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

Drug therapy model with time delays for HIV infection with virus-to-cell and cell-to-cell... 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 $$1-\eta$$ 1 - η , where $$\eta \in [0,1]$$ η ∈ [ 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 $$(1-\eta )^2$$ ( 1 - η ) 2 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Mathematics and Computing Springer Journals

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

Journal of Applied Mathematics and Computing, Volume 59 (2) – Jun 4, 2018
15 pages

/lp/springer_journal/drug-therapy-model-with-time-delays-for-hiv-infection-with-virus-to-6hprKlwtLK
Publisher
Springer Journals
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theory of Computation; Mathematics of Computing
ISSN
1598-5865
eISSN
1865-2085
DOI
10.1007/s12190-018-1196-6
Publisher site
See Article on Publisher Site

### Abstract

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 $$1-\eta$$ 1 - η , where $$\eta \in [0,1]$$ η ∈ [ 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 $$(1-\eta )^2$$ ( 1 - η ) 2 .

### Journal

Journal of Applied Mathematics and ComputingSpringer Journals

Published: Jun 4, 2018

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