Summary: The Ebola Virus Disease is a zoonosis whose reservoir is fruit bats among other primates. Once the virus enters a human population from its supposed zoonotic reservoir, it can then spread through contact with infected persons or their body fluids. The people that are most susceptible to infection are close relatives of infected persons, healthcare givers and those dealing with deceased persons. We classify these people as being hyper-Susceptible and develop a mathematical model to study the impact of hyper-Susceptibility on the dynamics of Ebola virus disease outbreak. The model is shown to have a globally stable disease-free equilibrium point whenever the basic reproduction number \(\mathcal{R}_0\) is less than unity. The model is also shown to exhibit forward bifurcation, which suggests the possibility of eradication through keeping \(\mathcal{R}_0\) below unity. Disease spread is also shown to be highly sensitive to contact rate, transmission probability, death rate and hyper-Susceptibility. Numerical simulation of the model is also done to confirm the analytical results established.