Multiple Stable Periodic Oscillations in a Mathematical Model of CTL Response to HTLV-I Infection
- 283 Downloads
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.
KeywordsIn-host models HTLV-I infection CTL response Time delays Hopf bifurcation Multiple stable periodic solutions
Unable to display preview. Download preview PDF.
- Beretta, E., Carletti, M. et al. (2006). Stability analysis of a mathematical model of the immune response with delays. In Y. Iwasa, K. Sato, & Y. Takeuchi (Eds.), Mathematics for life science and medicine (pp. 179–208). Berlin: Springer. Google Scholar
- Koup, R. A., Safrit, J. T., et al. (1994). Temporal association of cellular immune responses with the initial control of viremia in primary human immunodeficiency virus type 1 syndrome. J. Virol., 68, 4650–4655. Google Scholar
- Kubota, R., Osame, M., & Jacobson, S. (2000). Retrovirus: human T-cell lymphotropic virus type I associated diseases and immune dysfunction. In M. W. Cunningham & R. S. Fujinami (Eds.), Effects of microbes on the immune system (pp. 349–371). Philadelphia: Lippincott Williams & Wilkins. Google Scholar
- Lang, J., & Li, M. Y. (2010). Stable and transient periodic oscillations in a mathematical model for CTL response to HTLV-I infection. Preprint. Google Scholar
- LaSalle, J., & Lefschetz, S. (1961). Stability by Liapunov’s direct method. New York: Academic Press. Google Scholar
- Li, M. Y., & Shu, H. (2010). Global dynamics of a mathematical model for HTLV-I infection of CD4+ T cells with delayed CTL response. Preprint. Google Scholar
- Wodarz, D., & Bangham, C. R. M. (2000). Evolutionary dynamics of HTLV-I. J. Mol. Evol., 50, 448–455. Google Scholar