Existing traffic flow models almost are used to characterize traffic behavior or to describe fundamental diagram (flow-density relationship) in some kinds of traffic conditions. From the viewpoint of static traffic characteristic, they mainly provide information of traffic states (free flow or congestion) and trend of traffic variation in a highway section. However, dynamic properties observed in short time interval reveal that hysteresis phenomenon are likely to occur during traffic state-transitions. The hysteresis phenomenon is visible in the transition paths both in the flow-density and velocity-density diagrams. The cause of hysteresis is either due to drivers' asymmetrical desired control speed in anticipation and relaxation modes or on traffic conditions of demand and supply in upstream and downstream. The hysteresis transition shows how the traffic quality degenerates and recovers during minutes to hours. It is thus expected that a better traffic flow modeling and control can be achieved if hysteresis transition can be correctly modeled and predicted. The paper develops a generalized mathematical hysteresis model based on Duhem operator. The hysteresis model proposed can describe hysteresis phenomenon in each state-to-state transition. Identification process is also introduced to make our model more flexible in different traffic conditions. Besides modeling, issue related to flow stage transitions and congested trend can be predicted or estimated, and, accordingly, some traffic control strategies can also be devised. For the traffic control, a performance index is proposed to evaluate transportation quality and served as measure of traffic improvement or degradation. Some control rules and traffic assignment are recommended to improve transportation efficiency. Simulation results are provided to illustrate transitions between free flow states and congested states. The simulation results also show that our model can represent the hysteresis phenomenon in different state transitions.