Delaying parameter values/inflow and outflowing rates in deSolve - r

Question

I am using the R package deSolve to solve systems of ordinary differential equations. In the 'systems dynamics' literature, delays of the inflowing and outflowing rates can be modelled using average delay times. For instance, the rate of a change of a stock Y at time t could be:
dy(t)/dt = inflow(t) - ( outflow(t) / D )
where the delay time D is, e.g. 4 time steps. The delay is assumed to be an average delay time.
However, another way of modelling delays would be to assume a more discrete event case, where the outflow is equal to the amount inflowing to the stock D time units previously, thus:
dy(t)/dt = inflow(t) - inflow(t - D)
In deSolve, we can use the lagvalue and lagderiv functions with the dede solver function to specify delay differential equations which utilise lagged values of the state variables, but I cannot seem to find a way of asking deSolve to use lagged values of the inflow/outflow rates.
For example, take the simple model:
m<- function(t,y,p){
with(as.list(c(y,p)),{
inflow <- 100
outflow <- y*.5
dy <- inflow - outflow
return(list(c(dy), inflow=inflow, outflow=outflow))
})}
fit <- ode(func=m, y=c(100),t=seq(0,10,1),p=c(), method="euler")
time 1 inflow outflow
1 0 100.0000 100 50.00000
2 1 150.0000 100 75.00000
3 2 175.0000 100 87.50000
4 3 187.5000 100 93.75000
5 4 193.7500 100 96.87500
6 5 196.8750 100 98.43750
7 6 198.4375 100 99.21875
8 7 199.2188 100 99.60938
9 8 199.6094 100 99.80469
10 9 199.8047 100 99.90234
11 10 199.9023 100 99.95117
Using dede, I can make the outflow a lagged value of the state variable at D = 2 time steps previous:
m2<- function(t,y,p){
with(as.list(c(y,p)),{
inflow <- 100
if(t < D) outflow <- y*.5
if(t >= D) outflow <- lagvalue(t-D,1)*.5
dy <- inflow - outflow
return(list(c(dy), inflow=inflow, outflow=outflow))
})}
fit2 <- dede(func=m, y=c(100),t=seq(0,10,1),p=c(D=2))
time 1 inflow outflow
1 0 100.0000 100 50.00000
2 1 139.3469 100 69.67344
3 2 163.2120 100 81.60602
4 3 177.6870 100 88.84349
5 4 186.4665 100 93.23323
6 5 191.7915 100 95.89575
7 6 195.0213 100 97.51064
8 7 196.9803 100 98.49013
9 8 198.1684 100 99.08422
10 9 198.8891 100 99.44456
11 10 199.3262 100 99.66312
But now imagine I want the outflow to actually be the inflow D=2 time steps previous. I want something like:
**** Code will not run ****
m3<- function(t,y,p){
with(as.list(c(y,p)),{
inflow <- 100
if(t < D) outflow <- 0
if(t >= D) outflow <- lagvalue(t-D,inflow)
dy <- inflow - outflow
return(list(c(dy), inflow=inflow, outflow=outflow))
})}
...
As far as I can see, deSolve does not allow this. Is there an easy way to allow it?
The reason I am interested in mixing a continuous and discrete event type model is in modelling supply chains, where the average time delay may not be accurate for certain products.