# American Institute of Mathematical Sciences

2015, 2015(special): 913-922. doi: 10.3934/proc.2015.0913

## An in-host model of HIV incorporating latent infection and viral mutation

 1 Department of Applied Mathematics and Statistics, Colorado School of Mines, 1500 Illinois St, Golden, CO 80401 2 Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80401, United States

Received  September 2014 Revised  August 2015 Published  November 2015

We construct a seven-component model of the in-host dynamics of the Human Immunodeficiency Virus Type-1 (i.e, HIV) that accounts for latent infection and the propensity of viral mutation. A dynamical analysis is conducted and a theorem is presented which characterizes the long time behavior of the model. Finally, we study the effects of an antiretroviral drug and treatment implications.
Citation: Stephen Pankavich, Deborah Shutt. An in-host model of HIV incorporating latent infection and viral mutation. Conference Publications, 2015, 2015 (special) : 913-922. doi: 10.3934/proc.2015.0913
##### References:
 [1] M. Nowak and R. May, Virus Dynamics: Mathematical Principles of Immunology and Virology,, Oxford University Press, (2000). Google Scholar [2] S. Pankavich, The effects of latent infection on the dynamics of HIV,, Differential Equations and Dynamical Systems, (2015), 12591. Google Scholar [3] C. Parkinson and S. Pankavich, Mathematical Analysis of an in-host Model of Viral Dynamics with Spatial Heterogeneity,, submitted., (). Google Scholar [4] A. Perelson, D. Kirschner, and R. Boer, Dynamics of HIV Infection of $CD4^+$ T cells,, Math. Biosci., 114 (1993), 81. Google Scholar [5] A. Perelson and P. Nelson, Mathematical analysis of HIV-1 dynamics in vivo,, SIAM Review, 41 (1999), 3. Google Scholar [6] A. Perelson and R. Ribeiro, Modeling the within-host dynamics of HIV infection,, BMC Biology, 11 (2013). Google Scholar [7] P. Roemer, E. Jones, M. Raghupathi, and S. Pankavich, Analysis and Simulation of the three-component model of HIV dynamics,, SIAM Undergraduate Research Online, 7 (2014), 89. Google Scholar [8] L. Rong, Z. Feng, and A. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment,, Bull. Math. Biol., 69 (2007), 2027. Google Scholar [9] L. Rong and A. Perelson, Modeling HIV persistence, the latent reservoir, and viral blips,, Journal of Theoretical Biology, 260 (2009), 308. Google Scholar [10] L. Rong and A. Perelson, Modeling Latently Infected Cell Activation: Viral and Latent Reservoir Persistence, and Viral Blips in HIV-infected Patients on Potent Therapy,, PLoS Computational Biology, 5 (2009). Google Scholar [11] R. Shonkwiler and J. Herod, An Introduction with Maple and Matlab,, in Undergraduate Texts in Mathematics: Mathematical Biology, (2009). Google Scholar

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##### References:
 [1] M. Nowak and R. May, Virus Dynamics: Mathematical Principles of Immunology and Virology,, Oxford University Press, (2000). Google Scholar [2] S. Pankavich, The effects of latent infection on the dynamics of HIV,, Differential Equations and Dynamical Systems, (2015), 12591. Google Scholar [3] C. Parkinson and S. Pankavich, Mathematical Analysis of an in-host Model of Viral Dynamics with Spatial Heterogeneity,, submitted., (). Google Scholar [4] A. Perelson, D. Kirschner, and R. Boer, Dynamics of HIV Infection of $CD4^+$ T cells,, Math. Biosci., 114 (1993), 81. Google Scholar [5] A. Perelson and P. Nelson, Mathematical analysis of HIV-1 dynamics in vivo,, SIAM Review, 41 (1999), 3. Google Scholar [6] A. Perelson and R. Ribeiro, Modeling the within-host dynamics of HIV infection,, BMC Biology, 11 (2013). Google Scholar [7] P. Roemer, E. Jones, M. Raghupathi, and S. Pankavich, Analysis and Simulation of the three-component model of HIV dynamics,, SIAM Undergraduate Research Online, 7 (2014), 89. Google Scholar [8] L. Rong, Z. Feng, and A. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment,, Bull. Math. Biol., 69 (2007), 2027. Google Scholar [9] L. Rong and A. Perelson, Modeling HIV persistence, the latent reservoir, and viral blips,, Journal of Theoretical Biology, 260 (2009), 308. Google Scholar [10] L. Rong and A. Perelson, Modeling Latently Infected Cell Activation: Viral and Latent Reservoir Persistence, and Viral Blips in HIV-infected Patients on Potent Therapy,, PLoS Computational Biology, 5 (2009). Google Scholar [11] R. Shonkwiler and J. Herod, An Introduction with Maple and Matlab,, in Undergraduate Texts in Mathematics: Mathematical Biology, (2009). Google Scholar
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