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Model leaky, two-dose vaccination in an epidemic using Vacamole

Source: R/model_vacamole.R
model_vacamole.Rd

Simulate an epidemic using the Vacamole model for Covid-19 developed at RIVM, the National Institute for Public Health and the Environment in the Netherlands. This model is aimed at estimating the impact of 'leaky' vaccination on an epidemic. See Details and References for more information.

Usage

model_vacamole(
  population,
  transmission_rate = 1.3/7,
  transmission_rate_vax = 0.8 * transmission_rate,
  infectiousness_rate = 1/2,
  hospitalisation_rate = 1/1000,
  hospitalisation_rate_vax = 0.8 * hospitalisation_rate,
  mortality_rate = 1/1000,
  mortality_rate_vax = 0.8 * mortality_rate,
  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.

transmission_rate_vax

A numeric of values between 0.0 and 1.0 giving the transmission_rate of the infection to individuals who have received two doses of the vaccine. The default values is 80% of the transmission_rate of the infection to individuals who are not doubly vaccinated.

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.

hospitalisation_rate

A numeric for the hospitalisation rate of infectious individuals.

hospitalisation_rate_vax

A numeric of values between 0.0 and 1.0 giving the hospitalisation rate of infectious individuals who have received two doses of the vaccine. The default value is 80% of the hospitalisation rate of individuals who are not doubly vaccinated.

mortality_rate

A numeric for the mortality rate of infectious or hospitalised individuals.

mortality_rate_vax

A numeric of values between 0.0 and 1.0 giving the mortality of infectious and hospitalised individuals who have received two doses of the vaccine. The default value is 80% of the mortality rate of individuals who are not doubly vaccinated.

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

An optional <vaccination> object representing a vaccination regime with two doses followed during the course of the epidemic, with a start and end time, and age-specific vaccination rates for each dose. See vaccination().

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: Vacamole Covid-19 model with leaky, two-dose vaccination

The Vacamole model has the compartments "susceptible", "vaccinated_one_dose", "vaccinated_two_dose", "exposed", "infectious" "infectious_vaccinated", "hospitalised", "hospitalised_vaccinated", "recovered", and "dead".

This model allows for:

  1. A 'hospitalised' compartment along with a hospitalisation rate;

  2. Two doses of vaccination, with 'leaky' protection, i.e., vaccination does not prevent infection completely but allows for a reduction in the infection rate, as well as reduced rates of moving into states considered more serious, such as 'hospitalised' or 'dead'.

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.

  • Transmission rate (\(\beta\), transmission_rate): 0.186, resulting from an \(R_0\) = 1.3 and an infectious period of 7 days. The transmission rate for doubly vaccinated individuals (\(\beta_v\)) is 80% of \(\beta\), 0.1488.

  • Infectiousness rate (\(\sigma\), infectiousness_rate): 0.5, assuming a pre-infectious period of 2 days.

  • Hospitalisation rate (\(\eta\), hospitalistion_rate): 1.0 / 1000, assuming that one in every thousand infectious individuals is hospitalised. The hospitalisation rate of doubly vaccinated individuals (\(\eta_v\)) is 80% of \(\eta\), 0.8 / 1000.

  • Mortality rate (\(\omega\), mortality_rate): 1.0 / 1000, assuming that one in every thousand infectious and hospitalised individuals dies. The mortality rate of the doubly vaccinated (\(\omega_v\)) is 80% of \(\omega\), 0.8 / 1000.

  • Recovery rate (\(\gamma\), recovery_rate): 0.143, assuming an infectious period of 7 days.

References

Ainslie, K. E. C., Backer, J. A., Boer, P. T. de, Hoek, A. J. van, Klinkenberg, D., Altes, H. K., Leung, K. Y., Melker, H. de, Miura, F., & Wallinga, J. (2022). A scenario modelling analysis to anticipate the impact of COVID-19 vaccination in adolescents and children on disease outcomes in the Netherlands, summer 2021. Eurosurveillance, 27(44), 2101090. doi:10.2807/1560-7917.ES.2022.27.44.2101090

Examples

# create a population, note eleven columns for compartments
population <- population(
  contact_matrix = matrix(1),
  demography_vector = 67e6,
  initial_conditions = matrix(
    c(0.9999, 0, 0, 0, 0, 0.0001, 0, 0, 0, 0, 0),
    nrow = 1, ncol = 11L
  )
)

# create a vaccination regime
double_vax <- vaccination(
  nu = matrix(1e-3, ncol = 2, nrow = 1),
  time_begin = matrix(c(10, 30), nrow = 1),
  time_end = matrix(c(50, 80), nrow = 1)
)

# run epidemic simulation with vaccination but no intervention
# with a single set of parameters
data <- model_vacamole(
  population = population,
  vaccination = double_vax
)

# view some data
head(data)
#>     time demography_group         compartment    value
#>    <num>           <char>              <char>    <num>
#> 1:     0     demo_group_1         susceptible 66993300
#> 2:     0     demo_group_1 vaccinated_one_dose        0
#> 3:     0     demo_group_1 vaccinated_two_dose        0
#> 4:     0     demo_group_1             exposed        0
#> 5:     0     demo_group_1  exposed_vaccinated        0
#> 6:     0     demo_group_1          infectious     6700

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

# view some data
head(data)
#>    transmission_rate infectiousness_rate hospitalisation_rate mortality_rate
#>                <num>               <num>                <num>          <num>
#> 1:         0.1857143                 0.5                0.001          0.001
#> 2:         0.2000000                 0.5                0.001          0.001
#> 3:         0.2142857                 0.5                0.001          0.001
#>    recovery_rate transmission_rate_vax hospitalisation_rate_vax
#>            <num>                 <num>                    <num>
#> 1:     0.1428571             0.1485714                    8e-04
#> 2:     0.1428571             0.1600000                    8e-04
#> 3:     0.1428571             0.1714286                    8e-04
#>    mortality_rate_vax time_end param_set      population intervention
#>                 <num>    <num>     <int>          <list>       <list>
#> 1:              8e-04      100         1 <population[4]>             
#> 2:              8e-04      100         2 <population[4]>             
#> 3:              8e-04      100         3 <population[4]>             
#>    vaccination time_dependence increment scenario                 data
#>         <list>          <list>     <num>    <int>               <list>
#> 1:                   <list[1]>         1        1 <data.table[1111x4]>
#> 2:                   <list[1]>         1        1 <data.table[1111x4]>
#> 3:                   <list[1]>         1        1 <data.table[1111x4]>
tail(data)
#>    transmission_rate infectiousness_rate hospitalisation_rate mortality_rate
#>                <num>               <num>                <num>          <num>
#> 1:         0.1857143                 0.5                0.001          0.001
#> 2:         0.2000000                 0.5                0.001          0.001
#> 3:         0.2142857                 0.5                0.001          0.001
#>    recovery_rate transmission_rate_vax hospitalisation_rate_vax
#>            <num>                 <num>                    <num>
#> 1:     0.1428571             0.1485714                    8e-04
#> 2:     0.1428571             0.1600000                    8e-04
#> 3:     0.1428571             0.1714286                    8e-04
#>    mortality_rate_vax time_end param_set      population intervention
#>                 <num>    <num>     <int>          <list>       <list>
#> 1:              8e-04      100         1 <population[4]>             
#> 2:              8e-04      100         2 <population[4]>             
#> 3:              8e-04      100         3 <population[4]>             
#>    vaccination time_dependence increment scenario                 data
#>         <list>          <list>     <num>    <int>               <list>
#> 1:                   <list[1]>         1        1 <data.table[1111x4]>
#> 2:                   <list[1]>         1        1 <data.table[1111x4]>
#> 3:                   <list[1]>         1        1 <data.table[1111x4]>