def death_rate(state, clone, mu, model):
    """
    Calculates the death rate for ``clone`` in ``state`` in the approximating process X^{``model``}.

    Parameters
    ----------
    state : list[int]
        Number of cells per clonotype.
    clone : int
        Specified clone.
    mu : float
        Single cell death rate.
    model : int
        Auxiliary process (0 = X^1, 1 = X^2).

    Returns
    -------
    float
        Death rate for clone in state.
    """

    if model == 1:
        if state[clone] > 1:
            return state[clone] * mu
        else:
            return 0.0
    if model == 2:
        return (state[clone] - 1) * mu