add edits after delivery

episodes/simulating-transmission.Rmd

@@ -47,7 +47,7 @@ Install packages if their are not already installed
 
 ```r
 if (!base::require("pak")) install.packages("pak")
-pak::pak(c("epiverse-trace/epidemics", "socialmixr", "tidyverse"))
+pak::pak(c("epiverse-trace/epidemics", "socialmixr", "scales", "tidyverse"))
 ```
 
 If you have any error message,
@@ -208,12 +208,19 @@ contact_data <- socialmixr::contact_matrix(
 )
 
 # prepare contact matrix
-contact_matrix <- t(contact_data$matrix)
+socialcontact_matrix <- t(contact_data$matrix)
 
 # print
-contact_matrix
+socialcontact_matrix
 ```
 
+Remember that the matrix satisfies the `symmetric = TRUE` condition at the level of total number of contacts.
+
+The total number of contacts between groups $i$ and $j$ is calculated as the mean number of contacts (`contact_data$matrix`) multiplied by the number of individuals in group $i$ (`contact_data$demography$population`)
+
+```{r}
+contact_data$matrix * contact_data$demography$population
+```
 
 :::::::::::::::::::::::::::::::::
 ::::::::::::::::::::::::::::::::::::::::::::::::
@@ -224,7 +231,7 @@ The result is a square matrix with rows and columns for each age group. Contact
 
 ### Normalisation
 
-In `{epidemics}` the contact matrix normalisation happens within the function call, so we don't need to normalise the contact matrix before we pass it to `population()` (see section 3. Population Structure). For details on normalisation, see the tutorial on [Contact matrices](../episodes/contact-matrices.md).
+In `{epidemics}` the contact matrix normalisation happens within the function call, so we don't need to normalise the contact matrix before we pass it to `epidemics::population()` (see section 3. Population Structure). For details on normalisation, see the tutorial on [Contact matrices](../episodes/contact-matrices.md).
 
 ::::::::::::::::::::::::::::::::::::::::::::::::
 
@@ -248,12 +255,16 @@ The initial conditions are the proportion of individuals in each disease state $
 The initial conditions in the first age category are $S(0)=1-\frac{1}{1,000,000}$, $E(0) =0$, $I(0)=\frac{1}{1,000,000}$, $R(0)=0$. This is specified as a vector as follows:
 
 ```{r initial_inf}
+# 1 in 1,000,000 is equivalent to 1e-6
 initial_i <- 1e-6
 initial_conditions_inf <- c(
   S = 1 - initial_i, E = 0, I = initial_i, R = 0, V = 0
 )
 ```
 
+Note that R uses scientific `e` notation where `e` tells you to multiple the base number by 10 raised to the power shown ([DataKwery, 2020](https://www.datakwery.com/post/2020-07-11-scientific-notation-in-r/)).
+The expression $1 \times 10^{-6}$ is equivalent to `1e-6`.
+
 For the age categories that are free from infection, the initial conditions are $S(0)=1$, $E(0) =0$, $I(0)=0$, $R(0)=0$. We specify this as follows,
 
 ```{r initial_free}
@@ -265,15 +276,15 @@ initial_conditions_free <- c(
 We combine the three initial conditions vectors into one matrix, 
 
 ```{r initial_conditions}
-# combine the initial conditions
+# combine the initial conditions into a matrix class object
 initial_conditions <- rbind(
-  initial_conditions_inf, # age group 1
+  initial_conditions_inf, # age group 1 (only group with infectious)
   initial_conditions_free, # age group 2
   initial_conditions_free # age group 3
 )
 
 # use contact matrix to assign age group names
-rownames(initial_conditions) <- rownames(contact_matrix)
+rownames(initial_conditions) <- rownames(socialcontact_matrix)
 initial_conditions
 ```
 
@@ -284,19 +295,22 @@ initial_conditions
 The population object requires a vector containing the demographic structure of the population. The demographic vector must be a named vector containing the number of individuals in each age group of our given population. In this example, we can extract the demographic information from the `contact_data` object that we obtained using the `socialmixr` package.
 
 ```{r demography}
+# extract the demography vector
 demography_vector <- contact_data$demography$population
-names(demography_vector) <- rownames(contact_matrix)
+
+# use contact matrix to assign age group names
+names(demography_vector) <- rownames(socialcontact_matrix)
 demography_vector
 ```
 
-To create our population object, from the `{epidemics}` package we call the function `population()` specifying a name, the contact matrix, the demography vector and the initial conditions.
+To create our population object, from the `{epidemics}` package we call the function `epidemics::population()` specifying a name, the contact matrix, the demography vector and the initial conditions.
 
 ```{r population}
 library(epidemics)
 
-uk_population <- population(
+uk_population <- epidemics::population(
   name = "UK",
-  contact_matrix = contact_matrix,
+  contact_matrix = socialcontact_matrix,
   demography_vector = demography_vector,
   initial_conditions = initial_conditions
 )
@@ -374,11 +388,11 @@ For models that are described by [differential equations](../learners/reference.
 An _ODE solver_ is the software used to find numerical solutions to differential equations. If interested on how a system of differential equations is solved in `{epidemics}`, we suggest you to read the section on [ODE systems and models](https://epiverse-trace.github.io/epidemics/articles/design-principles.html#ode-systems-and-models) at the "Design principles" vignette. 
 ::::::::::::::::::::::::::::::::::::::::::::::::
 
-Now we are ready to run our model using `model_default()` from the `{epidemics}` package. 
+Now we are ready to run our model using `epidemics::model_default()` from the `{epidemics}` package. 
 
 Let's specify `time_end=600` to run the model for 600 days.
 ```{r run_model}
-output <- model_default(
+output <- epidemics::model_default(
   # population
   population = uk_population,
   # rates
@@ -516,7 +530,7 @@ beta <- r_samples / infectious_period
 2. Run the model 100 times with $R_0$ equal to a different sample each time
 
 ```{r samples}
-output_samples <- model_default(
+output_samples <- epidemics::model_default(
   population = uk_population,
   transmission_rate = beta,
   infectiousness_rate = infectiousness_rate,