Mathematical Analysis of an Ebola Differential Infectivity Model

West Africa and the Democratic Republic of Congo have in the recent years experienced majority of the Ebola Virus Disease (EVD) burden. Deaths from EVD occur yearly but naturally peak during the dry season. The average EVD fatality rate is approximated at 50%. Studies done on the dynamics of EVD transmission have not captured the differential infectivity aspects of the disease. In this work, a nonlinear differential infectivity model with variation in infectiousness that captures the dynamics of EVD to assess the role of varied infectivity on EVD with possible intervention measures is formulated. Stability analysis of the model shows that the model is conditionally locally and globally stable. The model is also shown to exhibit hopf bifurcation, which shows that the transmission dynamics of the disease are periodic in nature. Numerical simulation results showed that intervention measures to control the disease is more efficient at the onset of the infection to reduce the spread of the disease. The findings are significant in designing intervention measures aimed at reducing infections.