Improved understanding of human adaptation can be used to design better (semi-)automated systems that can support the human controller when task characteristics suddenly change. This paper evaluates the effectiveness of a model-based adaptive control technique, Model Reference Adaptive Control (MRAC), for describing the adaptive control policy used by human operators while controlling a time-varying system in a pursuit-tracking task. Ten participants took part in an experiment in which they controlled a time-varying system whose dynamics changed twice between approximate single and double integrator dynamics, and vice versa. Our proposed MRAC controller is composed of a feedforward and a feedback controller and an internal reference model that is used to drive an adaptive control policy. MRAC's adaptive control gains, the internal model parameters, and the learning rates were estimated from the experiment data using non-linear optimization aimed at maximizing the quality-of-fit of participants' control outputs. Participants' control behavior rapidly changed when the dynamics of the controlled system changed, in particular for transitions from single to double integrator dynamics. The MRAC model was indeed able to accurately capture the transient dynamics exhibited by the participants when the system changed from an approximate single to a double integrator, however, for the opposite transition the MRAC gains were always adapted too slowly. Therefore, in its current form, our MRAC model can be used to approximate human adaptation in pursuit tracking tasks when a change in the dynamics of the controlled system requires significant (rate) feedback controller adaptation to maintain satisfactory closed-loop control performance.