How to build kinetic models with integrals using the POMP package

[believe-bing]

Recently, I intend to use the pomp package to build a differential equation that enables blood glucose prediction (Model frame.pdf). In contrast to the previous infectious disease model, this differential equation contains integrals as follows:

I can implement it in R in the following way: by saving both the previously generated time variable and the blood glucose concentration (Gpl) in the global variables t_saved and Gpl_saved, and then linearly interpolating them via the approx function (The data used in the example: Test_data.csv). The codes we used as follows:

unique_indices <- !duplicated(t_saved)
t_saved_unique <- t_saved[unique_indices]
Gpl_saved_unique <- Gpl_saved[unique_indices]

t_lowerbound <- t - t_integralwindow
if ((t > t_integralwindow) && (length(t_saved_unique) > 1)) {
  Gpl_lowerbound <- approx(
    t_saved_unique,
    Gpl_saved_unique,
    xout = t_lowerbound,
    rule = 2
  )$y
} else {
  Gpl_lowerbound <- Gpl_saved_unique[1]
}

t_saved <- c(t_saved, t)
Gpl_saved <- c(Gpl_saved, Gpl)

I tried to build the above model using POMP but failed, can you give me some advice? The codes we used to build model were In the docx. (POMP_Codes.docx)

[kingaa]

I'm not sure how to parse your equation 13 since there are no limits on the integral, nor is it clear what the various G quantities are. However, it might be pertinent to point out that pomp, as the name implies, is for dealing with Markov processes and that, if the future of a state variable depends on an integral over its past history, the process is not Markovian, unless the integrals are of a rather special kind.... Might this have something to do with the problems you're having?