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In this paper, we propose a within-host HIV-1 epidemic model with cell-to-virus and cell-to-cell transmission. By mathematical analysis, we obtain the basic reproduction number \(\mathcal {R}_{0}\), which determines the viral persistence and the basic reproduction number \(\mathcal {R}_{0}^{\mathrm{cc}}\) with respect to cell-to-cell transmission which is not strong enough, i.e., it is less than 1. If the basic reproduction number is less than 1, then the viral-free steady state \(E_{0}\) is globally asymptotically stable, which is proved by fluctuation lemma and comparison method; if \(\mathcal {R}_{0}>1\) is greater than 1, the endemic steady state \(E^{*}\) is globally asymptotically stable, which is proved by constructing the Lyapunov functional. Antiretoviral therapy is implemented to suppress the viral replication. Protease inhibitors for cell-to-cell transmission play an important role in controlling cell-to-cell infection. Under some circumstances, the effects of the cell-to-cell infection process are more sensitive than those of cell-to-virus transmission.

Analysis and control of an age-structured HIV-1 epidemic model with different transmission mechanisms