Journal of Applied Mathematics and Computing

, Volume 59, Issue 1–2, pp 677–691 | Cite as

Drug therapy model with time delays for HIV infection with virus-to-cell and cell-to-cell transmissions

  • Nicoleta TarfuleaEmail author
Original Research


In this paper, we analyze models of drug therapy for a HIV model with multiple delays considered in Chen et al. (J Math Anal Appl 442:642–672, 2016). As expected, in the presence of perfect inhibitors the populations of infected cells, virus, and effector cells decay exponentially to zero. When protease inhibitors are used, the production of infectious virions is diminished, as shown in our drug therapy model. First, we prove that the solution is positive and bounded from above. Our main result states that both the infected cell and infectious virus populations are asymptotically bounded by terms proportional to \(1-\eta \), where \(\eta \in [0,1]\) represents the protease inhibitor(s) effectiveness. Furthermore, under an additional condition, the infectious virus population is asymptotically bounded by a constant multiple of \((1-\eta )^2\).


HIV infection Treatment Protease inhibitors Delay Stability 

Mathematics Subject Classification

34A34 34D20 37N25 92B05 



This work was partially supported by a grant from the Simons Foundation (\(\#\, 429449 \) to Nicoleta E. Tarfulea).


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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.Department of MathematicsPurdue University NorthwestHammondUSA

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