Table of Contents
International Scholarly Research Notices
Volume 2017, Article ID 2124789, 10 pages
https://doi.org/10.1155/2017/2124789
Research Article

The In Vivo Dynamics of HIV Infection with the Influence of Cytotoxic T Lymphocyte Cells

Institute of Mathematical Sciences, Strathmore University, P.O. Box 59857, Nairobi 00200, Kenya

Correspondence should be addressed to Purity Ngina; ude.eromhtarts@anignp

Received 19 June 2017; Revised 25 September 2017; Accepted 15 October 2017; Published 14 November 2017

Academic Editor: Shengqiang Liu

Copyright © 2017 Purity Ngina et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. World Health Organization, World Health Statistics 2015, World Health Organization, 2015.
  2. A. Attarian and H. Tran, “An optimal control approach to structured treatment interruptions for hiv patients: a personalized medicine perspective,” Applied Mathematics, vol. 8, no. 7, pp. 934–955, 2017. View at Publisher · View at Google Scholar
  3. P. M. Ngina, R. W. Mbogo, and L. S. Luboobi, “Mathematical modelling of in-vivo dynamics of HIV subject to the influence of the CD8+ T-cells,” Applied Mathematics, vol. 8, no. 8, pp. 1153–1179, 2017. View at Publisher · View at Google Scholar
  4. D. L. Paterson, S. Swindells, J. Mohr et al., “Adherence to protease inhibitor therapy and outcomes in patients with HIV infection,” Annals of Internal Medicine, vol. 133, no. 1, pp. 21–30, 2000. View at Google Scholar · View at Scopus
  5. R. Waema and O. E. Olowofeso, “Mathematical modeling for human immunodeficiency virus (HIV) transmission using generating function approach,” Kragujevae Journal of Science, vol. 27, pp. 115–130, 2005. View at Google Scholar
  6. T. Assone, A. Paiva, L. A. M. Fonseca, and J. Casseb, “Genetic markers of the host in persons living with HTLV-1, HIV and HCV infections,” Viruses, vol. 8, no. 2, article no. 38, 2016. View at Publisher · View at Google Scholar · View at Scopus
  7. D. Wodarz and M. A. Nowak, “Immune responses and viral phenotype: do replication rate and cytopathogenicity influence virus load?” Computational and Mathematical Methods in Medicine, vol. 2, no. 2, pp. 113–127, 2000. View at Google Scholar
  8. G. S. Ogg, S. Kostense, M. R. Klein et al., “Longitudinal phenotypic analysis of human immunodeficiency virus type 1- specific cytotoxic T lymphocytes: Correlation with disease progression,” Journal of Virology, vol. 73, no. 11, pp. 9153–9160, 1999. View at Google Scholar · View at Scopus
  9. E. F. Arruda, C. M. Dias, C. V. de Magalhães, D. H. Pastore, R. C. Thomé, and H. M. Yang, “An optimal control approach to HIV immunology,” Applied Mathematics, vol. 6, no. 6, pp. 1115–1130, 2015. View at Publisher · View at Google Scholar
  10. K. Hattaf and N. Yousfi, “Dynamics of HIV infection model with therapy and cure rate,” International Journal of Tomography & Simulation, vol. 16, no. W11, pp. 74–80, 2011. View at Google Scholar
  11. O. M. Ogunlaran and S. C. Oukouomi Noutchie, “Mathematical model for an effective management of HIV infection,” BioMed Research International, vol. 2016, Article ID 4217548, 6 pages, 2016. View at Publisher · View at Google Scholar · View at Scopus
  12. H. Zarei, A. V. Kamyad, and S. Effati, “Multiobjective optimal control of HIV dynamics,” Mathematical Problems in Engineering, vol. 2010, Article ID 568315, 29 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  13. K. Zhuang and H. Zhu, “Stability and bifurcation analysis for an improved HIV model with time delay and cure rate,” WSEAS Transactions on Mathematics, vol. 12, no. 8, pp. 860–869, 2013. View at Google Scholar · View at Scopus
  14. P. K. Srivastava, M. Banerjee, and P. Chandra, “Modeling the drug therapy for HIV infection,” Journal of Biological Systems, vol. 17, no. 2, pp. 213–223, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  15. W. R. Mbogo, L. S. Luboobi, and J. W. Odhiambo, “Stochastic model for in-host HIV dynamics with therapeutic intervention,” ISRN Biomathematics, vol. 2013, Article ID 103708, 11 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  16. O. Diekmann, J. A. Heesterbeek, and J. A. Metz, “On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations,” Journal of Mathematical Biology, vol. 28, no. 4, pp. 365–382, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  17. E. Wiah and H. Mohammed, “Nonlinear dynamics and chaos in HIV/AIDS epidemic model with treatment,” Applied Mathematics, vol. 4, no. 3, pp. 86–96, 2014. View at Google Scholar
  18. P. Van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, no. 1, pp. 29–48, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  19. E. X. DeJesus and C. Kaufman, “Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations,” Physical Review A: Atomic, Molecular and Optical Physics, vol. 35, no. 12, pp. 5288–5290, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. A. A. Okoye and L. J. Picker, “CD4+ T-cell depletion in HIV infection: mechanisms of immunological failure,” Immunological Reviews, vol. 254, no. 1, pp. 54–64, 2013. View at Publisher · View at Google Scholar · View at Scopus
  21. K. A. Reimann, J. T. Li, R. Veazey et al., “A chimeric simian/human immunodeficiency virus expressing a primary patient human immunodeficiency virus type 1 isolate env causes an AIDS-like disease after in vivo passage in rhesus monkeys,” Journal of Virology, vol. 70, no. 10, pp. 6922–6928, 1996. View at Google Scholar · View at Scopus
  22. Y. Nishimura, C. R. Brown, J. J. Mattapallil et al., “Resting naïve CD4+ T cells are massively infected and eliminated by X4-tropic simian-human immunodeficiency viruses in macaques,” Proceedings of the National Acadamy of Sciences of the United States of America, vol. 102, no. 22, pp. 8000–8005, 2005. View at Publisher · View at Google Scholar · View at Scopus
  23. G. D. Bren, S. A. Trushin, J. Whitman, B. Shepard, and A. D. Badley, “HIV gp120 induces, NF-κB dependent, HIV replication that requires procaspase 8,” PLoS ONE, vol. 4, no. 3, Article ID e4875, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. H. Su, N. Bidère, L. Zheng et al., “Requirement for caspase-8 in NF-κB activation by antigen receptor,” Science, vol. 307, no. 5714, pp. 1465–1468, 2005. View at Publisher · View at Google Scholar · View at Scopus