More than 20 outbreaks of Ebola virus disease have occurred in Africa since 1976, and yet no adequate treatment is available. Hence, prevention, control measures and supportive treatment remain the only means to avoid the disease. Among these measures, contact tracing occupies a prominent place. In this paper, we propose a simple mathematical model that incorporates imperfect contact tracing, quarantine and hospitalization (or isolation). The control reproduction number Rc of each sub-model and for the full model are computed. Theoretically, we prove that when Rc is less than one, the corresponding model has a unique globally asymptotically stable disease-free equilibrium. Conversely, when Rc is greater than one, the disease-free equilibrium becomes unstable and a unique globally asymptotically stable endemic equilibrium arises. Furthermore, we numerically support the analytical results and assess the efficiency of different control strategies. Our main observation is that, to eradicate EVD, the combination of high contact tracing (up to 90%) and effective isolation is better than all other control measures, namely: (1) perfect contact tracing, (2) effective isolation or full hospitalization, (3) combination of medium contact tracing and medium isolation.