denim DSL

Denim DSL

In denim, each line of code must be a transition. The syntax for defining a transition in denim DSL is as followed:

compartment_A -> compartment_B = transition

Model definition written in denim DSL must be parsed by the function denim_dsl()

Math expression

For math expression, some basic supported operators include: + for addition, - for minus, * for multiplication, / for division, ^ for power. Users can also define additional model parameters in the math expression.

Math expressions in denim are parsed using muparser. For a full list of operators, visit the muparser website at https://beltoforion.de/en/muparser/features.php.

Distribution functions

Several built-in functions are provided to describe transitions based on the distribution of dwell time:

For parametric distributions: d_lognormal(), d_gamma(), d_weibull(), d_exponential()
For non-parametric distributions: nonparametric()

Each of these functions accepts either fixed numeric values or model parameters as inputs for their distributional parameters. Note that current version of denim does not accept mathematical expression as a distribution’s parameters.

Define a classic SIR model

A classic SIR model can be defined in denim as followed

sir_model <- denim_dsl({
  S -> I = beta * (I/N) * S * timeStep
  I -> R = d_exponential(rate = gamma)
})

Any variable on the right hand side (RHS) of the transitions definition (that are not compartments) will be considered model parameters and their values must be provided later on.

In this example, model parameters are: N, beta, S, gamma.

timeStep is a special variable in denim that automatically uses the time step defined in simulation configuration as it’s value. Note that this special variable can ONLY be used within math expression.

Users can also choose to provide fixed values as the distributional parameter as followed

sir_model <- denim_dsl({
  S -> I = beta*(I/N)*S*timeStep
  I -> R = d_exponential(rate = 1/4)
})

Similar to R, users can also add comments in denim DSL by starting the comment with # sign.

sir_model <- denim_dsl({
  # this is a comment
  S -> I = beta*(I/N)*S*timeStep
  I -> R = d_exponential(rate = 1/4) # this is another comment
})

Run model

To run the model, users must provide:

Values for model parameters (in this example, N, beta, S and gamma).
Initial population for the compartments.
Simulation configurations.

Parameters and initial values can be defined as named vectors or named lists in R.

# parameters for the model
parameters <- c(
  beta = 0.4,
  N = 1000,
  gamma = 1/7
)
# initial population for each compartment 
initValues <- c(
  S = 999, 
  I = 50,
  R = 0
)

Simulation configurations are provided as parameters for sim() function which runs the model, where:

timeStep is the duration of each time step in the model.
simulationDuration is the duration to run the simulation.

mod <- sim(sir_model, 
    parameters = parameters, 
    initialValues = initValues, 
    timeStep = 0.01,
    simulationDuration = 40)

plot(mod, ylim = c(1, 1000))

Time varying transition

Aside from timeStep, denim also have another special variable time for time varying transition (e.g. for modeling seasonality). Note that this variable can ONLY be used within math expression.

Example: time varying transition

time_varying_mod <- denim_dsl({
  A -> B = 20 * (1+cos(omega * time)) * timeStep
})

# parameters for the model
parameters <- c(
  omega = 2*pi/10
)
# initial population for each compartment 
initValues <- c(A = 1000, B = 0)

mod <- sim(time_varying_mod, 
    parameters = parameters, 
    initialValues = initValues, 
    timeStep = 0.01,
    simulationDuration = 40)

plot(mod, ylim = c(0, 1000))

R list

Users can also define the model structure as a list in R. For example, the SIR model from previous example can be represented as followed.

sir_model_list <- list(
  "S -> I" = "beta * (I/N) * S * timeStep",
  "I -> R" = d_exponential(rate = "gamma")
)

sir_model_list
#> $`S -> I`
#> [1] "beta * (I/N) * S * timeStep"
#> 
#> $`I -> R`
#> Discretized exponential distribution
#> Rate = gamma

Note that the transitions (S -> I, I -> R), mathematical expression (beta * (I/N) * S * timeStep), and the model parameter (gamma) must now be provided as strings.

We can then run the model in the same manner as previously demonstrated.

# parameters for the model
parameters <- c(
  beta = 0.4,
  N = 1000,
  gamma = 1/7
)
# initial population for each compartment 
initValues <- c(
  S = 999, 
  I = 50,
  R = 0
)
# run the simulation
mod <- sim(sir_model_list, 
    parameters = parameters, 
    initialValues = initValues, 
    timeStep = 0.01,
    simulationDuration = 40)
# plot output
plot(mod, ylim = c(1, 1000))

When should I define model as a list in R?

While denim DSL offers cleaner and more readable syntax to define model structure, using R list may be more familiar to R users and better suited for integration to a more R-centric workflow.

For example, consider a use case below, where we explore how model dynamics change under three different I -> R dwell time distributions (d_gamma, d_weibull, d_lognormal) using map2.

library(tidyverse)
#> Warning: package 'ggplot2' was built under R version 4.3.1
#> Warning: package 'tidyr' was built under R version 4.3.1
#> Warning: package 'readr' was built under R version 4.3.1
#> Warning: package 'purrr' was built under R version 4.3.3
#> Warning: package 'dplyr' was built under R version 4.3.1
#> Warning: package 'stringr' was built under R version 4.3.1
#> Warning: package 'lubridate' was built under R version 4.3.3
# configurations for 3 different I->R transitions
model_config <- tibble(
  IR_dists = c(d_gamma, d_weibull, d_lognormal),
  IR_pars = list(c(rate = 0.1, shape = 3), c(scale = 5, shape = 0.3), c(mu = 0.3, sigma = 2))
)

model_config %>% 
  mutate(
    plots = map2(IR_dists, IR_pars, \(dist, par){
      transitions <- list(
        "S -> I" = "beta * S * (I / N) * timeStep",
        # This is not applicable when using denim_dsl()
        "I -> R" = do.call(dist, as.list(par))
      )
      
      # model settings
      denimInitialValues <- c(S = 980, I = 20, R = 0)
      parameters <- c(
        beta = 0.4,
        N = 1000
      )
      
      # compare output 
      mod <- sim(transitions = transitions, 
                 initialValues = denimInitialValues, 
                 parameters = parameters, 
                 simulationDuration = 60, 
                 timeStep = 0.05)
      
      plot(mod, ylim = c(0,1000))
    })
  ) %>% 
  pull(plots)

#> [[1]]
#> [[1]]$rect
#> [[1]]$rect$w
#> [1] 29.28376
#> 
#> [[1]]$rect$h
#> [1] 744.8276
#> 
#> [[1]]$rect$left
#> [1] 33.11624
#> 
#> [[1]]$rect$top
#> [1] 872.4138
#> 
#> 
#> [[1]]$text
#> [[1]]$text$x
#> [1] 55.20715 55.20715 55.20715
#> 
#> [[1]]$text$y
#> [1] 686.2069 500.0000 313.7931
#> 
#> 
#> 
#> [[2]]
#> [[2]]$rect
#> [[2]]$rect$w
#> [1] 29.28376
#> 
#> [[2]]$rect$h
#> [1] 744.8276
#> 
#> [[2]]$rect$left
#> [1] 33.11624
#> 
#> [[2]]$rect$top
#> [1] 872.4138
#> 
#> 
#> [[2]]$text
#> [[2]]$text$x
#> [1] 55.20715 55.20715 55.20715
#> 
#> [[2]]$text$y
#> [1] 686.2069 500.0000 313.7931
#> 
#> 
#> 
#> [[3]]
#> [[3]]$rect
#> [[3]]$rect$w
#> [1] 29.28376
#> 
#> [[3]]$rect$h
#> [1] 744.8276
#> 
#> [[3]]$rect$left
#> [1] 33.11624
#> 
#> [[3]]$rect$top
#> [1] 872.4138
#> 
#> 
#> [[3]]$text
#> [[3]]$text$x
#> [1] 55.20715 55.20715 55.20715
#> 
#> [[3]]$text$y
#> [1] 686.2069 500.0000 313.7931

denim DSL

Model definition in denim

Denim DSL

Define a classic SIR model

Time varying transition

R list