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In this paper, we propose a fractional-order viral infection model, which includes latent infection, a Holling type II response function, and a time-delay representing viral production. Based on the characteristic equations for the model, certain sufficient conditions guarantee local asymptotic stability of infection-free and interior steady states. Whenever the time-delay crosses its critical value (threshold parameter), a Hopf bifurcation occurs. Furthermore, we use LaSalle’s invariance principle and Lyapunov functions to examine global stability for infection-free and interior steady states. Our results are illustrated by numerical simulations.