Skip to main content

Advertisement

Log in

A model for coupling within-host and between-host dynamics in an infectious disease

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Studies on the modeling of the coupled dynamics of infectious diseases at both the population level (the epidemic process or between-host dynamics) and at the cell level (the early viremia or within-host dynamics) are scarce. Most of them deal with these two processes separately by postulating assumptions that render them decoupled.

In this work, we present a new model that allows the two dynamic processes to explicitly depend on each other. It is shown that new properties can emerge from the coupled system and more complex dynamics may be expected.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Anderson, R.M., May, R.M.: Infectious Diseases of Humans. Oxford University Press, Oxford (1991)

    Google Scholar 

  2. Callaway, D., Perelson, A.: HIV-1 infection and low steady state viral loads. Bull. Math. Biol. 64, 29–64 (2002)

    Article  Google Scholar 

  3. Coombs, D., Gilchrist, M.A., Ball, C.L.: Evaluating the importance of within- and between-host selection pressures on the evolution of chronic pathogens. Theor. Popul. Biol. 72, 576–591 (2007)

    Article  Google Scholar 

  4. De Boer, R.J., Perelson, A.S.: Target cell limited and immune control models of HIV infection: a comparison. J. Theor. Biol. 190, 201–214 (1998)

    Article  Google Scholar 

  5. Dixit, N., Perelson, A.: Complex patterns of viral load decay under antiretroviral therapy: influence of pharmacokinetics and intracellular delay. J. Theor. Biol. 226, 95–109 (2004)

    Article  MathSciNet  Google Scholar 

  6. Fraser, C., Hollingsworth, T.D., Chapman, R., de Wolf, F., Hanage, W.P.: Variation in HIV set-point viral load: Epidemiological analysis and an evolutionary hypothesis. Proc. Natl. Acad. Sci. USA 104(44), 17441–17446 (2007)

    Article  Google Scholar 

  7. Gilchrist, M.A., Coombs, D.: Evolution of virulence: interdependence, constrains, and selection using nested models. Theor. Popul. Biol. 69, 145–153 (2006)

    Article  MATH  Google Scholar 

  8. Markowitz, M., Vesanen, M., Tenner-Racz, K., Cao, Y., Binley, J.M., Talai, A., et al.: A novel antiviral intervention results in more accurate assessment of human immunodeficiency virus type 1 replication dynamics and T-cell decay in vivo. J. Virol. 77, 5037–5038 (2003)

    Article  Google Scholar 

  9. Nowak, M.A., May, R.M.: Mathematical biology of HIV infectious-antigenic variation and diversity threshold. Math. Biosci., 106, 1–21 (1991)

    Article  MATH  Google Scholar 

  10. Nowak, M.A., May, R.M.: Virus Dynamics. Mathematical Principles of Immunology and Virology. Oxford University Press, Oxford (2000)

    MATH  Google Scholar 

  11. Perelson, A., Kirschner, D., De Boer, R.: The dynamics of HIV infection of CD4+ T cells. Math. Biosci. 114, 81–125 (1993)

    Article  MATH  Google Scholar 

  12. Perelson, A., Nelson, P.W.: Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41, 3–44 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ramratnam, B., Bonhoeffer, S., Binley, J., Hurley, A., Zhang, L., Mittler, J.E., et al.: Rapid production and clearance of HIV-1 and hepatitis C virus assessed by large volume plasma apheresis. Lancet 354, 1782–1785 (1999)

    Article  Google Scholar 

  14. Regoes, R.R., Wodarz, D., Nowak, M.A.: Virus Dynamics: the effect of target cell limitation and immune response on virus evolution. J. Theor. Biol. 191, 451–462 (1998)

    Article  Google Scholar 

  15. Thieme, H.R.: Mathematics in Population Biology. Princeton Series in Theoretical and Computational Biology. Princeton University Press, Princeton (2003)

    Google Scholar 

  16. Wodarz, D.: Killer Cell Dynamics. Mathematical and Computational Approach to Immunology. Interdisciplinary Applied Mathematics, vol. 32. Springer, Berlin (2007)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jorge Velasco-Hernandez.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feng, Z., Velasco-Hernandez, J., Tapia-Santos, B. et al. A model for coupling within-host and between-host dynamics in an infectious disease. Nonlinear Dyn 68, 401–411 (2012). https://doi.org/10.1007/s11071-011-0291-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-011-0291-0

Keywords

Navigation