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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1989 Mar;86(6):2026–2030. doi: 10.1073/pnas.86.6.2026

Stability analysis of simple models for immune cells interacting with normal pathogens and immune system retroviruses.

G Reibnegger 1, D Fuchs 1, A Hausen 1, E R Werner 1, G Werner-Felmayer 1, M P Dierich 1, H Wachter 1
PMCID: PMC286839  PMID: 2522657

Abstract

A mathematical analysis is presented for several simple dynamical systems that might be considered as crude descriptions for the situation when an immune system retrovirus, immune cells, and normal autonomously replicating pathogens interact. By stability analysis of the steady-state solutions, the destabilizing effect of the immune system retrovirus is described. The qualitative behavior of the solutions depending on the system parameters is analyzed in terms of trajectories moving in a phase space in which the axes are defined by the population numbers of the interacting biological entities.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Bowen D. L., Lane H. C., Fauci A. S. Immunopathogenesis of the acquired immunodeficiency syndrome. Ann Intern Med. 1985 Nov;103(5):704–709. doi: 10.7326/0003-4819-103-5-704. [DOI] [PubMed] [Google Scholar]
  2. Cooper L. N. Theory of an immune system retrovirus. Proc Natl Acad Sci U S A. 1986 Dec;83(23):9159–9163. doi: 10.1073/pnas.83.23.9159. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Glass L., Kauffman S. A. Co-operative components, spatial localization and oscillatory cellular dynamics. J Theor Biol. 1972 Feb;34(2):219–237. doi: 10.1016/0022-5193(72)90157-9. [DOI] [PubMed] [Google Scholar]
  4. Glass L., Kauffman S. A. The logical analysis of continuous, non-linear biochemical control networks. J Theor Biol. 1973 Apr;39(1):103–129. doi: 10.1016/0022-5193(73)90208-7. [DOI] [PubMed] [Google Scholar]
  5. Quinn T. C., Piot P., McCormick J. B., Feinsod F. M., Taelman H., Kapita B., Stevens W., Fauci A. S. Serologic and immunologic studies in patients with AIDS in North America and Africa. The potential role of infectious agents as cofactors in human immunodeficiency virus infection. JAMA. 1987 May 15;257(19):2617–2621. [PubMed] [Google Scholar]
  6. Reibnegger G., Fuchs D., Hausen A., Werner E. R., Dierich M. P., Wachter H. Theoretical implications of cellular immune reactions against helper lymphocytes infected by an immune system retrovirus. Proc Natl Acad Sci U S A. 1987 Oct;84(20):7270–7274. doi: 10.1073/pnas.84.20.7270. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Samuelson P. A. Generalized predator-prey oscillations in ecological and economic equilibrium. Proc Natl Acad Sci U S A. 1971 May;68(5):980–983. doi: 10.1073/pnas.68.5.980. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Wachter H., Fuchs D., Hausen A., Reibnegger G., Werner E. R., Dierich M. P. Who will get AIDS? Lancet. 1986 Nov 22;2(8517):1216–1217. doi: 10.1016/s0140-6736(86)92220-8. [DOI] [PubMed] [Google Scholar]

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