Global stability and backward bifurcation of a general viral infection model with virus-driven proliferation of target cells

Hongying Shu; Lin Wang

doi:10.3934/dcdsb.2014.19.1749

Article Contents

2014, Volume 19, Issue 6: 1749-1768. Doi: 10.3934/dcdsb.2014.19.1749

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Global stability and backward bifurcation of a general viral infection model with virus-driven proliferation of target cells

Hongying Shu^1, and
Lin Wang^1,

1.
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3

Received: April 2013

Revised: October 2013

Published: August 2014

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Abstract

In this paper, a general viral model with virus-driven proliferation of target cells is studied. Global stability results are established by employing the Lyapunov method and a geometric approach developed by Li and Muldowney. It is shown that under certain conditions, the model exhibits a global threshold dynamics, while if these conditions are not met, then backward bifurcation and bistability are possible. An example is presented to provide some insights on how the virus-driven proliferation of target cells influences the virus dynamics and the drug therapy strategies.

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Mathematics Subject Classification: Primary: 92B05, 34D23; Secondary: 34D20.

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