A mathematical model of ebola virus disease

Abstract

In this thesis, a modified SLIR model is formulated to describe the dynamics of Ebola virus disease. This model is peculiar in the sense that an infectious deceased compartment incorporated into the models, this is due to the fact that an infected deceased remains infectious as long as the virus remain in the blood. An isolated compartment is also added to the standard SLIR model. Mathematical analysis reveals that the disease free equilibrium is globally asymptotically stable when the basic reproduction number $\R_0 < 1$ and unstable if $\R_0 > 1$, while the endemic equilibrium is globally asymptotically stable when $\R_0 > 1$ and is not biologically relevant when $\R_0 < 1$. From the analysis of our model, we conclude that isolation of infected individuals will help a great deal in controlling the spread of the virus alongside with proper burial for infected deceased individuals.