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An analysis of the delay-dependent HIV-1 protease inhibitor model

M. Divya

Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Tamilnadu 600005, India

E-mail Address: divyamasilamani1@gmail.com

Corresponding author.

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and

M. Pitchaimani

Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Tamilnadu 600005, India

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https://doi.org/10.1142/S1793524518500316Cited by:1 (Source: Crossref)

Abstract

In this paper, we have studied about the sensitivity analysis of the human immunodeficiency virus (HIV) protease inhibitor (PI) model and estimated the length of the delay. We have fabricated an HIV PI model accompanied with humoral immunity. Stability analysis of the constructed model about its steady states has been deliberated. We have evaluated some numerical simulations for PI model with humoral immunity by using the existing patient data.

Keywords:

AMSC: 34C, 34D, 34N

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References

1. H. T. Banks, S. Dediu and S. L. Ernstberger, Sensitivity functions and their uses in inverse problems, Technical Report CRSC-TR07-12 (Center for Research in Scientific Computation, North Carolina State Unversity, 2007). Google Scholar
2. H. T. Banks, S. L. Ernstberger and S. L. Grove, Standard errors and confidence intervals in inverse problems: Sensitivity and associated pitfalls, J. Inverse Ill-Posed Probl. 15 (2007) 1–18. Crossref, Google Scholar
3. C. Chiyaka, W. Garira and S. Dube, Modelling immune response and drug therapy in human malaria infection, Comput. Math. Meth. Med. 9(2) (2008) 143–163. Crossref, Web of Science, Google Scholar
4. R. V. Culshaw and S. Ruan, A delay-differential equation model of HIV infection of CD4+ T-cells, Math. Biosci. 165 (2000) 27–39. Crossref, Web of Science, Google Scholar
5. N. M. Dixit and A. S. Perelson, Complex patterns of viral load decay under antiretroviral therapy: Influence of pharmacokinetics and intracellular delay, J. Theor. Biol. 226 (2004) 95–109. Crossref, Web of Science, Google Scholar
6. L. H. Erbe, H. I. Freedman and V. S. H. Rao, Three-species food-chain models with mutual interference and time delays, Math. Biosci. 80 (1986) 57–80. Crossref, Web of Science, Google Scholar
7. M. Eslami, Theory of Sensitivity in Dynamic Systems. An Introduction (Springer-Verlag, New York, 1994), pp. 74–113. Crossref, Google Scholar
8. H. I. Freedman and V. S. H. Rao, The trade-off between mutual interference and time lags in predator–prey systems, Bull. Math. Biol. 45 (1983) 991–1004. Crossref, Web of Science, Google Scholar
9. A. V. M. Herz, S. Bonhoeffer, R. M. Anderson, R. M. May and M. A. Nowak, Viral dynamics in vivo: Limitations on estimates of intracellular delay and virus decay, Proc. Natl. Acad. Sci. USA 93 (1996) 7247–7251. Crossref, Web of Science, Google Scholar
10. J. Hofbauer and K. Sigmund, Adaptive dynamics and evolutionary stability, Appl. Math. Lett. 3 (1990) 75–79. Crossref, Google Scholar
11. T. Kajiwara and T. Sasaki, A note on the stability analysis of pathogen-immune interaction dynamics, Discrete Contin. Dynam. Syst. Ser. B 4(3) (2004) 615–622. Crossref, Web of Science, Google Scholar
12. J. E. Mittler, B. Sulzer, A. U. Neumann and A. S. Perelson, Influence of delayed viral production on viral dynamics in HIV-1 infected patients, Math. Biosci. 152 (1998) 143–163. Crossref, Web of Science, Google Scholar
13. A. Murase, T. Sasaki and T. Kajiwara, Stability analysis of pathogen-immune interaction dynamics, Math. Biol. 51 (2005) 247–267. Crossref, Web of Science, Google Scholar
14. J. D. Murray, Mathematical Biology (Springer, New York, 1989), pp. 507–508. Crossref, Google Scholar
15. P. W. Nelson, J. D. Murray and A. S. Perelson, A model of HIV-1 pathogenesis that includes an intracellular delay, Math. Biosci. 163 (2000) 201–215. Crossref, Web of Science, Google Scholar
16. P. W. Nelson and A. S. Perelson, Mathematical analysis of delay differential equation models of HIV-1 infection, Math. Biosci. 179 (2002) 73–94. Crossref, Web of Science, Google Scholar
17. M. A. Nowak and C. R. M. Bangham, Population dynamics of immune responses to persistent viruses, Science 272 (1996) 74–79. Crossref, Web of Science, Google Scholar
18. A. S. Perelson, Modelling viral and immune system dynamics, Nat. Rev. Immunol. 2(1) (2002) 28–36. Crossref, Web of Science, Google Scholar
19. A. Perelson, A. Neumann, M. Markowitz, J. Leonard and D. Ho, HIV-1 dynamics in vivo: Virion clearance rate of HIV-1 infected compartments during combination therapy, Nature 387 (1997) 188. Crossref, Web of Science, Google Scholar
20. M. Pitchaimani, C. Monica and M. Divya, Stability analysis for HIV infection delay model with protease inhibitor, Biosystems 114 (2013) 118–124. Crossref, Web of Science, Google Scholar
21. A. Saltelli, K. Chan and E. M. Scott (eds.), Sensitivity analysis, in Wiley Series in Probability and Statistics (John Wiley and Sons Ltd., 2000). Google Scholar