Comparing public health outcomes of interventions

Estimated time: 75 minutes

Overview

Questions

• How can I quantify the effect of an intervention?

Objectives

• Compare intervention scenarios

Prerequisites

• Complete tutorials Simulating transmission and Modelling interventions

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

Outbreak response : Intervention types.

Introduction

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In this tutorial we will compare intervention scenarios against each other. To quantify the effect of the intervention we need to compare our intervention scenario to a counter factual scenario. The counter factual is the scenario in which nothing changes, often referred to as the ‘do nothing’ scenario. The counter factual scenario may include no interventions, or if we are investigating the potential impact of an additional intervention in the later stages of an outbreak there may be existing interventions in place.

We must also decide what our outcome of interest is to make comparisons between intervention and counter factual scenarios. The outcome of interest can be:

• a model outcome, e.g. number of infections or hospitalisations,
• a metric such as the epidemic peak time or size,
• a measure that uses the model outcomes such as QALY/DALYs.

Instructor Note

In this tutorial we introduce the concept of the counter factual and how to compare scenarios (counter factual versus intervention) against each other.

Vacamole model

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The Vacamole model is a deterministic model based on a system of ODEs in Ainslie et al. 2022 to describe the effect of vaccination on COVID-19 dynamics. The model consists of 11 compartments, individuals are classed as one of the following:

• susceptible, \(S\),
• partial vaccination (\(V_1\)), fully vaccination (\(V_2\)),
• exposed, \(E\) and exposed while vaccinated, \(E_V\),
• infectious, \(I\) and infectious while vaccinated, \(I_V\),
• hospitalised, \(H\) and hospitalised while vaccinated, \(H_V\),
• dead, \(D\),
• recovered, \(R\).

The diagram below describes the flow of individuals through the different compartments.

Running a counterfactual scenario using the Vacamole model

1. Run the model with the default parameter values for the UK population assuming that :

• 1 in a million individual are infectious (and not vaccinated) at the start of the simulation
• The contact matrix for the United Kingdom has age bins:
  • age between 0 and 20 years,
  • age between 20 and 40,
  • 40 years and over.
• There is no vaccination scheme in place

2. Using the output, plot the number of deaths through time

HINT : Running the model with default parameter values

We can run the Vacamole model with default parameter values by just specifying the population object and number of time steps to run the model for:

R

output <- model_vacamole(
  population = uk_population,
  time_end = 300
)

SOLUTION

1. Run the model

R

library(epidemics)

R

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

OUTPUT

Using POLYMOD social contact data. To cite this in a publication, use the 'get_citation()' function

OUTPUT

Removing participants that have contacts without age information. To change this behaviour, set the 'missing.contact.age' option

R

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

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

# prepare initial conditions
initial_i <- 1e-6

initial_conditions <- c(
  S = 1 - initial_i,
  V1 = 0, V2 = 0,
  E = 0, EV = 0,
  I = initial_i, IV = 0,
  H = 0, HV = 0, D = 0, R = 0
)

initial_conditions <- rbind(
  initial_conditions,
  initial_conditions,
  initial_conditions
)
rownames(initial_conditions) <- rownames(contact_matrix)

# prepare population object
uk_population <- population(
  name = "UK",
  contact_matrix = contact_matrix,
  demography_vector = demography_vector,
  initial_conditions = initial_conditions
)

# run model
output <- model_vacamole(
  population = uk_population,
  time_end = 300
)

2. Plot the number of deaths through time

R

library(ggplot2)

ggplot(output[output$compartment == "dead", ]) +
  geom_line(
    aes(time, value, colour = demography_group),
    linewidth = 1
  ) +
  scale_colour_brewer(
    palette = "Dark2",
    labels = rownames(contact_matrix),
    name = "Age group"
  ) +
  scale_y_continuous(
    labels = scales::comma
  ) +
  labs(
    x = "Simulation time (days)",
    y = "Individuals"
  ) +
  theme(
    legend.position = "top"
  ) +
  theme_bw(
    base_size = 15
  )

Package vignettes

We recommend to read the vignette on Modelling responses to a stochastic Ebola virus epidemic to use a discrete time, stochastic compartmental model of Ebola used during the 2014 West African EVD outbreak.

Key Points

• The counter factual scenario must be defined to make comparisons