By using the generalized bracket approach of nonequilibrium thermodynamics, we recently developed a new two-species model for wormlike micelles based on the flow-induced breakage of the longer species. In this work, we complete the model by adding diffusion in a thermodynamically consistent manner. Furthermore, we discuss the behavior of a limiting case of the model in transient Couette flow between two coaxial cylinders, which is a flow that exhibits spatial inhomogeneities and has widely been studied for wormlike micellar solutions. The flow problem was spatially discretized using a Chebyshev method. A Crank-Nicolson scheme was employed for time discretization. At each time step, the nonlinear system of discretized flow equations was solved using a preconditioned Newton-Krylov solver. The model parameters were obtained by fitting experimental data of a previously studied wormlike micellar system. We found that the model can capture the trends observed in steady simple shear, small-amplitude oscillatory shear, and step strain. The main feature of the model is a strong elastic recoil during the start-up of simple shear flow. (C) 2014 Elsevier B.V. All rights reserved.