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

show all references

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

[1]

Stephen Pankavich, Christian Parkinson. Mathematical analysis of an in-host model of viral dynamics with spatial heterogeneity. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1237-1257. doi: 10.3934/dcdsb.2016.21.1237

[2]

Yu Yang, Yueping Dong, Yasuhiro Takeuchi. Global dynamics of a latent HIV infection model with general incidence function and multiple delays. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 783-800. doi: 10.3934/dcdsb.2018207

[3]

Sukhitha W. Vidurupola, Linda J. S. Allen. Basic stochastic models for viral infection within a host. Mathematical Biosciences & Engineering, 2012, 9 (4) : 915-935. doi: 10.3934/mbe.2012.9.915

[4]

Yu Ji. Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection. Mathematical Biosciences & Engineering, 2015, 12 (3) : 525-536. doi: 10.3934/mbe.2015.12.525

[5]

Yan-Xia Dang, Zhi-Peng Qiu, Xue-Zhi Li, Maia Martcheva. Global dynamics of a vector-host epidemic model with age of infection. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1159-1186. doi: 10.3934/mbe.2017060

[6]

Chang Gong, Jennifer J. Linderman, Denise Kirschner. A population model capturing dynamics of tuberculosis granulomas predicts host infection outcomes. Mathematical Biosciences & Engineering, 2015, 12 (3) : 625-642. doi: 10.3934/mbe.2015.12.625

[7]

Yilong Li, Shigui Ruan, Dongmei Xiao. The Within-Host dynamics of malaria infection with immune response. Mathematical Biosciences & Engineering, 2011, 8 (4) : 999-1018. doi: 10.3934/mbe.2011.8.999

[8]

Liancheng Wang, Sean Ellermeyer. HIV infection and CD4+ T cell dynamics. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1417-1430. doi: 10.3934/dcdsb.2006.6.1417

[9]

Patrick W. Nelson, Michael A. Gilchrist, Daniel Coombs, James M. Hyman, Alan S. Perelson. An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells. Mathematical Biosciences & Engineering, 2004, 1 (2) : 267-288. doi: 10.3934/mbe.2004.1.267

[10]

Yu Wu, Xiaopeng Zhao, Mingjun Zhang. Dynamics of stochastic mutation to immunodominance. Mathematical Biosciences & Engineering, 2012, 9 (4) : 937-952. doi: 10.3934/mbe.2012.9.937

[11]

Jinliang Wang, Jiying Lang, Xianning Liu. Global dynamics for viral infection model with Beddington-DeAngelis functional response and an eclipse stage of infected cells. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 3215-3233. doi: 10.3934/dcdsb.2015.20.3215

[12]

Don A. Jones, Hal L. Smith, Horst R. Thieme. Spread of viral infection of immobilized bacteria. Networks & Heterogeneous Media, 2013, 8 (1) : 327-342. doi: 10.3934/nhm.2013.8.327

[13]

H. T. Banks, Robert Baraldi, Karissa Cross, Kevin Flores, Christina McChesney, Laura Poag, Emma Thorpe. Uncertainty quantification in modeling HIV viral mechanics. Mathematical Biosciences & Engineering, 2015, 12 (5) : 937-964. doi: 10.3934/mbe.2015.12.937

[14]

Claude-Michel Brauner, Danaelle Jolly, Luca Lorenzi, Rodolphe Thiebaut. Heterogeneous viral environment in a HIV spatial model. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 545-572. doi: 10.3934/dcdsb.2011.15.545

[15]

Jinliang Wang, Jiying Lang, Yuming Chen. Global dynamics of an age-structured HIV infection model incorporating latency and cell-to-cell transmission. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3721-3747. doi: 10.3934/dcdsb.2017186

[16]

Zhaohui Yuan, Xingfu Zou. Global threshold dynamics in an HIV virus model with nonlinear infection rate and distributed invasion and production delays. Mathematical Biosciences & Engineering, 2013, 10 (2) : 483-498. doi: 10.3934/mbe.2013.10.483

[17]

Huiyan Zhu, Xingfu Zou. Dynamics of a HIV-1 Infection model with cell-mediated immune response and intracellular delay. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 511-524. doi: 10.3934/dcdsb.2009.12.511

[18]

Nikolay Pertsev, Konstantin Loginov, Gennady Bocharov. Nonlinear effects in the dynamics of HIV-1 infection predicted by mathematical model with multiple delays. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020141

[19]

Cameron J. Browne, Sergei S. Pilyugin. Minimizing $\mathcal R_0$ for in-host virus model with periodic combination antiviral therapy. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3315-3330. doi: 10.3934/dcdsb.2016099

[20]

Miguel Atencia, Esther García-Garaluz, Gonzalo Joya. The ratio of hidden HIV infection in Cuba. Mathematical Biosciences & Engineering, 2013, 10 (4) : 959-977. doi: 10.3934/mbe.2013.10.959

 Impact Factor: 

Metrics

  • PDF downloads (18)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]