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

Hossein Pourbashash; Sergei S. Pilyugin; Patrick De Leenheer; Connell McCluskey

doi:10.3934/dcdsb.2014.19.3341

Article Contents

2014, Volume 19, Issue 10: 3341-3357. Doi: 10.3934/dcdsb.2014.19.3341

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

1.
Department of Mathematics, University of Florida, 1400 Stadium Road, Gainesville, FL 32611
2.
Department of Mathematics, Wilfrid Laurier University, 75 University Avenue West, Waterloo, ON, N2L 3C5

Received: February 2013

Revised: April 2013

Published: December 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 37N25, 97M60; Secondary: 34A34, 34D23.

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