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# Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

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1572-9176
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# Stability analysis of delay integro-differential equations of HIV-1 infection model

Nigar Ali
/ Gul Zaman
• Corresponding author
• Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan
• Email
• Other articles by this author:
/ Il Hyo Jung
Published Online: 2018-03-11 | DOI: https://doi.org/10.1515/gmj-2018-0011

## Abstract

In this paper, the analysis of an HIV-1 epidemic model is presented by incorporating a distributed intracellular delay. The delay term represents the latent period between the time that the target cells are contacted by the virus and the time the virions penetrated into the cells. To understand the analysis of our proposed model, the Rouths–Hurwiz criterion and general theory of delay differential equations are used. It is shown that the infection free equilibrium and the chronic-infection equilibrium are locally as well as globally asymptotically stable, under some conditions on the basic reproductive number ${R}_{0}$. Furthermore, the obtained results show that the value of ${R}_{0}$ can be decreased by increasing the delay. Therefore, any drugs that can prolong the latent period will help to control the HIV-1 infection.

MSC 2010: 92D25; 49J15; 93D20; 91G20

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Revised: 2017-08-15

Accepted: 2017-09-13

Published Online: 2018-03-11

Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X,

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