A Biomathematical Approach to HIV and AIDS

Part of the Undergraduate Texts in Mathematics book series (UTM)


Acquired immunodeficiency syndrome (AIDS) is medically devastating to its victims, and wreaks financial and emotional havoc on everyone, infected or not. The purpose of this chapter is to model and understand the behavior of the causative agent of AIDS—the human immunodeficiency virus (HIV). This will necessitate discussions of viral replication and immunology. By the end of this chapter, the student should have a firm understanding of the way that HIV functions and be able to apply that understanding to a mathematical treatment of HIV infection and epidemiology. Viruses are very small biological structures whose reproduction requires a host cell. In the course of viral infection the host cell is changed or even killed. The host cells of HIV are specific and very unique: They are cells of our immune system. This is of monumental importance to the biological and medical aspects of HIV infection and its aftermath. HIV infects several kinds of cells, but perhaps its most devastating cellular effect is that it kills helper T-lymphocytes. Helper T-lymphocytes play a key role in the process of gaining immunity to specific pathogens; in fact, if one’s helper T-lymphocytes are destroyed, the entire specific immune response fails. Note the irony: HIV kills the very cells that are required by our bodies to defend us from pathogens, including HIV itself! The infected person then contracts a variety of (often rare) diseases to which uninfected persons are resistant, and that person is said to have AIDS.


Host Cell Adaptive Immune System Viral Nucleic Acid Clonal Deletion Cold Virus 
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References and Suggested Further Reading

  1. [1]
    Blood cells, immunity: W. T. Keeton and J. L. Gould, Biological Science, 5th ed., Norton, New York, 1993.Google Scholar
  2. [2]
    Immunity: Special issue on the immune system, Sci. Amer., 269–3 (1993).Google Scholar
  3. [3]
    HIV and AIDS: What science knows about AIDS [full issue], Sci. Amer., 259-4 (1988).Google Scholar
  4. [4]
    HIV and AIDS: M. A. Nowak and A. J. McMichael, How HIV defeats the immune system, Sci. Amer., 273–2 (1995), 58.CrossRefGoogle Scholar
  5. [5]
    HIV and T cells: A. S. Perelson, Modeling the interaction of the immune system with HIV, in C. Castillo-Chavez, ed., Mathematical and Statistical Approaches to AIDS Epidemiology, Lecture Notes in Biomathematics, Vol. 83, Springer-Verlag, New York, 1989, 350–370.Google Scholar
  6. [6]
    HIV and T cells: A. S. Perelson, D. E. Kirschner, and R. J. De Boer, The dynamics of HIV infection of CD4+ T cells, Math. Biosci., 114 (1993), 81–125.MATHCrossRefGoogle Scholar
  7. [7]
    HIV and T cells: K. E. Kirschner and A. S. Perelson, A model for the immune system response to HIV:AZT treatment studies, in O. Arino, D. E. Axelrod, M. Kimmel, and M. Langlais, eds., Mathematical Population Dynamics: Analysis of Heterogeneity and the Theory of Epidemics, Wuerz Publishing, Winnipeg, ON, Canada, 1995, 295–310.Google Scholar
  8. [8]
    HIV and T cells: A. S. Perelson, Two theoretical problems in immunology: AIDS and epitopes, in G. Cowan, D. Pines, and D. Meltzer, eds., Complexity: Metaphors, Models and Reality, Addison–Wesley, Reading, MA, 185–197.Google Scholar
  9. [9]
    The immune response: W. C. Greene, AIDS and the immune system, Sci. Amer., 269–3 (special issue) (1993).Google Scholar
  10. [10]
    Mutations of HIV: M. A. Nowak, R. M. May, and R. M. Anderson, The evolutionary dynamics of HIV-1 quasi species and the development of immunodeficiency disease, AIDS, 4 (1990), 1095–1103.CrossRefGoogle Scholar
  11. [11]
    Mutations of HIV: M. A. Nowak and R. M. May, Mathematical biology of HIV infections: Antigenic variation and diversity threshold, Math. Biosci., 106 (1991), 1–21.MATHCrossRefGoogle Scholar
  12. [12]
    Calculations of the time from HIV infection to AIDS symptoms: P. Bacchetti, M. R. Segal, and N. P. Jewell, Backcalculation of HIV infection rates, Statist. Sci., 8-2 (1993), 82–119.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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