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The Effects of Latent Infection on the Dynamics of HIV

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Abstract

One way in which the human immunodeficiency virus (HIV-1) replicates within a host is by infecting activated CD\(4+\) T-cells, which then produce additional copies of the virus. Even with the introduction of antiretroviral drug therapy, which has been very successful over the past decade, a large obstacle to the complete eradication of the virus is the presence of viral reservoirs in the form of latently infected CD\(4+\) T-cells. We consider a model of HIV infection that describes T-cell and viral interactions, as well as, the production and activation of latently infected T-cells. Upon determining equilibrium states of the latent cell model, the local and global asymptotic behavior of solutions is examined, and the basic reproduction number of the system is computed to be strictly less than that of the corresponding three-component model, which omits the effects of latent infection. In particular, this implies that a wider variety of parameter values will lead to viral eradication as \(t \rightarrow \infty \) due to the appearance of latent CD\(4+\) T-cells. With this realization we discuss possible alternative notions for eradication and persistence of infection other than traditional dynamical tools. These results are further illustrated by a number of numerical simulations.

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Acknowledgments

This work is supported by the National Science Foundation under awards DMS-0908413 and DMS-1211667. We also thank Prof. Mrinal Raghupathi (USNA) and ENS Peter Roemer (USN) for helpful comments.

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  1. Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO, 80401, USA

    Stephen Pankavich

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Pankavich, S. The Effects of Latent Infection on the Dynamics of HIV. Differ Equ Dyn Syst 24, 281–303 (2016). https://doi.org/10.1007/s12591-014-0234-6

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