Advertisement

Nonlinear Dynamics

, Volume 68, Issue 3, pp 401–411 | Cite as

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

  • Zhilan Feng
  • Jorge Velasco-HernandezEmail author
  • Brenda Tapia-Santos
  • Maria Conceição A. Leite
Original Paper

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.

Keywords

Disease persistence Early viremia Multistability Multiparameter bifurcation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Anderson, R.M., May, R.M.: Infectious Diseases of Humans. Oxford University Press, Oxford (1991) Google Scholar
  2. 2.
    Callaway, D., Perelson, A.: HIV-1 infection and low steady state viral loads. Bull. Math. Biol. 64, 29–64 (2002) CrossRefGoogle Scholar
  3. 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) CrossRefGoogle Scholar
  4. 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) CrossRefGoogle Scholar
  5. 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) MathSciNetCrossRefGoogle Scholar
  6. 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) CrossRefGoogle Scholar
  7. 7.
    Gilchrist, M.A., Coombs, D.: Evolution of virulence: interdependence, constrains, and selection using nested models. Theor. Popul. Biol. 69, 145–153 (2006) zbMATHCrossRefGoogle Scholar
  8. 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) CrossRefGoogle Scholar
  9. 9.
    Nowak, M.A., May, R.M.: Mathematical biology of HIV infectious-antigenic variation and diversity threshold. Math. Biosci., 106, 1–21 (1991) zbMATHCrossRefGoogle Scholar
  10. 10.
    Nowak, M.A., May, R.M.: Virus Dynamics. Mathematical Principles of Immunology and Virology. Oxford University Press, Oxford (2000) zbMATHGoogle Scholar
  11. 11.
    Perelson, A., Kirschner, D., De Boer, R.: The dynamics of HIV infection of CD4+ T cells. Math. Biosci. 114, 81–125 (1993) zbMATHCrossRefGoogle Scholar
  12. 12.
    Perelson, A., Nelson, P.W.: Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41, 3–44 (1999) MathSciNetzbMATHCrossRefGoogle Scholar
  13. 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) CrossRefGoogle Scholar
  14. 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) CrossRefGoogle Scholar
  15. 15.
    Thieme, H.R.: Mathematics in Population Biology. Princeton Series in Theoretical and Computational Biology. Princeton University Press, Princeton (2003) Google Scholar
  16. 16.
    Wodarz, D.: Killer Cell Dynamics. Mathematical and Computational Approach to Immunology. Interdisciplinary Applied Mathematics, vol. 32. Springer, Berlin (2007) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Zhilan Feng
    • 1
  • Jorge Velasco-Hernandez
    • 2
    Email author
  • Brenda Tapia-Santos
    • 3
  • Maria Conceição A. Leite
    • 4
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Programa de Matemáticas Aplicadas y ComputaciónInstituto Mexicano del PetróleoMéxico CityMéxico
  3. 3.Facultad de MatemáticasUniversidad VeracruzanaMéxico CityMéxico
  4. 4.Department of MathematicsUniversity of OklahomaNormanUSA

Personalised recommendations