Mathematical analysis of Ebola virus population dynamics

Povzetek

In this paper, a non-linear mathematical model for the population dynamics of Ebola virus disease in existence of vaccination was developed and analyzed. Existence of equilibrium point was carried out, which shows us that the model consists of two equilibrium point. Local stability analyses of DFE have been carried out, it was found that the DFE is locally asymptotically stable if the threshold called reproduction number can be brought to a number less than unity. Comparison theorem was used to access the globally Stability of DFE, it was found that the DFE is globally asymptotically stable if the reproduction number can be brought to a number less than unity. LAS of endemic equilibrium point was done using Centre manifold theorem, it was established that the endemic equilibrium point is locally asymptotically stable if the reproduction number is greater than one. We were able to prove the global stability of endemic equilibrium point using Lyapunov function of Goh-Volterra type, it shows us that the endemic equilibrium point is globally asymptotically stable if the reproduction number is less than one. The numerical simulation shows that vaccinating a good number of people in a society can mitigate the Ebola virus disease (EVD).