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avallecam merged 3 commits into from
Nov 14, 2025
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Review baseline en #122

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c57a54c
fix prereq
avallecam Nov 14, 2025
6a40b74
make contact matrix a challenge
avallecam Nov 14, 2025
a42b125
add guides to tutors
avallecam Nov 14, 2025
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185 changes: 73 additions & 112 deletions episodes/simulating-transmission.Rmd
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Original file line number Diff line number Diff line change
Expand Up @@ -5,16 +5,11 @@ exercises: 30 # exercise time in minutes
---

```{r setup, echo= FALSE, message = FALSE, warning = FALSE}
library(ggplot2)
library(dplyr)
library(tidyverse)
library(DiagrammeR)
library(webshot)
library(epidemics)
webshot::install_phantomjs(force = TRUE)
```


:::::::::::::::::::::::::::::::::::::: questions

- How do I simulate disease spread using a mathematical model?
Expand All @@ -34,14 +29,31 @@ webshot::install_phantomjs(force = TRUE)

::::::::::::::::::::::::::::::::::::: prereq

+ Complete tutorial on [Contact matrices](../episodes/contact-matrices.md).

Learners should familiarise themselves with following concept dependencies before working through this tutorial:

**Mathematical Modelling** : [Introduction to infectious disease models](https://doi.org/10.1038/s41592-020-0856-2), [state variables](../learners/reference.md#state), [model parameters](../learners/reference.md#parsode), [initial conditions](../learners/reference.md#initial), [differential equations](../learners/reference.md#ordinary).

**Epidemic theory** : [Transmission](https://doi.org/10.1155/2011/267049), [Reproduction number](https://doi.org/10.3201/eid2501.171901).

**R packages installed**: `{epidemics}`, `{socialmixr}`, `{tidyverse}`.

:::::::::::::::::::::::::::::::::

:::::::::: spoiler

Install packages if their are not already installed

```r
if (!base::require("pak")) install.packages("pak")
pak::pak(c("epidemics", "socialmixr", "tidyverse"))
```

If you have any error message,
go to the [main setup page](../learners/setup.md#software-setup).

::::::::::

## Introduction

Expand All @@ -55,103 +67,16 @@ library(socialmixr)
library(tidyverse)
```

:::::::::::::::::::::: instructor

```{r traj, echo = FALSE, message = FALSE, fig.width = 10, eval = TRUE}
# load contact and population data from socialmixr::polymod
polymod <- socialmixr::polymod
contact_data <- socialmixr::contact_matrix(
polymod,
countries = "United Kingdom",
age.limits = c(0, 20, 40),
symmetric = TRUE
)

# prepare contact matrix
contact_matrix <- t(contact_data$matrix)

# prepare the demography vector
demography_vector <- contact_data$demography$population
names(demography_vector) <- rownames(contact_matrix)

# initial conditions: one in every 1 million is infected
initial_i <- 1e-6
initial_conditions_inf <- c(
S = 1 - initial_i, E = 0, I = initial_i, R = 0, V = 0
)

initial_conditions_free <- c(
S = 1, E = 0, I = 0, R = 0, V = 0
)

# build for all age groups
initial_conditions <- rbind(
initial_conditions_inf,
initial_conditions_free,
initial_conditions_free
)
rownames(initial_conditions) <- rownames(contact_matrix)

# prepare the population to model as affected by the epidemic
uk_population <- epidemics::population(
name = "UK",
contact_matrix = contact_matrix,
demography_vector = demography_vector,
initial_conditions = initial_conditions
)

# time periods
preinfectious_period <- 3.0
infectious_period <- 7.0
basic_reproduction <- 1.46

# rates
infectiousness_rate <- 1.0 / preinfectious_period
recovery_rate <- 1.0 / infectious_period
transmission_rate <- basic_reproduction / infectious_period

# run an epidemic model using `epidemic()`
output_plot <- epidemics::model_default(
population = uk_population,
transmission_rate = transmission_rate,
infectiousness_rate = infectiousness_rate,
recovery_rate = recovery_rate,
time_end = 600, increment = 1.0
)

output_plot %>%
filter(compartment %in% c("exposed", "infectious")) %>%
ggplot() +
geom_line(
aes(
x = time,
y = value,
colour = demography_group,
linetype = compartment
),
linewidth = 1.2
) +
scale_y_continuous(
labels = scales::comma
) +
scale_colour_brewer(
palette = "Dark2",
name = "Age group"
) +
theme_bw() +
labs(
x = "Simulation time (days)",
linetype = "Compartment",
y = "Individuals"
)
```


:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: instructor
Use slides to introduce the topics of:

By the end of this tutorial, learners should be able to replicate the above image on their own computers.
- Scenario modelling and
- Contact matrix.

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Then start with the livecoding.

::::::::::::::::::::::

## Simulating disease spread

Expand Down Expand Up @@ -254,37 +179,38 @@ A contact matrix represents the average number of contacts between individuals i

## Load contact and population data

Using the R package `socialmixr`, run the following lines of R code to obtain the contact matrix for the United Kingdom for the year age bins:
Using the R package `socialmixr`, obtain the contact matrix for the United Kingdom for the year age bins:

+ age between 0 and 20 years,
+ age between 20 and 40,
+ 40 years and over.

```r
polymod <- socialmixr::polymod
contact_data <- socialmixr::contact_matrix(
survey = polymod,
countries = "United Kingdom",
age.limits = c(0, 20, 40),
symmetric = TRUE
)
# prepare contact matrix
contact_matrix <- t(contact_data$matrix)
contact_matrix
```
Use the survey available at `socialmixr::polymod`

:::::::::::::::: hint

+ Complete tutorial on [Contact matrices](../episodes/contact-matrices.md).

::::::::::::::::

:::::::::::::::::::::::: solution

```{r polymod_uk, echo = FALSE, message = FALSE}
```{r polymod_uk, echo = TRUE, message = FALSE}
# Access the contact survey data
polymod <- socialmixr::polymod

# Generate the contact matrix
contact_data <- socialmixr::contact_matrix(
polymod,
countries = "United Kingdom",
age.limits = c(0, 20, 40),
symmetric = TRUE
)

# prepare contact matrix
contact_matrix <- t(contact_data$matrix)

# print
contact_matrix
```

Expand All @@ -302,6 +228,19 @@ In `{epidemics}` the contact matrix normalisation happens within the function ca

::::::::::::::::::::::::::::::::::::::::::::::::

:::::::::::::::::::::: instructor

Make a pause.

Use slides to introduce the topics of:

- Initial conditions and
- Population structure.

Then continue with the livecoding.

::::::::::::::::::::::

### 2. Initial conditions

The initial conditions are the proportion of individuals in each disease state $S$, $E$, $I$ and $R$ for each age group at time 0. In this example, we have three age groups age between 0 and 20 years, age between 20 and 40 years and over. Let's assume that in the youngest age category, one in a million individuals are infectious, and the remaining age categories are infection free.
Expand Down Expand Up @@ -364,6 +303,18 @@ uk_population <- population(
```


:::::::::::::::::::::: instructor

Make a pause.

Use slides to introduce the topics of:

- Model parameters and
- New infections.

Then continue with the livecoding.

::::::::::::::::::::::


### 4. Model parameters
Expand Down Expand Up @@ -527,6 +478,16 @@ newinfections_bygroup %>%

:::::::::::::::::::::::

:::::::::::::::::::::: instructor

Stop the livecoding.

Suggest learners to read the rest of the episode.

Return to slides.

::::::::::::::::::::::

## Accounting for uncertainty

The epidemic model is [deterministic](../learners/reference.md#deterministic), which means it runs like clockwork: the same parameters will always lead to the same trajectory. A deterministic model is one where the outcome is completely determined by the initial conditions and parameters, with no random variation. However, reality is not so predictable. There are two main reasons for this: the transmission process can involve randomness, and we may not know the exact epidemiological characteristics of the pathogen we're interested in. In the next episode, we will consider 'stochastic' models (i.e. models where we can define the process that creates randomness in transmission). In the meantime, we can include uncertainty in the value of the parameters that go into the deterministic model. To account for this, we must run our model for different parameter combinations.
Expand Down
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