Create an intervention for an epidemic model

Prepare an object of the <intervention> super-class that specifies a modification of the model parameters.

A <contacts_intervention> is used to simulate a non-pharmaceutical intervention (NPI) regime that reduces the population's social contacts.

A <rate_intervention> is used to simulate a reduction in the model's rate parameters (such as the transmission rate \(\beta\)), and can be used to represent pharmaceutical interventions such as improved treatment, but also NPIs such as wearing masks.

Interventions have a single start and end time that applies to all demographic groups in the population, but can have groups-specific effects on the reduction of contacts.

Combine <intervention>-inheriting objects to create sequential or overlapping intervention regimes using c() on two or more <intervention>-inheriting objects.

Usage

intervention(name = NA_character_, type, time_begin, time_end, reduction)

is_intervention(x)

is_contacts_intervention(x)

is_rate_intervention(x)

# S3 method for class 'contacts_intervention'
c(x, ...)

# S3 method for class 'rate_intervention'
c(x, ...)

Arguments

name

String for the name of the intervention.

type

String for the type of intervention. May be one of "contacts" or "rate", for a <contacts_intervention> or <rate_intervention> respectively.

time_begin

Single number for the start time of the intervention.

time_end

Single number for the end time of the intervention.

reduction

For <contacts_intervention>s, a matrix with as many rows as the number of demographic groups in the type population, and a single column. Each element gives the group-specific proportion reduction in contacts.

For <rate_intervention>s, a single number giving the proportion reduction in a model parameter contacts.

See details for how c() can be used to combine interventions of the same sub-class.

x

An <intervention> object, or an object to be checked as an <intervention> object.

...

intervention objects to combine with x to create a multi-dose <intervention> object.

Value

An object of the <intervention> S3 super-class, with possible sub-classes <contact_intervention> and <rate_intervention>.

Concatenating two or more <intervention>-inheriting objects using c()

also returns a <intervention>-inheriting object of the same sub-class. This object holds the intervention-specific start and end times, and reductions specified by all the constituent intervention actions (by demographic group if an intervention on contacts).

The combined effect of these actions on the population is handled internally by epidemic model functions.

A "null" intervention generated using .no_contacts_intervention(population)

or .no_rate_intervention() returns a <intervention> of the appropriate sub-class that has its start and end times, and its effect all set to 0.0.

is_intervention(), is_contacts_intervention(), and is_rate_intervention() each return a logical value for whether the object is of the <intervention>, <contacts_intervention>, or <rate_intervention> class, respectively.

Details

Epidemic models that can accommodate interventions on contacts are able to accommodate any number of interventions with different start and end times and different group-specific effects.

Epidemic models that can accommodate interventions on rates are also able to accommodate any number of interventions with different start and end times, but with only a uniform effect on the relevant rate.

When multiple contact interventions are combined using c(), the reduction in contacts is stacked column wise to form a matrix \([i, j]\).

When multiple rate interventions are combined using c(), the reduction in the rate is concatenated into a vector of the same length as the number of interventions.

Models such as model_default_cpp() are set up to treat interventions with overlapping periods (i.e., overlap between the time when they are active ) as having an additive effect on contact or rate reductions.

For contact reductions, the group-specific effect of \(J\) overlapping interventions is thus a vector \(\sum_{j = 1}^J x_{ij}\), for each demographic group \(i\). This is handled internally by the epidemic model code. For example, a contact reduction matrix for two perfectly overlapping interventions (\(J = 2\)) with different effects across three demographic groups (\(I = 3\)) would be represented as: \(\begin{bmatrix}0.1 & 0.05\\0.1 & 0.1\\0.1 & 0.0\end{bmatrix}\) In epidemic models, the cumulative group-specific effect when both interventions are active would be \((0.15, 0.2, 0.1)\).

For rate reductions, the effect of overlapping interventions that reduce a particular rate is also considered to be additive.

Examples

# assuming a population with two age groups, 0 -- 18, and 18+
# an example in which schools are closed for 30 days (or other time units)
close_schools <- intervention(
  name = "close schools",
  type = "contacts",
  time_begin = 50,
  time_end = 80,
  reduction = matrix(c(0.5, 0.01)) # reduces contacts differentially
)
close_schools
#> <contacts_intervention> object
#> 
#>  Intervention name: 
#> "close schools"
#> 
#>  Begins at: 
#> [1] 50
#> 
#>  Ends at: 
#> [1] 80
#> 
#>  Reduction: 
#>              Interv. 1
#> Demo. grp. 1      0.50
#> Demo. grp. 2      0.01

# Check for intervention class
is_contacts_intervention(close_schools)
#> [1] TRUE

# Concatenating interventions
# create first intervention
npi_1 <- intervention(
  type = "contacts",
  time_begin = 30,
  time_end = 60,
  reduction = matrix(0.1)
)

# second intervention
npi_2 <- intervention(
  type = "contacts",
  time_begin = 45,
  time_end = 75,
  reduction = matrix(0.1)
)

c(npi_1, npi_2)
#> <contacts_intervention> object
#> 
#>  Intervention name: 
#> NA
#> 
#>  Begins at: 
#>      npi_1 npi_2
#> [1,]    30    45
#> 
#>  Ends at: 
#>      npi_1 npi_2
#> [1,]    60    75
#> 
#>  Reduction: 
#>              Interv. 1 Interv. 2
#> Demo. grp. 1       0.1       0.1