Global analysis of age-structured within-host virus model

Cameron J. Browne; Sergei S. Pilyugin

doi:10.3934/dcdsb.2013.18.1999

Article Contents

2013, Volume 18, Issue 8: 1999-2017. Doi: 10.3934/dcdsb.2013.18.1999

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Global analysis of age-structured within-host virus model

Cameron J. Browne^1, and
Sergei S. Pilyugin^1,

1.
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105

Received: February 29, 2012

Revised: November 30, 2012

Published: September 2013

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Abstract

A mathematical model of a within-host viral infection with explicit age-since-infection structure for infected cells is presented. A global analysis of the model is conducted. It is shown that when the basic reproductive number falls below unity, the infection dies out. On the contrary, when the basic reproductive number exceeds unity, there exists a unique positive equilibrium that attracts all positive solutions of the model. The global stability analysis combines the existence of a compact global attractor and a Lyapunov function.

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Mathematics Subject Classification: Primary: 37N25, 92B05; Secondary: 37B25.

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