Skip to main content

Part of the book series: Industrial and Applied Mathematics ((INAMA))

  • 668 Accesses

Abstract

HIV infections in response to modern drug therapies have been furnished through the cell population model representing long-term dynamics of the disease. We have also considered that T cells can be created by a proliferation of existing uninfected target CD4\(^{+}\) T cells in our human body. T cell proliferation has a noteworthy and effective role towards the disease dynamics of HIV/AIDS. Our mathematical models are based on the interactions of susceptible T cells, virus producing cells, and cytotoxic T cells that would be able to provide a complete understanding of the long-term dynamics of the system.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bonhoeffer, S., Coffin, J.M., Nowak, M.A.: Human immunodeficiency virus drug therapy and virus load. J. Virol. 71(3275–3278), 137 (1997)

    Google Scholar 

  2. Perelson, A.S., Krischner, D.E., De-Boer, R.: Dynamics of HIV infection of CD4 T cells. Math. Biosci. 114(81–125), 118 (1993)

    Google Scholar 

  3. Perelson, A.S., Neuman, A.U., Markowitz, M., Leonard, J.M., Ho, D.D.: HIV 1 dynamics in vivo: viron clearance rate, infected cell life span, and viral generation time. Sci. 271, 1582–1586 (1996)

    Article  Google Scholar 

  4. Wang, L., Li, M.Y.: Mathematical analysis of the global dynamics of a model for HIV infection. Math. Biosci. 200(44–57), 173 (2006)

    MathSciNet  Google Scholar 

  5. Culshaw, R.V., Rawn, S., Spiteri, R.J.: Optimal HIV treatment by maximising immuno response. J. Math. Biol. 48, 545–562 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Roy, P.K., Chatterjee A.N.: T-cell Proliferation in a mathematical model of CTL activity through HIV-1 infection. In: Proceedings of The World Congress on Engineering 2010, WCE 2010, 30 June–2 July 2010, London. Lecture Notes in Engineering and Computer Science, pp. 615–620 (2010)

    Google Scholar 

  7. Iwami, S., Miura, T., Nakaoka, S., Takuchi, Y.: Immune impairment in HIV infection: existence of risky and immunodeficiency thresholds. J. Theor. Biol. 260, 490–501 (2009)

    Article  MathSciNet  Google Scholar 

  8. Wodarz, D., Nowak, M.A.: Specific therapy regimes could lead to long-term immunological control to HIV. Proc. Natl. Acad. Sci. USA 96(25), 14464–14469 (1999)

    Article  Google Scholar 

  9. Culshaw, R.V., Ruan, S.: A delay-differentianal equation model of HIV infection of CD4\(^{+}\)T-cells. Math. Biosci. 165, 425–444 (2000)

    Article  Google Scholar 

  10. Perelson, A.S., Nelson, P.W.: Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41(3–41), 122 (1999)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Priti Kumar Roy .

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media Singapore

About this chapter

Cite this chapter

Roy, P.K. (2015). T Cell Proliferation. In: Mathematical Models for Therapeutic Approaches to Control HIV Disease Transmission. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-287-852-6_3

Download citation

Publish with us

Policies and ethics