Stability of a viral infection model with state-dependent delay, CTL and antibody immune responses

Alexander Rezounenko

doi:10.3934/dcdsb.2017074

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2017, Volume 22, Issue 4: 1547-1563. Doi: 10.3934/dcdsb.2017074

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Stability of a viral infection model with state-dependent delay, CTL and antibody immune responses

Alexander Rezounenko

V.N.Karazin Kharkiv National University, Kharkiv, 61022, Ukraine, Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, P.O. Box 18, 18208 Praha, CR

Received: February 29, 2016

Revised: June 30, 2016

Published: August 2017

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Abstract

A virus dynamics model with intracellular state-dependent delay and nonlinear infection rate of Beddington-DeAngelis functional response is studied. The technique of Lyapunov functionals is used to analyze stability of the main interior infection equilibrium which describes the case of both CTL and antibody immune responses activated. We consider first a particular biologically motivated class of discrete state-dependent delays. The general case is investigated next. The stability of the infection-free and the immune-exhausted equilibria is also discussed.

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Mathematics Subject Classification: Primary: 93C23, 34K20; Secondary: 97M60.

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