Bulletin of Mathematical Biology

, Volume 73, Issue 8, pp 1774–1793

Multiple Stable Periodic Oscillations in a Mathematical Model of CTL Response to HTLV-I Infection

Original Article

DOI: 10.1007/s11538-010-9591-7

Cite this article as:
Li, M.Y. & Shu, H. Bull Math Biol (2011) 73: 1774. doi:10.1007/s11538-010-9591-7


Stable periodic oscillations have been shown to exist in mathematical models for the CTL response to HTLV-I infection. These periodic oscillations can be the result of mitosis of infected target CD4+ cells, of a general form of response function, or of time delays in the CTL response. In this study, we show through a simple mathematical model that time delays in the CTL response process to HTLV-I infection can lead to the coexistence of multiple stable periodic solutions, which differ in amplitude and period, with their own basins of attraction. Our results imply that the dynamic interactions between the CTL immune response and HTLV-I infection are very complex, and that multi-stability in CTL response dynamics can exist in the form of coexisting stable oscillations instead of stable equilibria. Biologically, our findings imply that different routes or initial dosages of the viral infection may lead to quantitatively and qualitatively different outcomes.


In-host modelsHTLV-I infectionCTL responseTime delaysHopf bifurcationMultiple stable periodic solutions

Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinP.R. China
  2. 2.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada