+ transmission, $k$, at levels of 0.01, 0.1, 0.5, 1, 4, and Infinity?
+* Method: 
+ * We use a negative binomial model with $mu = 1.5$ and
+ $size = c(0.01, 0.1, 0.5, 1, 4, Inf)$.
+ * We run 10, 000 simulations per each combination of $mu$ and $size$
+ * We aggregate chain sizes by generation and extract the generation
+ where cumulative chain size = 100.
+ * We find the percentage of simulations that reached the 100 case size
+ threshold.
+* Outcome: The distribution (boxplot) of the realized generations per value of
+ $k$. This reproduces Fig 2c of @lloyd-smith2005.
+
+# References