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

[Hannah Meredith]

Hi David,

Thank you for your suggestion- I will look into it some more.

Thanks again,
Hannah

On Wed, Apr 18, 2018 at 5:09 PM, David Winsemius <dwinsemius using comcast.net>
wrote:

>
> > 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]]
> >
> > ______________________________________________
> > R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide http://www.R-project.org/
> posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
> David Winsemius
> Alameda, CA, USA
>
> 'Any technology distinguishable from magic is insufficiently advanced.'
>  -Gehm's Corollary to Clarke's Third Law
>
>
>
>
>
>


-- 
Hannah Meredith | PhD
Whitaker Scholar
London School of Hygiene and Tropical Medicine

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