Abstract: A Filippov system has been proposed to describe the following diagnosis measure in HIV control: once the number of the diagnosed HIV infected individuals is above a certain level, the enhanced diagnosis measure is carried out; otherwise, a general diagnosis ratio is adopted. The sliding mode region and the sliding mode dynamics are explored by using equivalent control method. We also examine the global dynamics of the model based on the sliding mode dynamics and qualitative analysis. The main results show that the number of HIV infected cases can stabilize at a relatively high level or relatively low level if the threshold value is enough high or enough low. By choosing an appropriate threshold value, the number of HIV infected individuals fluctuates around this threshold level. Therefore, it is important to choose a threshold value properly for HIV control, according to which one can determine whether or not it is necessary to implement the enhanced diagnosis measure.

Key words: Filippov model, HIV infection, pseudo-equilibrium, crossing cycle, intervention