Abstract
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.
Highlights
Since the discovery of the first case of acquired immunodeficiency syndrome (AIDS), the disease has been in a major concern in global health
Even though the treatment does not lead to permanent cure of human immunodeficiency virus (HIV) infection, it extends the life of HIV-1-infected individuals and individuals under such treatment survive in asymptomatic chronic stages with low viral load
Recent investigations showed that the persistence of latent viral reservoirs is responsible for viral rebound. Such a reservoir is insensitive to highly active antiretroviral therapy (HAART) and able to self-re-establish
Summary
Since the discovery of the first case of acquired immunodeficiency syndrome (AIDS), the disease has been in a major concern in global health. In order to obtain the condition for the existence of an endemic steady state, we define the basic reproduction number as Proof Let (xi, yi(·), v) be a steady state of system (1.3), and it satisfies the following equations: Proof Linearizing system (1.3) at virus-free steady state E0, we obtain the associated characteristic equation
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