starter model

inst/starter_models/sir_waning/README.md

@@ -1,15 +1,69 @@
----
-title: "SIR with waning immunity"
-index_entry: "a basic SIR model with a flow from R back to S"
-author: Steve Walker
----
+SIR with waning immunity
+================
+Jen Freeman, Steve Walker
 
-Endemic pathogens can sometimes be modelled by sending R back to S, thereby controlling susceptible depletion such that new infections keep arising indefinitely.
+-   <a href="#packages-used" id="toc-packages-used">Packages Used</a>
+-   <a href="#model-specification" id="toc-model-specification">Model
+    Specification</a>
+-   <a href="#states" id="toc-states">States</a>
+-   <a href="#parameters" id="toc-parameters">Parameters</a>
+-   <a href="#dynamics" id="toc-dynamics">Dynamics</a>
+-   <a href="#references" id="toc-references">References</a>
+
+Endemic pathogens can sometimes be modelled by sending R back to S,
+thereby controlling susceptible depletion such that new infections keep
+arising indefinitely. This is an extension of the
+[sir](https://github.com/canmod/macpan2/tree/main/inst/starter_models/sir)
+model to include such immunity waning.
+
+# Packages Used
+
+The code in this article uses the following packages.
+
+``` r
+library(ggplot2)
+library(dplyr)
+library(tidyr)
+library(macpan2)
+```
+
+# Model Specification
+
+This model has been specified in the `sir_waning` directory
+[here](https://github.com/canmod/macpan2/blob/main/inst/starter_models/sir_waning/tmb.R)
+and is accessible from the `macpan2` model library (see [Example
+Models](https://canmod.github.io/macpan2/articles/example_models.html)
+for details). We can read in the model specification using the
+`mp_tmb_library` command.
+
+``` r
+spec = mp_tmb_library(
+    "starter_models"
+  , "sir_waning"
+  , package = "macpan2"
+)
+```
+
+This specification can be used to draw the following flow diagram using
+code found in the [source for this
+article](https://github.com/canmod/macpan2/blob/main/inst/starter_models/sir_waning/README.Rmd).
+
+    #> Warning in topological_sort_engine(flows, states, warn_not_dag = TRUE): 
+    #> State network is not acyclic (i think),
+    #> and therefore cannot be topologically sorted.
+    #> Defaulting to original order where necessary.
+
+    #> Warning in topological_sort_engine(flows, states, warn_not_dag = TRUE): 
+    #> State network is not acyclic (i think),
+    #> and therefore cannot be topologically sorted.
+    #> Defaulting to original order where necessary.
+
+![](./figures/diagram-1.png)<!-- -->
 
 # States
 
 | variable | description                       |
-| -------- | --------------------------------- |
+|----------|-----------------------------------|
 | S        | Number of susceptible individuals |
 | I        | Number of infectious individuals  |
 | R        | Number of recovered individuals   |
@@ -19,12 +73,12 @@ The size of the total population is, $N = S + I + R$.
 # Parameters
 
 | variable | description                     |
-| -------- | ------------------------------- |
+|----------|---------------------------------|
 | $\beta$  | per capita transmission rate    |
 | $\gamma$ | per capita recovery rate        |
 | $\phi$   | per capita waning immunity rate |
 
-# Dynamics 
+# Dynamics
 
 $$
 \begin{align*}
@@ -34,7 +88,4 @@ $$
 \end{align*}
 $$
 
-# Model Specification
-
-This model has been specified in the `sir_waning` directory [here](https://github.com/canmod/macpan2/blob/main/inst/starter_models/sir_waning/tmb.R) and is accessible from the `macpan2` model library (see [Example Models](https://canmod.github.io/macpan2/articles/example_models.html) for details). 
-
+# References