The Ebola Virus Disease (EVD) can persist in some body fluids after clinical recovery. In Guinea and the Democratic Republic of the Congo, there are well-documented cases of EVD reemergence that were associated with previous outbreaks. In many cases, male EVD survivors were associated with the re-introduction of new outbreaks. This has shown that even after controlling an EVD outbreak, a close biomedical monitoring of survivors and contacts is critical to avoiding future outbreaks. Thus, in order to explore the main features of EVD transmission dynamics in the context of re-emergence, we used a compartmental model by considering vaccination around EVD contacts. Analytical and numerical analyses of the model were conducted. The model is mathematically and epidemiologically well-posed. We computed the reproductive number (R0) and the disease equilibrium points (disease-free equilibrium and endemic equilibrium) for the re-emerging outbreak. The stability analysis of the model around those equilibrium points was performed. The model undergoes a backward bifurcation at R0 close to 1, regardless R0 < 1, the disease will not be eradicated. This means that R0 cannot be considered as an intervention control measure in our model.