A fluid model retaining hydrodynamic nonlinearities together with a linear approximation of the Landau damping and of the finite Larmor radius effects is constructed to describe the dynamics of quasi-transverse low-frequency waves in a homogeneous magnetized plasma. It accurately reproduces the kinetic theory predictions for the mirror instability, including its quenching at small transverse scales. The dispersion relation of kinetic Alfv¿n waves is also recovered. This model should provide an efficient tool for numerical simulations of nonlinear mirror mode dynamics, at least near threshold.