American Institute of Mathematical Sciences

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

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

Stephen Pankavich 1, and  Deborah Shutt 2,

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.
Keywords: ART., latent infection, in-host dynamics, HIV, viral mutation.
Mathematics Subject Classification: Primary: 37N25, 92B05; Secondary: 34D2.
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, ISBN: 9780198504177. Google Scholar

[2]

S. Pankavich, The effects of latent infection on the dynamics of HIV, Differential Equations and Dynamical Systems, (2015), doi: 10.1007/s12591-014-0234-6. 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), 81-125. Google Scholar

[5]

A. Perelson and P. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Review, 41 (1999), 3-44. Google Scholar

[6]

A. Perelson and R. Ribeiro, Modeling the within-host dynamics of HIV infection, BMC Biology, 11 (2013), 96. 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), 89-106. Google Scholar

[8]

L. Rong, Z. Feng, and A. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment, Bull. Math. Biol., 69 (2007), 2027-2060. Google Scholar

[9]

L. Rong and A. Perelson, Modeling HIV persistence, the latent reservoir, and viral blips, Journal of Theoretical Biology, 260 (2009), 308-331. 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), doi: 10.1371/journal.pcbi.1000533. Google Scholar

[11]

R. Shonkwiler and J. Herod, An Introduction with Maple and Matlab, in Undergraduate Texts in Mathematics: Mathematical Biology, Springer, New York, 2009. Google Scholar

show all references

References:
[1]

M. Nowak and R. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, 2000, ISBN: 9780198504177. Google Scholar

[2]

S. Pankavich, The effects of latent infection on the dynamics of HIV, Differential Equations and Dynamical Systems, (2015), doi: 10.1007/s12591-014-0234-6. 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), 81-125. Google Scholar

[5]

A. Perelson and P. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Review, 41 (1999), 3-44. Google Scholar

[6]

A. Perelson and R. Ribeiro, Modeling the within-host dynamics of HIV infection, BMC Biology, 11 (2013), 96. 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), 89-106. Google Scholar

[8]

L. Rong, Z. Feng, and A. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment, Bull. Math. Biol., 69 (2007), 2027-2060. Google Scholar

[9]

L. Rong and A. Perelson, Modeling HIV persistence, the latent reservoir, and viral blips, Journal of Theoretical Biology, 260 (2009), 308-331. 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), doi: 10.1371/journal.pcbi.1000533. Google Scholar

[11]

R. Shonkwiler and J. Herod, An Introduction with Maple and Matlab, in Undergraduate Texts in Mathematics: Mathematical Biology, Springer, New York, 2009. Google Scholar

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