exercises

Author: stevencarlislewalker

exploration-exercises.md

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+Exploration Exercises
+================
+
+## `ggplot` Recipes
+
+Simulations from `macpan2` come in a standard format with columns
+described
+[here](https://canmod.github.io/macpan2/articles/quickstart.html#generating-simulations),
+and full documentation
+[here](https://canmod.github.io/macpan2/reference/mp_trajectory.html#value).
+The key point is that there is always a `time`, `matrix`, and `value`
+column. Let’s focus on those. We can use this SIR example.
+
+``` r
+library(macpan2); library(ggplot2)
+```
+
+    ## 
+    ## Attaching package: 'ggplot2'
+
+    ## The following object is masked _by_ '.GlobalEnv':
+    ## 
+    ##     theme_bw
+
+``` r
+sir = mp_tmb_library("starter_models", "sir", package = "macpan2")
+sim = mp_simulator(sir, time_steps = 25, outputs = "infection")
+dat = mp_trajectory(sim)
+print(dat)
+```
+
+    ##       matrix time row col     value
+    ## 1  infection    1   0   0 0.1980000
+    ## 2  infection    2   0   0 0.2169692
+    ## 3  infection    3   0   0 0.2376233
+    ## 4  infection    4   0   0 0.2600847
+    ## 5  infection    5   0   0 0.2844793
+    ## 6  infection    6   0   0 0.3109346
+    ## 7  infection    7   0   0 0.3395786
+    ## 8  infection    8   0   0 0.3705380
+    ## 9  infection    9   0   0 0.4039349
+    ## 10 infection   10   0   0 0.4398849
+    ## 11 infection   11   0   0 0.4784928
+    ## 12 infection   12   0   0 0.5198490
+    ## 13 infection   13   0   0 0.5640248
+    ## 14 infection   14   0   0 0.6110669
+    ## 15 infection   15   0   0 0.6609922
+    ## 16 infection   16   0   0 0.7137807
+    ## 17 infection   17   0   0 0.7693697
+    ## 18 infection   18   0   0 0.8276464
+    ## 19 infection   19   0   0 0.8884416
+    ## 20 infection   20   0   0 0.9515225
+    ## 21 infection   21   0   0 1.0165878
+    ## 22 infection   22   0   0 1.0832626
+    ## 23 infection   23   0   0 1.1510954
+    ## 24 infection   24   0   0 1.2195575
+    ## 25 infection   25   0   0 1.2880447
+
+If we are simulating a single variable, the `matrix` column will be
+constant and so we will use recipes like this.
+
+``` r
+(dat
+  |> ggplot()
+  + geom_line(aes(time, value))
+)
+```
+
+![](figures/ggplot-1.png)<!-- -->
+
+If we have multiple variables we can use the `matrix` column in our
+visualizations to keep track of different variables.
+
+``` r
+sim = mp_simulator(sir, time_steps = 25, outputs = mp_flow_vars(sir))
+dat = mp_trajectory(sim)
+(dat
+  |> ggplot()
+  + geom_line(aes(time, value))
+  + facet_wrap(~matrix)
+)
+```
+
+![](figures/multimat-1.png)<!-- -->
+
+``` r
+(dat
+  |> ggplot()
+  + geom_line(aes(time, value, colour = matrix))
+)
+```
+
+![](figures/multimat-2.png)<!-- -->
+
+## Functional Forms of Flow Rates
+
+We have so far focused on specifying flows with either constant
+per-capita rates or mass-action rates. There are a variety of
+[mathematical
+functions](https://canmod.github.io/macpan2/reference/engine_functions)
+that you can use to build more complex functional forms for these rates.
+
+| <img src="images/exercise.svg" width="120" />                                                                                                                                                                                                          |
+|:-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| Building a simple model with seasonal cycles in transmission. What are some other forms of complexity in the functional forms of rates? Try to implement them. Keep in mind that you can use tilde-based expressions to define intermediate variables. |
+
+## Unbalanced Flows
+
+So far we have used the
+[mp_per_capita_flow](https://canmod.github.io/macpan2/reference/mp_per_capita_flow)
+function that specifies perfectly balanced flows – the total number out
+of the `from` box is equal to the total number into the `to` box. But
+processes like birth/death and importation do not behave this way – for
+example, birth adds individuals to the `to` box without removing
+individuals from the `from` box. Viral shedding into wastewater is
+another process that is not a balanced flow. The above linked help page
+describes two other kinds of flows that are not balanced.
+
+| <img src="images/exercise.svg" width="120" />                                                                                                                                                                                     |
+|:----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
+| Modify one of your models to include birth and death. Allow for the possibility of more birth than death. If your model uses a constant total population size, `N`, you will need to add expressions that update `N` dynamically. |
+
+| <img src="images/exercise.svg" width="120" />      |
+|:---------------------------------------------------|
+| Add a wastewater compartment to an existing model. |
+
+## Initializing Variables
+
+So far we have initialized variables by adding numerical values to the
+`default` list.
+
+## Relationships Parameters and Simulations