Abstract
To explore the impacts of pulse vaccination on the dynamical behaviors
of virus, the current paper investigates the threshold dynamics of a
viral infection model with impulsive CTL immune response. We first
discuss the existence of the infection-free steady state, and define the
crucial CTL-activated viral infection reproduction number $R_0$.
Then, the fundamental extinction and uniform persistence behaviors of
virus are distinguished by various case of the threshold parameter
$R_0$. Finally, we still devote to studying special global
attractivity of the positive steady state by employing the Lyapunov
function. Our results indicate that high vaccination rates stimulate the
CTL response more effectively, and can eventually force the virus to
eradicate.