  This paper considers a mathematical model based on the transmission dynamics
of hepatitis C virus (HCV) infection. In addition to the usual compartments for
susceptible, exposed, and infected individuals, this model includes
compartments for individuals who are under treatment and those who have had
vaccination against HCV infection. It is assumed that the immunity provided by
the vaccine fades with time. The basic reproduction number, $R_0$, and the
equilibrium solutions of the model are determined. The model exhibits the
phenomenon of backward bifurcation where a stable disease-free equilibrium
co-exists with a stable endemic equilibrium whenever $R_0$ is less than unity.
It is shown that the use of only a perfect vaccine can eliminate backward
bifurcation completely. Furthermore, a unique endemic equilibrium of the model
is proved to be globally asymptotically stable under certain restrictions on
the parameter values. Numerical simulation results are given to support the
theoretical predictions. [epidemiological model; equilibrium solutions;
backward bifurcation; global asymptotic stability; Lyapunov function.]
