Global behavior of delay differential equations model of HIV infection withapoptosis

Songbai  Guo; Wanbiao Ma

doi:10.3934/dcdsb.2016.21.103

Article Contents

2016, Volume 21, Issue 1: 103-119. Doi: 10.3934/dcdsb.2016.21.103

This issue Previous Article Global existence and boundedness in a parabolic-elliptic Keller-Segel system with general sensitivity Next Article Global phase portraits of uniform isochronous centers with quartic homogeneous polynomial nonlinearities

Global behavior of delay differential equations model of HIV infection with apoptosis

Songbai Guo^1, and
Wanbiao Ma^1,

1.
Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083

Received: February 2015

Revised: May 2015

Published: January 2016

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Abstract

In this paper, a class of delay differential equations model of HIV infection dynamics with nonlinear transmissions and apoptosis induced by infected cells is proposed, and then the global properties of the model are considered. It shows that the infection-free equilibrium of the model is globally asymptotically stable if the basic reproduction number $R_{0}<1$, and globally attractive if $R_{0}=1$. The positive equilibrium of the model is locally asymptotically stable if $R_{0}>1$. Furthermore, it also shows that the model is permanent, and some explicit expressions for the eventual lower bounds of positive solutions of the model are given.

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Mathematics Subject Classification: Primary: 37N25, 34A34; Secondary: 93D20, 34D23.

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