# A Biomathematical Approach to HIV and AIDS

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

## Abstract

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.

## Keywords

Host Cell Adaptive Immune System Viral Nucleic Acid Clonal Deletion Cold Virus
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References and Suggested Further Reading

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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
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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.