Model an SEIR-V epidemic with interventions — model

Simulate an epidemic using a deterministic, compartmental epidemic model with the compartments "susceptible", "exposed", "infectious", "recovered", and "vaccinated". This model can accommodate heterogeneity in social contacts among demographic groups, as well as differences in the sizes of demographic groups.

The population, transmission_rate, infectiousness_rate, and recovery_rate arguments are mandatory, while passing an intervention and vaccination are optional and can be used to simulate scenarios with different epidemic responses or different levels of the same type of response. See Details for more information.

Usage

model_default(
  population,
  transmission_rate = 1.3/7,
  infectiousness_rate = 1/2,
  recovery_rate = 1/7,
  intervention = NULL,
  vaccination = NULL,
  time_dependence = NULL,
  time_end = 100,
  increment = 1
)

Arguments

population: An object of the population class, which holds a population contact matrix, a demography vector, and the initial conditions of each demographic group. See population().
transmission_rate: A numeric for the rate at which individuals move from the susceptible to the exposed compartment upon contact with an infectious individual. Often denoted as \(\beta\), with \(\beta = R_0 / \text{infectious period}\). See Details for default values.
infectiousness_rate: A numeric for the rate at which individuals move from the exposed to the infectious compartment. Often denoted as \(\sigma\), with \(\sigma = 1.0 / \text{pre-infectious period}\). This value does not depend upon the number of infectious individuals in the population. See Details for default values.
recovery_rate: A numeric for the rate at which individuals move from the infectious to the recovered compartment. Often denoted as \(\gamma\), with \(\gamma = 1.0 / \text{infectious period}\). See Details for default values.
intervention: A named list of <intervention>s representing optional non-pharmaceutical or pharmaceutical interventions applied during the epidemic. Only a single intervention on social contacts of the class <contacts_intervention> is allowed as the named element "contacts". Multiple <rate_interventions> on the model parameters are allowed; see Details for the model parameters for which interventions are supported.
vaccination: A <vaccination> object representing an optional vaccination regime with a single dose, followed during the course of the epidemic, with a start and end time, and age-specific vaccination rates.
time_dependence: A named list where each name is a model parameter, and each element is a function with the first two arguments being the current simulation time, and x, a value that is dependent on time (x represents a model parameter). See Details for more information, as well as the vignette on time- dependence vignette("time_dependence", package = "epidemics").
time_end: The maximum number of timesteps over which to run the model. Taken as days, with a default value of 100 days. May be a numeric vector.
increment: The size of the time increment. Taken as days, with a default value of 1 day.

Value

A <data.table>. If the model parameters and composable elements are all scalars, a single <data.table> with the columns "time", "compartment", "age_group", and "value", giving the number of individuals per demographic group in each compartment at each timestep in long (or "tidy") format is returned.

If the model parameters or composable elements are lists or list-like, a nested <data.table> is returned with a list column "data", which holds the compartmental values described above. Other columns hold parameters and composable elements relating to the model run. Columns "scenario" and "param_set" identify combinations of composable elements (population, interventions, vaccination regimes), and infection parameters, respectively.

Details: SEIRV model suitable for directly transmitted infections

Model parameters

This model only allows for single, population-wide rates of transitions between compartments per model run.

However, model parameters may be passed as numeric vectors. These vectors must follow Tidyverse recycling rules: all vectors must have the same length, or, vectors of length 1 will be recycled to the length of any other vector.

The default values are:

Transmission rate (\(\beta\), transmission_rate): 0.186, assuming an \(R_0\) = 1.3 and an infectious period of 7 days.
Infectiousness rate (\(\sigma\), infectiousness_rate): 0.5, assuming a pre-infectious period of 2 days.
Recovery rate (\(\gamma\), recovery_rate): 0.143, assuming an infectious period of 7 days.

Examples

# create a population
uk_population <- population(
  name = "UK population",
  contact_matrix = matrix(1),
  demography_vector = 67e6,
  initial_conditions = matrix(
    c(0.9999, 0.0001, 0, 0, 0),
    nrow = 1, ncol = 5L
  )
)

# run epidemic simulation with no vaccination or intervention
# and three discrete values of transmission rate
data <- model_default(
  population = uk_population,
  transmission_rate = c(1.3, 1.4, 1.5) / 7.0, # uncertainty in R0
)

# view some data
data
#>    transmission_rate infectiousness_rate recovery_rate time_end param_set
#>                <num>               <num>         <num>    <num>     <int>
#> 1:         0.1857143                 0.5     0.1428571      100         1
#> 2:         0.2000000                 0.5     0.1428571      100         2
#> 3:         0.2142857                 0.5     0.1428571      100         3
#>         population intervention vaccination time_dependence increment scenario
#>             <list>       <list>      <list>          <list>     <num>    <int>
#> 1: <population[4]>                                <list[1]>         1        1
#> 2: <population[4]>                                <list[1]>         1        1
#> 3: <population[4]>                                <list[1]>         1        1
#>                   data
#>                 <list>
#> 1: <data.table[505x4]>
#> 2: <data.table[505x4]>
#> 3: <data.table[505x4]>

# run epidemic simulations with differences in the end time
# may be useful when considering different start dates with a fixed end point
data <- model_default(
  population = uk_population,
  time_end = c(50, 100, 150)
)

data
#>    transmission_rate infectiousness_rate recovery_rate time_end param_set
#>                <num>               <num>         <num>    <num>     <int>
#> 1:         0.1857143                 0.5     0.1428571       50         1
#> 2:         0.1857143                 0.5     0.1428571      100         2
#> 3:         0.1857143                 0.5     0.1428571      150         3
#>         population intervention vaccination time_dependence increment scenario
#>             <list>       <list>      <list>          <list>     <num>    <int>
#> 1: <population[4]>                                <list[1]>         1        1
#> 2: <population[4]>                                <list[1]>         1        1
#> 3: <population[4]>                                <list[1]>         1        1
#>                   data
#>                 <list>
#> 1: <data.table[255x4]>
#> 2: <data.table[505x4]>
#> 3: <data.table[755x4]>