CD4 and AIDS: Given the fact that HIV infected cases with CD4 level lower than 200 are also defined as AIDS patients in China, we extend the CD4-staged structure model used by Birrell et al. [30] and Van Sighem et al. [31] by merging these two groups together and only considering three CD4 stages, i.e. [500,∞),[350,500) and [200,350).