Abstract
Much uncertainty surrounds the detailed mechanisms whereby the human immunodeficiency virus (HIV) causes the acquired immunodeficiency syndrome (AIDS) after a long and variable asymptomatic period. The virus impairs immune responses by infecting and/or killing one of the most important cell populations of the immune system, the CD4 cells. HIV mutates so rapidly that many different variants arise (and coexist) during an individual infection. This article reviews mathematical models that outline the potential importance of this variability as a major factor for the development of AIDS. The essential idea is that the virus evades immune pressure by the continuous production of new mutants resistant to current immunological attack (= antigenic variation). This results in the accumulation of antigenic diversity during the asymptomatic period of the infection. The existence of an antigenic diversity threshold is derived from the interaction between the virus population and the immune cells: CD4 cells mount immune responses, some of which are directed against specific HIV variants, but each virus strain can induce killing of all CD4 cells regardless of their specificity. Therefore increasing HIV diversity enables the virus population to escape from control by the immune system. In this context the observed variability is responsible for the fact that the virus establishes a persistant infection without being cleared by the immune response and induces AIDS after a long and variable incubation period. HIV infections are evolutionary processes on the time scale of a few years. The mathematical models are based on ordinary differential equations. Virus mutation is described by a stochastic process.
Keywords
- Human Immunodeficiency Virus
- Human Immunodeficiency Virus Infection
- Virus Population
- Diversity Threshold
- Escape Mutant
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R.M. Anderson, R.M. May, M.C. Boily, G.R Garnett, and J.T. Rowley, The spread of HIV-1 in Africa, Nature 352 (1991), 581–589.
R.M. Anderson and R.M. May, Infectious Diseases of Humans, Oxford University Press, 1991.
P. Balfe, P. Simmonds, C.A. Ludlam, J.O. Bishop, and A.J. Leigh Brown, Concurrent evolution of HIV-1 in patients infected from the same source, J. Virol. 64 (1990), 6221.
R.W. Coombs, A.C. Collier, and J.P. Allain, Plasma viremia in HIV infection, N Eng. J. Med. 321 (1989), 1626–1631.
LR. Epstein, Competitive coexistence of self reproducing macro-molecules, J. Theor. Biol. 78 (1979), 271–298.
A.G. Fisher, B. Ensoli, D. Looney, A. Rose, R.C. Gallo, M.S. Saag, G.M. Shaw, B.H. Hahn, and F. Wong-Staal, Biologically diverse molecular variants within a single HIV-1 isolate, Nature 334 (1988), 444–447.
D.D. Ho, T. Mougdil, and M. Alam, Quantitation of HIV-1 in the blood of infected persons, N. Eng. J. Med. 321 (1989), 1621–1625.
J. Hofbauer, P. Schuster, and K. Sigmund, Competition and cooperation in catalytic self replication, J. Math. Biol. 11 (1981), 155–168.
J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems, Cambridge University Press, 1988.
A.R. McLean and M.A. Nowak, The interaction between HIV and other pathogens, J. Theor. Biol. 155 (1992), 69–86.
A. Meyerhans, R. Cheynier, J. Albert, M. Seth, S. Kwok, J. Sninsky, L. Morfeldt-Manson, B. Asjö, and S. Wain-Hobson, Temporal fluctuations in HIV population in vivo are not reflected by sequential HIV isolations, Cell 58 (1989), 901–910.
G.W. Nelson and A.S. Perelson, A mechanism of immune escape by slow replicating HIV strains, J. AIDS 5 (1992), 82–93.
M.A. Nowak, R.M. May, and R.M. Anderson, The evolutionary dynamics of HIV-1 population and the development of immunodeficiency disease, AIDS 4 (1990), 1095.
M.A. Nowak and R.M. May, Mathematical biology of HIV infections, antigenic variation and diversity threshold, Math. Biosci. 106 (1991), 1–21.
M.A. Nowak, R.M. Anderson, A.R. McLean, T. Wolfs, J. Goudsmit, and R.M. May, Antigenic diversity thresholds and the development of AIDS, Science 254 (1991), 963–969.
M.A. Nowak, Variability of HIV infections, J. Theor. Biol. 155 (1992), 1–20.
R.E. Phillips, S. Rowland-Jones, D.F. Nixon, F.M. Gotch, J.P. Edwards, A. O. Ogunlesi, J.G. Elvin, J.A. Rothbard, C.R.M. Bang-ham, C.R. Rizza, and A.J. McMichael, HIV genetic variation that can escape Cytotoxic T cell recognition, Nature 354 (1991), 453–459.
M.S. Saag, B.H. Hahn, J. Gibbons, Y. Li, E.S. Parks, W.P. Parks, and G.M. Shaw, Extensive Variation of HIV-1 in vivo, Nature 334 (1988), 440–444.
P. Simmonds, P. Balfe, J.F. Peutherer, C.A. Ludlam, J.O. Bishop, and A.J. Leigh-Brown, Analysis of sequence diversity in hypervariable regions of the external glycoprotein of HIV-1, J. Virol. 64 (1990), 5840.
P. Taylor and L. Jonker, Evolutionarily stable strategies and game dynamics, Math. Biosci. 40 (1978), 145–56.
B. Tindall and D.A. Cooper, Primary HIV infection, AIDS 5 (1991), 1–14.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Birkhäuser Verlag
About this chapter
Cite this chapter
Nowak, M.A. (1994). The Evolutionary Dynamics of HIV Infections. In: Joseph, A., Mignot, F., Murat, F., Prum, B., Rentschler, R. (eds) First European Congress of Mathematics Paris, July 6–10, 1992. Progress in Mathematics, vol 120. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9112-7_13
Download citation
DOI: https://doi.org/10.1007/978-3-0348-9112-7_13
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9912-3
Online ISBN: 978-3-0348-9112-7
eBook Packages: Springer Book Archive