Improved understanding of human adaptation can be used to design better autonomous systems and control systems that can support the human controller when the dynamics of the system that is being controlled suddenly change. This paper evaluates the effectiveness of a model-based adaptive control technique, Model-Based Reference Control (MRAC), for predicting the adaptive control policy shown by human operators while controlling a time-varying system in a pursuit-tracking task. Ten participants took part in an experiment, where they were asked to control a time-varying system whose dynamics changed twice and approximated a single and double integrator dynamics. A MRAC controller is composed of a feedforward and a feedback controller and an internal model that is used to drive the adaptive control policy. The active gains, the internal model parameters and the learning rates, have been estimated via an non-linear optimization aimed at maximizing quality of fitting of the participants' control output. The participant's control behavior rapidly changed when the dynamics of the controlled system changed, in particular when going from controlling a first to second order system. The MRAC model was able to accurately capture the transient dynamics exhibited by the participants when the system changed approximately from a first to a double integrator while it failed to do so when the system changed from double to first integrator. In the latter case the MRAC gains changed too slowly. Therefore MRAC can be used to approximate human adaptations in pursuit tracking tasks when a change in the dynamics of the controlled system requires an increase in the rate feedback controller to ensure accurate tracking of the reference signal.