Mathematical Model for Ebola Virus Infection in Human with Effectiveness of Drug Usage

Abstract

In this paper, we formulated a mathematical model of the dynamics of Ebola virus infection incorporating effectiveness of drug usage. The infection free and infection persistence equilibrium points were obtained. The control reproduction number was obtained which was used to analyse the local and global stability of the infectionfree equilibrium. Using the method of linearization, the infection-free equilibrium (IFE) state was found to be locally asymptotically stable if R_c < 1 and unstable if R_c > 1. By constructing lyapunov function, the infection-free equilibrium was found to be globally asymptotically unstable if R_c > 1. Numerical simulation of the model was done. It is observed that, as percentage of effectiveness of drug administration increases, the control reproduction number decreases. This suggests that with the help of drugs usage, the immunes system have the ability to suppress the increase of infected cells, as well as virus load which shown that the virus does not maintain an infection in the system.

Keywords: Drug Usage; Ebola virus; Global stability; Immune response; Mathematical model