Delayed state for delay differential equations

delay(state, T) evaluates an ODE state at the past time t - T, turning an ordinary differential equation model into a delay differential equation (DDE). The semantics match the delay() function of Monolix.

Usage

delay(state, T)

Arguments

state

An ODE state (compartment) defined in the model whose past value is required.

T

The delay duration. May be a constant, a parameter, a covariate, or any model expression. The value returned is the state at time t - T.

Value

Inside an rxode2 model, the value of state at the past time t - T. Before the start of integration the constant initial-condition history is used.

Details

Delayed states are interpolated from the solver's dense output, so delay models are solved on a dense path: the default method becomes the dense AutoSwitch composite "dop853+ros4", and the dense methods "dop853", "dop5", "bs", "ros4" and "cvode" also work, as does "liblsoda" with dense = TRUE (without it, "liblsoda" switches to "dop853+ros4"). The step size is capped to the smallest delay, and methods that cannot record dense history raise an error. The dense-output and delay-history machinery is adapted from the dde package by Rich FitzJohn and Wes Hinsley (Imperial College of Science, Technology and Medicine).

See also

rxSolve()

Other Special functions: boxCox(), erf(), gammap(), gammapDer(), gammapInv(), gammaq(), gammaqInv(), logit(), lowergamma(), mexpit(), mlogit(), phi(), phiU(), probit(), uppergamma()

Author

Matthew L. Fidler

Examples

# \donttest{
# Classic linear delay differential equation y'(t) = -y(t - 1)
dde <- rxode2({
  y(0) <- 1
  d/dt(y) <- -delay(y, 1)
})
#>  
#>  

s <- rxSolve(dde, et(seq(0, 5, by = 0.1)))
#>  
#>  

# Delayed (Hutchinson) logistic growth
hutch <- rxode2({
  r <- 0.5
  K <- 10
  tau <- 1
  N(0) <- 2
  d/dt(N) <- r * N * (1 - delay(N, tau) / K)
})
#>  
#>  

s2 <- rxSolve(hutch, et(seq(0, 40, by = 0.5)))
#>  
#>  
# }