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Global analysis of within host virus models with cell-to-cell viral transmission

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  • Recent experimental studies have shown that HIV can be transmitted directly from cell to cell when structures called virological synapses form during interactions between T cells. In this article, we describe a new within-host model of HIV infection that incorporates two mechanisms: infection by free virions and the direct cell-to-cell transmission. We conduct the local and global stability analysis of the model. We show that if the basic reproduction number ${\mathcal R}_0\leq 1$, the virus is cleared and the disease dies out; if ${\mathcal R}_0>1$, the virus persists in the host. We also prove that the unique positive equilibrium attracts all positive solutions under additional assumptions on the parameters. Finally, a multi strain model incorporating cell-to-cell viral transmission is proposed and shown to exhibit a competitive exclusion principle.
    Mathematics Subject Classification: Primary: 37N25, 97M60; Secondary: 34A34, 34D23.

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