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In addition to direct virus infection of target cells, HIV can also be transferred from infected to uninfected cells (cell-to-cell transmission). These two routes might facilitate viral production and the establishment of the latent virus pool, which is considered as a major obstacle to HIV cure. We studied an HIV infection model including the two infection routes and the time since latent infection. The basic reproductive ratio R0 was derived. The existence, positivity, and boundedness of the solution are proved. We investigated the existence of steady states and their stability, which were shown to depend on R0. We established the global asymptotic dynamical behavior by proving the existence of the global compact attractor and uniform persistence of the system and by applying the method of Lyapunov functionals. In the end, we formulated and solved the optimal control problem for the age-structured model. The necessary condition for minimization of the viral level and the cost of drug treatment was obtained, and numerical simulations of various optimal control strategies were performed.

An Age-Structured Model of HIV Latent Infection with Two Transmission Routes: Analysis and Optimal Control