[R] Event-triggered change in value with a time-delay

[David Winsemius]

> On Apr 18, 2018, at 1:04 AM, Hannah Meredith <hrmeredith12 using gmail.com> wrote:
> 
> Hello,
> 
> I am solving a set of ODEs using deSolve and have run into a problem I
> would appreciate some advice on. One of the parameters (m) in the ODEs
> changes between two states when one of the variables (D) crosses a
> threshold (D_T) for the first time in either direction. Additionally, when
> the variable crosses the threshold (either by increasing or decreasing),
> there is a time delay (delay) before the parameter shifts values.

I think you migh not have fully reviewed the available functions in that package. Doing an sos::findFn-search on ODE's with time delay brings up help pages for the `dede` function in deSolve. 

For the conditional value of the within regime-fixed parameter `m`, couldn't you just use this:

    ... + m*(6.8+ 3.2*(D < D_T))

Caveat: very lightly tested in your toy example, which did generate a result where D cross that threshold without blowing up.

-- 

David.


> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Toy model:
> # define parameters
> P <- c(m = 10,
>       R_1 = 0.5,
>       R_2 = 0.1,
>       D_0 = 50,
>       D_T = 5,
>       delay = 3
> )
> # set initial values
> y_0 <- c(D = 0, Y = 1)
> 
> # set timesteps
> times <- seq(0, 100, length = 101)
> 
> # define function
> bit <- function(t,y,parms){
>  with(as.list(c(parms,y)),{
> 
> 
>    # How I would implement the change if there was no time delay
>    # m <- ifelse(D>=D_T, m*.68, m)
> 
>    # Option 1: nested if statements with time delay
>    # if (D >= D_T) {
>    #   t_start1 <- t + delay
>    #   if (t >= t_start1){
>    #     m <- 6.8
>    #   }
>    # }
>    # if (D < D_T) {
>    #   t_start2<- t + delay
>    #   if (t >= t_start2){
>    #     m <- 10
>    #   }
>    # }
> 
> 
>    dD <- D_0 * (R_1 / (R_1 - R_2)) * (-R_2 * exp(-R_2 * t) + R_1 *
> exp(-R_1 * t))
>    dY <- Y + m;
>    res <- c(dD, dY)
>    list(res, m = m)
>  })
> }
> 
> 
> # Solve model
> library(deSolve)
> out <- ode(y = y_0, times = times, func = bit, parms = P)
> out.df <- as.data.frame(out)
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> I have come up with a number of ideas, but I either haven't been able to
> get them to work or don't know if R has a command for it:
> 
> 1. Nested "if" statements with something to track time (as shown above).
> One issue here is* t-start *is redefined with each time step in the ode
> solver so *t* never reaches *t_start +delay*.
> 
> 2. Event triggered changes. From the examples I have found (link
> <https://cran.r-project.org/web/packages/deSolve/vignettes/deSolve.pdf> p.
> 24-25), the time at which the event happens is either pre-set or occurs at
> a root of the ODE.  Also- would this strategy require multiple events? One
> event in which the variable crossing the threshold triggers a timer,
> another for the timer triggering the parameter change?
> 
> 3. Lagvalue. This might take care of the time lag component, but I am still
> struggling to understand (1) how lagvalue works and (2) how to integrate
> both the threshold and timer components.
> 
>   if ( D < D_T )
>     m<- ifelse(lagvalue(t-delay)<=0, 6.8, 10)
>   end
> 
> 4. Sigmoidal function. Someone suggested this to me earlier, but I am not
> sure how this would work. Is it possible to have a sigmoidal function that
> switches repeatedly between two states (as opposed to the characteristic S
> curve that transitions once from one state to another)?
> 
> 5. Mathmematica has a WhenEvent function- is there something similar in R?
> 
> 
> Thank you for your time and any tips you might have!
> 
> 	[[alternative HTML version deleted]]
> 
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David Winsemius
Alameda, CA, USA

'Any technology distinguishable from magic is insufficiently advanced.'   -Gehm's Corollary to Clarke's Third Law