def sirx(w, t, p):
    """ SIR-X: Dynamic outbreaks with temporally increasing
    intervention

    inputs:
    w: vector of state variables [S,I,R,X]
    where
        S: Fraction of the population susceptible to the infection
        I: Fraction on the population infected
        R: Fraction of the population that recovered
        X: Fraction of the population that is quarantined

    t: time
    p: vector of parameter

    returns:
    right hand side of the system of differential equation
    """
    # unpack state variable
    s, i, r, x = w  # pylint: disable=W0612
    # unpack parameter
    alpha, beta, kappa_0, kappa = p
    ds_dt = -alpha * s * i - kappa_0 * s
    di_dt = alpha * s * i - beta * i - kappa_0 * i - kappa * i
    dr_dt = kappa_0 * s + beta * i
    dx_dt = (kappa_0 + kappa) * i

    return [ds_dt, di_dt, dr_dt, dx_dt]