def SIR(t, y, N, kappa, tau, nu):
    """
    Expresses SIR model in initial value ODE format, including time,
    state variables, and parameters required to compute the derivatives

    Parameters
    ---------------
    t : array
        Independent variable
    y : array-like
        Initial state of system, [S, I, R]
    parameters : array-like
        Parameters of model [N, kappa, tau, nu]

    Returns
    ----------------
    f : array-like
        Array of derivatives for the system to be numerically integrated
    """
    S, I, R = y

    dSdt = - kappa * tau / N * S * I
    dIdt = (kappa * tau / N * S - nu) * I
    dRdt = nu * I
    f = [dSdt, dIdt, dRdt]
    return f