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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

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

Pages: 3341 - 3357, Volume 19, Issue 10, December 2014      doi:10.3934/dcdsb.2014.19.3341

 
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Hossein Pourbashash - Department of Mathematics, University of Florida, 1400 Stadium Road, Gainesville, FL 32611, United States (email)
Sergei S. Pilyugin - Department of Mathematics, University of Florida, 1400 Stadium Road, Gainesville, FL 32611, United States (email)
Patrick De Leenheer - Department of Mathematics, University of Florida, 1400 Stadium Road, Gainesville, FL 32611, United States (email)
Connell McCluskey - Department of Mathematics, Wilfrid Laurier University, 75 University Avenue West, Waterloo, ON, N2L 3C5, Canada (email)

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.

Keywords:  Within-host virus model, cell-to-cell transmission, global stability, Lyapunov function, second compound matrices.
Mathematics Subject Classification:  Primary: 37N25, 97M60; Secondary: 34A34, 34D23.

Received: February 2013;      Revised: April 2013;      Available Online: October 2014.

 References