Abstract
A mathematical model of the dynamics of the immune system is considered to illustrate the effect of its response to HIV infection, i.e. on viral growth and on T-cell dynamics. The specific immune response is measured by the levels of cytotoxic lymphocytes in a human body. The existence and stability analyses are performed for infected steady state and uninfected steady state. In order to keep infection under control, roles of drug therapies are analyzed in the presence of efficient immune response. Numerical simulations are computed and exhibited to illustrate the support of the immune system to drug therapies, so as to ensure the decay of infection and to maintain the level of healthy cells.
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Appendix
Appendix
Parameter | Definition | Value (unit) | References |
|---|---|---|---|
s | Rate at which new T-cells are created from sources within the body, such as thymus | 10 (mm−3 day−1) | Perelson et al. (1993) |
k | Rate constant for CD4+ cells becoming infected by free virus | 0.000024 (mm3 day−1) | Perelson et al. (1993) |
N | Average number of viral particles produced by an infected cell | Varies | Perelson et al. (1993) |
\(T_{max}\) | Maximum CD4+ cell population level | 1500 (mm−3) | Perelson et al. (1993) |
b | Reverting rate of infected cells to uninfected class due to the non-completion of reverse transcription | 0.05 (day−1) | Essunger and Perelson (1994) |
\(\alpha\) | Transition rate from pre-RT class to post-RT infected class | 0.4 (day−1) | Essunger and Perelson (1994) |
\(\delta\) | Death rate of productively infected cells (\(T_2\)) | 0.24 (day−1) | Perelson et al. (1993) |
r | Rate of growth for the CD4+ cell population | 0.03 (day−1) | Perelson et al. (1993) |
\(\mu\) | Death rate of uninfected cells | 0.01 (day−1) | Mohri et al. (1998) |
\(\mu _1\) | Death rate of infected cells | 0.015 (day−1) | Mohri et al. (1998) |
\(\mu _v\) | Clearance rate of virus | 2.4 (day−1) | Perelson et al. (1993) |
p | Proliferation rate of CTLs | 1.02 (day−1) | Srivastava and Chandra (2008) |
\(d_x\) | Rate of clearance of infected cells (\(T_{2}\)) by CTLs | 0.01 (mm3 day−1) | Culshaw et al. (2004), Arnaout et al. (2000), Nowak and Bangham (1996) |
\(d_E\) | Death rate of CTLs | 0.1 (day−1) | Srivastava and Chandra (2008) |
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Kamboj, D., Sharma, M.D. Multidrug Therapy for HIV Infection: Dynamics of Immune System. Acta Biotheor 67, 129–147 (2019). https://doi.org/10.1007/s10441-018-9340-0
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DOI: https://doi.org/10.1007/s10441-018-9340-0