Original Article

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

  • Michael Y. LiAffiliated withDepartment of Mathematics, Harbin Institute of TechnologyDepartment of Mathematical and Statistical Sciences, University of Alberta Email author 
  • , Hongying ShuAffiliated withDepartment of Mathematics, Harbin Institute of TechnologyDepartment of Mathematical and Statistical Sciences, University of Alberta

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Abstract

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.

Keywords

In-host models HTLV-I infection CTL response Time delays Hopf bifurcation Multiple stable periodic solutions