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Modeling within-host viral dynamics: The role of CTL immune responses in the evolution of drug resistance
1. | Department of Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China |
2. | Department of Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China, Department of Mathematics, University of Florida, Gainesville, FL 32611, USA |
To study the emergence and evolution of drug resistance during treatment of HIV infection, we study a mathematical model with two strains, one drug-sensitive and the other drug-resistant, by incorporating cytotoxic T lymphocyte (CTL) immune response. The reproductive numbers for each strain with and without the CTL immune response are obtained and shown to determine the stability of the steady states. By sensitivity analysis, we evaluate how the changes of parameters influence the reproductive numbers. The model shows that CTL immune response can suppress the development of drug resistance. There is a dynamic relationship between antiretroviral drug administration, the prevalence of drug resistance, the total level of viral production, and the strength of immune responses. We further investigate the scenario under which the drug-resistant strain can outcompete the wild-type strain. If drug efficacy is at an intermediate level, the drug-resistant virus is likely to arise. The slower the immune response wanes, the slower the drug-resistant strain grows. The results suggest that immunotherapy that aims to enhance immune responses, combined with antiretroviral drug treatment, may result in a functional control of HIV infection.
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show all references
References:
[1] |
B. M. Adams, H. T. Banks, M. Davidian, H.-D. Kwon, H. T. Tran, S. N. Wynne and E. S. Rosenberg,
HIV dynamics: Modeling, data analysis, and optimal treatment protocols, J. Comput. Appl. Math., 184 (2005), 10-49.
doi: 10.1016/j.cam.2005.02.004. |
[2] |
K. Allali, J. Danane and Y. Kuang, Global analysis for an HIV infection model with CTL immune response and infected cells in eclipse phase, Appl. Sci., 7 (2017), 861. |
[3] |
R. A. Arnaout, N. Martin A and D. Wodarz,
HIV-1 dynamics revisited: Biphasic decay by Cytotoxic T Lymphocyte killing?, Proc. R. Soc. Lond. B, 267 (2000), 1347-1354.
doi: 10.1098/rspb.2000.1149. |
[4] |
N. P. Bhatia and G. P. Szegö, Stability Theory of Dynamical Systems, Springer Science & Business Media, 2002. |
[5] |
S. M. Blower, D. Hartel, H. Dowlatabadi, R. M. Anderson and R. M. May, Drugs, sex and HIV: A mathematical model for New York City, Proc. R. Soc. Lond. B, 331 (1991), 171-187. Google Scholar |
[6] |
S. Bonhoeffer, R. M. May, G. M. Shaw and M. A. Nowak,
Virus dynamics and drug therapy, P. Natl. A. Sci., 94 (1997), 6971-6976.
doi: 10.1073/pnas.94.13.6971. |
[7] |
J. Cao, J. McNevin, S. Holte, L. Fink, L. Corey and M. J. McElrath,
Comprehensive analysis of human immunodeficiency virus type 1 (HIV-1)-specific gamma interferon-secreting CD8+ T cells in primary HIV-1 infection, J. Virol., 77 (2003), 6867-6878.
doi: 10.1128/JVI.77.12.6867-6878.2003. |
[8] |
H. Y. Chen, M. Di Mascio, A. S. Perelson, D. D. Ho and L. Zhang,
Determination of virus burst size in vivo using a single-cycle SIV in rhesus macaques, P. Natl. A. Sci., 104 (2007), 19079-19084.
doi: 10.1073/pnas.0707449104. |
[9] |
M. Ciupe, B. Bivort, D. Bortz and P. Nelson,
Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models, Math. Biosci., 200 (2006), 1-27.
doi: 10.1016/j.mbs.2005.12.006. |
[10] |
F. Clavel and A. J. Hance,
HIV drug resistance, New. Engl. J. Med., 350 (2004), 1023-1035.
doi: 10.1056/NEJMra025195. |
[11] |
R. V. Culshaw, S. Ruan and R. J. Spiteri,
Optimal HIV treatment by maximising immune response, J. Math. Biol., 48 (2004), 545-562.
doi: 10.1007/s00285-003-0245-3. |
[12] |
M. P. Davenport, R. M. Ribeiro and A. S. Perelson,
Kinetics of virus-specific CD8+ T cells and the control of human immunodeficiency virus infection, J. Virol., 78 (2004), 10096-10103.
doi: 10.1128/JVI.78.18.10096-10103.2004. |
[13] |
M. P. Davenport, R. M. Ribeiro, L. Zhang, D. P. Wilson and A. S. Perelson,
Understanding the mechanisms and limitations of immune control of HIV, Immunlo. Rev., 216 (2007), 164-175.
doi: 10.1017/CBO9780511818097. |
[14] |
M. P. Davenport,
High-potency human immunodeficiency virus vaccination leads to delayed and reduced CD8+ T-cell expansion but improved virus control, J. Virol., 79 (2005), 10059-10062.
doi: 10.1128/JVI.79.15.10059-10062.2005. |
[15] |
S. G. Deeks, M. Smith, M. Holodniy and J. O. Kahn,
HIV-1 protease inhibitors: A review for clinicians, Jama, 277 (1997), 145-153.
doi: 10.1001/jama.1997.03540260059037. |
[16] |
P. Dubey, U. S. Dubey and B. Dubey,
Modeling the role of acquired immune response and antiretroviral therapy in the dynamics of HIV infection, Math. Comput. Simulat., 144 (2018), 120-137.
doi: 10.1016/j.matcom.2017.07.006. |
[17] |
M. A. Gilchrist, D. Coombs and A. S. Perelson,
Optimizing within-host viral fitness: Infected cell lifespan and virion production rate, J. Theor. Biol., 229 (2004), 281-288.
doi: 10.1016/j.jtbi.2004.04.015. |
[18] |
T. Guo and Z. Qiu, The effects of CTL immune response on HIV infection model with potent therapy, latently infected cells and cell-to-cell viral transmission,
doi: 10.3934/mbe.2019341. |
[19] |
T. Guo, Z. Qiu and L. Rong,
Analysis of an hiv model with immune responses and cell-to-cell transmission, Bull. Malays. Math. Sci. So., 43 (2020), 581-607.
doi: 10.1007/s40840-018-0699-5. |
[20] |
S. A. Kalams, P. J. Goulder, A. K. Shea, N. G. Jones, A. K. Trocha, G. S. Ogg and B. D. Walker,
Levels of human immunodeficiency virus type 1-specific cytotoxic T-lymphocyte effector and memory responses decline after suppression of viremia with highly active antiretroviral therapy, J. Virol., 73 (1999), 6721-6728.
doi: 10.1128/JVI.73.8.6721-6728.1999. |
[21] |
D. E. Kirschner and G. Webb,
Understanding drug resistance for monotherapy treatment of HIV infection, Bull. Math. Biol., 59 (1997), 763-785.
doi: 10.1007/BF02458429. |
[22] |
R. Koup, J. T. Safrit, Y. Cao, C. A. Andrews, G. McLeod, W. Borkowsky, C. Farthing and D. D. Ho,
Temporal association of cellular immune responses with the initial control of viremia in primary human immunodeficiency virus type 1 syndrome, J. Virol., 68 (1994), 4650-4655.
doi: 10.1128/JVI.68.7.4650-4655.1994. |
[23] |
M. Louie,
Determining the relative efficacy of highly active antiretroviral therapy, J.Infect. Dis., 187 (2003), 896-900.
doi: 10.1086/368164. |
[24] |
L. M. Mansky and H. M. Temin,
Lower in vivo mutation rate of human immunodeficiency virus type 1 than that predicted from the fidelity of purified reverse transcriptase, J. Virol., 69 (1995), 5087-5094.
doi: 10.1128/JVI.69.8.5087-5094.1995. |
[25] |
S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner,
A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254 (2009), 178-196.
doi: 10.1016/j.jtbi.2008.04.011. |
[26] |
R. D. Mason, M. I. Bowmer, C. M. Howley, M. Gallant, J. C. Myers and M. D. Grant,
Antiretroviral drug resistance mutations sustain or enhance CTL recognition of common HIV-1 pol epitopes, J. Immunol., 172 (2004), 7212-7219.
doi: 10.4049/jimmunol.172.11.7212. |
[27] |
A. R. McLean and M. A. Nowak,
Competition between zidovudine-sensitive and zidovudine-resistant strains of HIV, Aids, 6 (1992), 71-79.
doi: 10.1097/00002030-199201000-00009. |
[28] |
S. H. Michaels, R. Clark and P. Kissinger,
Declining morbidity and mortality among patients with advanced human immunodeficiency virus infection, New. Engl. J. Med., 339 (1998), 405-406.
doi: 10.1056/NEJM199808063390612. |
[29] |
P. Ngina, R. W. Mbogo and L. S. Luboobi,
HIV drug resistance: Insights from mathematical modelling, Appl. Math. Model., 75 (2019), 141-161.
doi: 10.1016/j.apm.2019.04.040. |
[30] |
M. Nowak and R. M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology: Mathematical Principles of Immunology and Virology, Oxford University Press, UK, 2000.
![]() |
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Parameter | Value | Ranges | Description | Reference |
Production rate of uninfected cells | [42] | |||
Death rate of uninfected cells | [34] | |||
Infection rate of uninfected cells by wild-type virus | [34] | |||
Infection rate of uninfected cells by drug-resistant virus | [42] | |||
Death rate of infected cells | [42] | |||
- | Clearance rate of infected cells by CTL killing | [48, 1] | ||
Generation rate of wild-type virus | [8, 17] | |||
Generation rate of drug-resistant virus | [8, 17] | |||
Clearance rate of wild-type and resistant virus | [39] | |||
generation rate of CTL | [55, 61] | |||
death rate of CTL | [48, 61] | |||
Single mutation rate | [24] | |||
Varied | Efficacy of RTI | see text | ||
Varied | Efficacy of PI | see text | ||
Varied | Resistance ratio of RTI | see text | ||
Varied | Resistance ratio of PI | see text |
Parameter | Value | Ranges | Description | Reference |
Production rate of uninfected cells | [42] | |||
Death rate of uninfected cells | [34] | |||
Infection rate of uninfected cells by wild-type virus | [34] | |||
Infection rate of uninfected cells by drug-resistant virus | [42] | |||
Death rate of infected cells | [42] | |||
- | Clearance rate of infected cells by CTL killing | [48, 1] | ||
Generation rate of wild-type virus | [8, 17] | |||
Generation rate of drug-resistant virus | [8, 17] | |||
Clearance rate of wild-type and resistant virus | [39] | |||
generation rate of CTL | [55, 61] | |||
death rate of CTL | [48, 61] | |||
Single mutation rate | [24] | |||
Varied | Efficacy of RTI | see text | ||
Varied | Efficacy of PI | see text | ||
Varied | Resistance ratio of RTI | see text | ||
Varied | Resistance ratio of PI | see text |
Conditions | System (1) | ||
Conditions | System (1) | ||
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