Drug therapy model with time delays for HIV infection with virus-to-cell and cell-to-cell transmissions
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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 \((1-\eta )^2\).
KeywordsHIV infection Treatment Protease inhibitors Delay Stability
Mathematics Subject Classification34A34 34D20 37N25 92B05
This work was partially supported by a grant from the Simons Foundation (\(\#\, 429449 \) to Nicoleta E. Tarfulea).