This paper presents a simple non-linear mathematical model to study the transmission dynamics of HIV/AIDS by incorporating the case detection and treatment. The model is first analyzed by assuming that only certain constant fractions of total HIV and total AIDS infectives are detected. The existence and stability of different equilibria of this model are discussed in detail. The basic reproduction number R0 of the model is computed and it is found that the disease free equilibrium of the model is globally stable for R0 < 1. When R0 > 1, the endemic equilibrium point exists and is also globally asymptotically stable. Further, these fractions of case detection are made time dependent to formulate the optimal control problem. This problem is analyzed using Pontryagin’s maximum principle [20]. The optimality of the system is deduced analytically and solved numerically. It is observed that optimal control strategy gives a better result compared to fixed control in minimizing the infected population. © 2015 Institute of Advanced Scientific Research.