From 59db85949d87e7f5a49959ec8ab69cb04af15b91 Mon Sep 17 00:00:00 2001
From: Rich FitzJohn <r.fitzjohn@imperial.ac.uk>
Date: Thu, 14 Nov 2024 13:29:21 +0000
Subject: [PATCH 1/4] Fix code background

---
 common.R | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/common.R b/common.R
index de629bf..14f61d8 100644
--- a/common.R
+++ b/common.R
@@ -17,5 +17,5 @@ r_output <- function(x) {
 }
 
 plain_output <- function(x) {
-  lang_output(x, "")
+  lang_output(x, "md") # not great, but at least renders nicely
 }

From 7d59e3b2188c64b4a6e2bd46c14238773dada1ec Mon Sep 17 00:00:00 2001
From: Rich FitzJohn <r.fitzjohn@imperial.ac.uk>
Date: Thu, 14 Nov 2024 13:30:48 +0000
Subject: [PATCH 2/4] Use common.R everywhere

---
 differentiability.qmd | 5 +++++
 installation.qmd      | 5 +++++
 monty.qmd             | 5 +++++
 references.qmd        | 5 +++++
 4 files changed, 20 insertions(+)

diff --git a/differentiability.qmd b/differentiability.qmd
index 5f9caff..9c7c516 100644
--- a/differentiability.qmd
+++ b/differentiability.qmd
@@ -1,3 +1,8 @@
 # Differentiability
 
+```{r}
+#| include: false
+source("common.R")
+```
+
 Random walk suppression and other uses
diff --git a/installation.qmd b/installation.qmd
index d9aa7b4..4df5484 100644
--- a/installation.qmd
+++ b/installation.qmd
@@ -1,5 +1,10 @@
 # Installation
 
+```{r}
+#| include: false
+source("common.R")
+```
+
 Package installation is hard, let's go shopping.
 
 ## Packages
diff --git a/monty.qmd b/monty.qmd
index 8ddca01..3a15487 100644
--- a/monty.qmd
+++ b/monty.qmd
@@ -1,5 +1,10 @@
 # Monty
 
+```{r}
+#| include: false
+source("common.R")
+```
+
 Before showing how to fit odin models to data, we'll focus for a bit on monty itself.  If you are anxious to get on and fit the model from @sec-data-filter, you might skip ahead to @sec-inference, where we resume this.
 
 There are a bunch of things we want to cover in this chapter so likely it will be split into a few:
diff --git a/references.qmd b/references.qmd
index 925f7c4..eebd42a 100644
--- a/references.qmd
+++ b/references.qmd
@@ -1,4 +1,9 @@
 # References {.unnumbered}
 
+```{r}
+#| include: false
+source("common.R")
+```
+
 ::: {#refs}
 :::

From adf14fa7f02aead45eb0d4441b23087f738f92cc Mon Sep 17 00:00:00 2001
From: Rich FitzJohn <r.fitzjohn@imperial.ac.uk>
Date: Thu, 14 Nov 2024 13:35:00 +0000
Subject: [PATCH 3/4] Add equation

---
 odin.qmd | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/odin.qmd b/odin.qmd
index d4aed6b..c4bea0e 100644
--- a/odin.qmd
+++ b/odin.qmd
@@ -13,7 +13,15 @@ library(odin2)
 
 ## A simple example {#sec-odin-sir}
 
-Here is a small system of equations for an "SIR" (Susceptible-Infected-Recovered) model, implemented as a set of ordinary differential equations:
+Here is a small system of differential equations for an "SIR" (Susceptible-Infected-Recovered) model:
+
+\begin{gather*}
+\frac{dS}{dt} = -\beta S \frac{I}{N}\\
+\frac{dI}{dt} = \beta S \frac{I}{N} - \gamma I\\
+\frac{dR}{dt} = \gamma I
+\end{gather*}
+
+And here is an implementation of these equations in `odin`:
 
 ```{r}
 sir <- odin({

From 0584d0d3a4aa9db852965fa24860c709f4dc460c Mon Sep 17 00:00:00 2001
From: Rich FitzJohn <r.fitzjohn@imperial.ac.uk>
Date: Thu, 14 Nov 2024 13:39:03 +0000
Subject: [PATCH 4/4] Small note on binomial

---
 stochasticity.qmd | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/stochasticity.qmd b/stochasticity.qmd
index a4c8583..9232ec8 100644
--- a/stochasticity.qmd
+++ b/stochasticity.qmd
@@ -61,6 +61,8 @@ sir <- odin({
 
 This is a discrete-time model (using `update()` and not `deriv()`) as stochastic models must run in discrete time.  We use `dt` to scale the rates, and adjusting `dt` will change the way that stochasticity affects the dynamics of the system.
 
+The call to `Binomial()` samples from a binomial distribution, returning the number of successes from `S` (or `I`) draws, each with probability `p_SI` (or `p_IR`).
+
 ```{r}
 sir
 ```