Partial solution for SEITL model

Here is a skeleton for the list of transitions and the function that returns the rates. You should write one line of code every where it is indicated.

SEITL_transitions <- list(
    # fill transition for infection
    # fill transition for onset of infectiousness
    # fill transition for recovery + temporary immunity
    # fill transition for long-term immunity
    # fill transition for NO long-term immunity
    )

SEITL_rateFunc <- function(state, theta, t) {

    # define model parameters in term of the natural parameters
    beta <- # fill HERE
    epsilon <- # fill HERE
    nu <- # fill HERE
    alpha <- # fill HERE
    tau <- # fill HERE
    
    # create temporary variables for states to simplify the writing of the rates below
    S <- state[["S"]]
    E <- state[["E"]]
    I <- state[["I"]]
    T <- state[["T"]]
    L <- state[["L"]]
    N <- # fill HERE
    
    # return rates
    return(c(
        # fill rate for infection
        # fill rate for onset of infectiousness
        # rfill rate for ecovery + temporary immunity
        # fill rate for long-term immunity
        # fill rate for NO long-term immunity
        ))
}

Once you have filled the gap you can come back to the practical. If you need more help in filling the gap, you can have a look at the solution.